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https://en.wikipedia.org/wiki/Fenchel%27s%20duality%20theorem
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In mathematics, Fenchel's duality theorem is a result in the theory of convex functions named after Werner Fenchel.
Let ƒ be a proper convex function on Rn and let g be a proper concave function on Rn. Then, if regularity conditions are satisfied,
where ƒ * is the convex conjugate of ƒ (also referred to as the Fenchel–Legendre transform) and g * is the concave conjugate of g. That is,
Mathematical theorem
Let X and Y be Banach spaces, and be convex functions and be a bounded linear map. Then the Fenchel problems:
satisfy weak duality, i.e. . Note that are the convex conjugates of f,g respectively, and is the adjoint operator. The perturbation function for this dual problem is given by .
Suppose that f,g, and A satisfy either
f and g are lower semi-continuous and where is the algebraic interior and , where h is some function, is the set , or
where are the points where the function is continuous.
Then strong duality holds, i.e. . If then supremum is attained.
One-dimensional illustration
In the following figure, the minimization problem on the left side of the equation is illustrated. One seeks to vary x such that the vertical distance between the convex and concave curves at x is as small as possible. The position of the vertical line in the figure is the (approximate) optimum.
The next figure illustrates the maximization problem on the right hand side of the above equation. Tangents are drawn to each of the two curves such that both tangents have th
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https://en.wikipedia.org/wiki/Planar%20array%20radar
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The planar array radar is a type of radar that uses a high-gain planar array antenna.
Operation
A fixed delay is established between horizontal arrays in the elevation plane. As the frequency is changed, the phase front across the aperture tends to tilt, with the result that the beam is moved in elevation. The differing frequencies cause each successive beam to be elevated slightly more than previous beams. A 27.5-degree elevation is scanned by the radar.
Advantages
Each beam group has full transmitter peak power, full antenna gain and full antenna sidelobe performance.
The use of frequency changes allows economical, simple and reliable inertialess elevation scanning.
Radars
AN/APG-66
References
Radar
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https://en.wikipedia.org/wiki/Demosaicing
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A demosaicing (also de-mosaicing, demosaicking or debayering) algorithm is a digital image process used to reconstruct a full color image from the incomplete color samples output from an image sensor overlaid with a color filter array (CFA). It is also known as CFA interpolation or color reconstruction.
Most modern digital cameras acquire images using a single image sensor overlaid with a CFA, so demosaicing is part of the processing pipeline required to render these images into a viewable format.
Many modern digital cameras can save images in a raw format allowing the user to demosaic them using software, rather than using the camera's built-in firmware.
Goal
The aim of a demosaicing algorithm is to reconstruct a full color image (i.e. a full set of color triples) from the spatially undersampled color channels output from the CFA. The algorithm should have the following traits:
Avoidance of the introduction of false color artifacts, such as chromatic aliases, zippering (abrupt unnatural changes of intensity over a number of neighboring pixels) and purple fringing
Maximum preservation of the image resolution
Low computational complexity for fast processing or efficient in-camera hardware implementation
Amenability to analysis for accurate noise reduction
Color filter array
A color filter array is a mosaic of color filters in front of the image sensor. Commercially, the most commonly used CFA configuration is the Bayer filter illustrated here. This has alternating re
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https://en.wikipedia.org/wiki/Keratoderma
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Keratoderma is a hornlike skin condition.
Classification
The keratodermas are classified into the following subgroups:
Congenital
Simple keratodermas
Diffuse palmoplantar keratodermas
Diffuse epidermolytic palmoplantar keratoderma
Diffuse nonepidermolytic palmoplantar keratoderma
mal de Meleda
Focal palmoplantar keratoderma
Striate palmoplantar keratoderma
Punctate palmoplantar keratoderma
Keratosis punctata palmaris et plantaris
Spiny keratoderma
Focal acral hyperkeratosis
Complex keratodermas
Diffuse palmoplantar keratoderma
Erythrokeratodermia variabilis
Palmoplantar keratoderma of Sybert
Olmsted syndrome
Naegeli–Franceschetti–Jadassohn syndrome
Focal palmoplantar keratoderma
Papillon–Lefèvre syndrome
Pachyonychia congenita type I
Pachyonychia congenita type II
Focal palmoplantar keratoderma with oral mucosal hyperkeratosis
Camisa disease
Ectodermal dysplasias
Clouston's hidrotic ectodermal dysplasia
Acrokeratotic poikiloderma
Dermatopathic pigmentosa reticularis
Syndromic keratodermas
Vohwinkel syndrome
Palmoplantar keratoderma associated with esophageal cancer
Palmoplantar keratoderma and spastic paraplegia
Naxos disease
Striate palmoplantar keratoderma, woolly hair, and left ventricular dilated cardiomyopathy
Keratitis-ichthyosis-deafness syndrome
Corneodermatosseous syndrome
Huriez syndrome
Oculocutaneous tyrosinemia
Cardiofaciocutaneous syndrome
Schöpf–Schulz–Passarge syndrome
Acquired
Acquired keratodermas
AIDS-associated
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https://en.wikipedia.org/wiki/Carothers%20equation
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In step-growth polymerization, the Carothers equation (or Carothers' equation) gives the degree of polymerization, , for a given fractional monomer conversion, .
There are several versions of this equation, proposed by Wallace Carothers, who invented nylon in 1935.
Linear polymers: two monomers in equimolar quantities
The simplest case refers to the formation of a strictly linear polymer by the reaction (usually by condensation) of two monomers in equimolar quantities. An example is the synthesis of nylon-6,6 whose formula is
from one mole of hexamethylenediamine, , and one mole of adipic acid, . For this case
In this equation
is the number-average value of the degree of polymerization, equal to the average number of monomer units in a polymer molecule. For the example of nylon-6,6 ( diamine units and diacid units).
is the extent of reaction (or conversion to polymer), defined by
is the number of molecules present initially as monomer
is the number of molecules present after time . The total includes all degrees of polymerization: monomers, oligomers and polymers.
This equation shows that a high monomer conversion is required to achieve a high degree of polymerization. For example, a monomer conversion, , of 98% is required for = 50, and = 99% is required for = 100.
Linear polymers: one monomer in excess
If one monomer is present in stoichiometric excess, then the equation becomes
r is the stoichiometric ratio of reactants, the excess reactant is conventio
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https://en.wikipedia.org/wiki/Clairaut%27s%20formula
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Clairaut's formula may refer to:
Clairaut's equation (mathematical analysis)
Clairaut's relation (differential geometry)
Clairaut's theorem (calculus)
Clairaut's theorem (gravity)
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https://en.wikipedia.org/wiki/Collagen%2C%20type%20II%2C%20alpha%201
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Collagen, type II, alpha 1 (primary osteoarthritis, spondyloepiphyseal dysplasia, congenital), also known as COL2A1, is a human gene that provides instructions for the production of the pro-alpha1(II) chain of type II collagen.
Function
This gene encodes the alpha-1 chain of type II collagen, a fibrillar collagen found in cartilage and the vitreous humor of the eye. Mutations in this gene are associated with achondrogenesis, chondrodysplasia, early onset familial osteoarthritis, SED congenita, Langer-Saldino achondrogenesis, Kniest dysplasia, Stickler syndrome type I, and spondyloepimetaphyseal dysplasia Strudwick type. In addition, defects in processing chondrocalcin, a calcium binding protein that is the C-propeptide of this collagen molecule, are also associated with chondrodysplasia. There are two transcripts identified for this gene.
Type II collagen, which adds structure and strength to connective tissues, is found primarily in cartilage, the jelly-like substance that fills the eyeball (the vitreous), the inner ear, and the center portion of the discs between the vertebrae in the spine (nucleus pulposus). Three pro-alpha1(II) chains twist together to form a triple-stranded, ropelike procollagen molecule. These procollagen molecules must be processed by enzymes in the cell. Once these molecules are processed, they leave the cell and arrange themselves into long, thin fibrils that cross-link to one another in the spaces around cells. The cross-linkages result in the fo
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https://en.wikipedia.org/wiki/Bulmer
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Bulmer may refer to:
People
Bulmer (surname)
Bulmer (family), an English family
Bulmer (directories), a Victorian era historian, surveyor and compiler of directories
Places
Bulmer, Essex, England
Bulmer, North Yorkshire, England
Other uses
Bulmer (typeface), an English transitional classification serif typeface
H. P. Bulmer, English cider manufacturer
- a British merchant ship damaged in a hurricane and condemned at Sadras in 1821
USS Bulmer, a United States Navy Clemson-class destroyer (named after Captain Roscoe Carlyle Bulmer USN) that was launched in 1920 and saw service during WW2.
See also
Bulmers (Republic of Ireland), Irish cider manufacturer
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https://en.wikipedia.org/wiki/Processing%20medium
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In industrial engineering, a processing medium is a gaseous, vaporous, fluid or shapeless solid material that plays an active role in manufacturing processes - comparable to that of a tool.
Examples
A processing medium for washing is a soap solution, a processing medium for steel melting is a plasma, and a processing medium for steam drying is superheated steam.
Synonyms
Operating medium
Working medium.
Engineering concepts
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https://en.wikipedia.org/wiki/Junket%20%28dessert%29
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Junket is a milk-based dessert, made with sweetened milk and rennet, the digestive enzyme that curdles milk. Some older cookery books call the dish curds and whey.
Preparation
To make junket, milk (usually with sugar and vanilla added) is heated to approximately 100°F and the rennet, which has been dissolved in water, is mixed in to cause the milk to set. The dessert is chilled prior to serving. Junket is often served with a sprinkling of grated nutmeg on top.
History
Junket evolved from an older French dish, jonquet, a dish of renneted cream in which the whey is drained from curdled cream, and the remaining curds are sweetened with sugar.
In medieval England, junket was a food of the nobility made with cream and flavoured with rosewater, spices, and sugar. It started to fall from favour during the Tudor era, being replaced by syllabubs on fashionable banqueting tables, and by the 18th century, had become an everyday food sold in the streets.
For most of the 20th century in the Eastern United States, junket made with milk instead of cream was a preferred food for ill children, mostly due to its sweetness and ease of digestion.
Dorothy Hartley, in her Food in England, has a section on rennet followed by a section on "Junkets, Curds and Whey or Creams". She cites rum as the most common flavouring, and clotted cream as the usual accompaniment. She notes that the practice of heating the milk is a new one; originally, junket was made with milk as it was obtained from the co
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https://en.wikipedia.org/wiki/Peroxisomal%20targeting%20signal
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In biochemical protein targeting, a peroxisomal targeting signal (PTS) is a region of the peroxisomal protein that receptors recognize and bind to. It is responsible for specifying that proteins containing this motif are localised to the peroxisome.
Overview
All peroxisomal proteins are synthesized in the cytoplasm and must be directed to the peroxisome. The first step in this process is the binding of the protein to a receptor. The receptor then directs the complex to the peroxisome. Receptors recognize and bind to a region of the peroxisomal protein called a peroxisomal targeting signal, or PTS.
Peroxisomes consist of a matrix surrounded by a specific membrane. Most peroxisomal matrix proteins contain a short sequence, usually three amino acids at the extreme carboxy tail of the protein, that serves as the PTS. The prototypic sequence (many variations exist) is serine-lysine-leucine (-SKL in the one letter amino acid code). This motif, and its variations, is known as the PTS1, and the receptor is termed the PTS1 receptor.
It was found that the PTS1 receptor is encoded by the PEX5 gene. PEX5 imports folded proteins into the peroxisome, shuttling between the peroxisome and cytosol. PEX5 interacts with a large number of other proteins, including Pex8p, 10p, 12p, 13p, 14p.
A few peroxisomal matrix proteins have a different, and less conserved sequence, at their amino termini. This PTS2 signal is recognized by the PTS2 receptor, encoded by the PEX7 gene.
"PEX" refers to a
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https://en.wikipedia.org/wiki/Band%203%20anion%20transport%20protein
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Band 3 anion transport protein, also known as anion exchanger 1 (AE1) or band 3 or solute carrier family 4 member 1 (SLC4A1), is a protein that is encoded by the gene in humans.
Band 3 anion transport protein is a phylogenetically-preserved transport protein responsible for mediating the exchange of chloride (Cl−) with bicarbonate (HCO3−) across plasma membranes. Functionally similar members of the AE clade are AE2 and AE3.
Function
Band 3 is present in the basolateral face of the α-intercalated cells of the collecting ducts of the nephron, which are the main acid-secreting cells of the kidney. They generate hydrogen ions and bicarbonate ions from carbon dioxide and water – a reaction catalysed by carbonic anhydrase. The hydrogen ions are pumped into the collecting duct tubule by vacuolar H+ ATPase, the apical proton pump, which thus excretes acid into the urine. kAE1 exchanges bicarbonate for chloride on the basolateral surface, essentially returning bicarbonate to the blood. Here it performs two functions:
Electroneutral chloride and bicarbonate exchange across the plasma membrane on a one-for-one basis. This is crucial for CO2 uptake by the red blood cell and conversion (by hydration catalysed by carbonic anhydrase) into a proton and a bicarbonate ion. The bicarbonate is then excreted (in exchange for a chloride) from the cell by band 3.
Physical linkage of the plasma membrane to the underlying membrane skeleton (via binding with ankyrin and protein 4.2). This appea
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https://en.wikipedia.org/wiki/P%E2%80%93n%20junction%20isolation
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p–n junction isolation is a method used to electrically isolate electronic components, such as transistors, on an integrated circuit (IC) by surrounding the components with reverse biased p–n junctions.
Introduction
By surrounding a transistor, resistor, capacitor or other component on an IC with semiconductor material which is doped using an opposite species of the substrate dopant, and connecting this surrounding material to a voltage which reverse-biases the p–n junction that forms, it is possible to create a region which forms an electrically isolated "well" around the component.
Operation
Assume that the semiconductor wafer is p-type material. Also assume a ring of n-type material is placed around a transistor, and placed beneath the transistor. If the p-type material within the n-type ring is now connected to the negative terminal of the power supply and the n-type ring is connected to the positive terminal, the 'holes' in the p-type region are pulled away from the p–n junction, causing the width of the nonconducting depletion region to increase. Similarly, because the n-type region is connected to the positive terminal, the electrons will also be pulled away from the junction.
This effectively increases the potential barrier and greatly increases the electrical resistance against the flow of charge carriers. For this reason there will be no (or minimal) electric current across the junction.
At the middle of the junction of the p–n material, a depletion region is cr
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https://en.wikipedia.org/wiki/Stuart%20Newman
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Stuart Alan Newman (born April 4, 1945 in New York City) is a professor of cell biology and anatomy at New York Medical College in Valhalla, NY, United States. His research centers around three program areas: cellular and molecular mechanisms of vertebrate limb development, physical mechanisms of morphogenesis, and mechanisms of morphological evolution. He also writes about social and cultural aspects of biological research and technology.
Career
Stuart Newman graduated from Jamaica High School in Queens, New York. He received an A.B. from Columbia College of Columbia University in 1965, and a Ph.D. in chemical physics from the University of Chicago in 1970, where he worked with the theoretical chemist, Stuart A. Rice. He was a postdoctoral fellow in the Department of Theoretical Biology, University of Chicago and the School of Biological Sciences, University of Sussex, UK, and before joining New York Medical College was an instructor in anatomy at the University of Pennsylvania and an assistant professor of biological sciences at the State University of New York at Albany.
He has been a visiting professor at the Pasteur Institute, Paris, the Commissariat à l'Energie Atomique-Saclay, the Indian Institute of Science, Bangalore, the University of Tokyo, Komaba, and was a Fogarty Senior International Fellow at Monash University, Australia. He is a member of the External Faculty of the Konrad Lorenz Institute for Evolution and Cognition Research, Klosterneuburg, Austria and in
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https://en.wikipedia.org/wiki/Origination%20of%20Organismal%20Form
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Origination of Organismal Form: Beyond the Gene in Developmental and Evolutionary Biology is an anthology published in 2003 edited by Gerd B. Müller and Stuart A. Newman. The book is the outcome of the 4th Altenberg Workshop in Theoretical Biology on "Origins of Organismal Form: Beyond the Gene Paradigm", hosted in 1999 at the Konrad Lorenz Institute for Evolution and Cognition Research. It has been cited over 200 times and has a major influence on extended evolutionary synthesis research.
Description of the book
The book explores the multiple factors that may have been responsible for the origination of biological form in multicellular life. These biological forms include limbs, segmented structures, and different body symmetries.
It explores why the basic body plans of nearly all multicellular life arose in the relatively short time span of the Cambrian Explosion. The authors focus on physical factors (structuralism) other than changes in an organism's genome that may have caused multicellular life to form new structures. These physical factors include differential adhesion of cells and feedback oscillations between cells.
The book also presents recent experimental results that examine how the same embryonic tissues or tumor cells can be coaxed into forming dramatically different structures under different environmental conditions.
One of the goals of the book is to stimulate research that may lead to a more comprehensive theory of evolution. It is frequently cited as
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https://en.wikipedia.org/wiki/Hyperviscosity%20syndrome
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Hyperviscosity syndrome is a group of symptoms triggered by an increase in the viscosity of the blood. Symptoms of high blood viscosity include spontaneous bleeding from mucous membranes, visual disturbances due to retinopathy, and neurologic symptoms ranging from headache and vertigo to seizures and coma.
Hyperviscosity occurs from pathologic changes of either cellular or protein fractions of the blood such as is found in polycythemias, multiple myeloma (particularly IgA and IgG3), leukemia, monoclonal gammopathies such as Waldenström macroglobulinemia, sickle cell anemia, and sepsis.
Types of hyperviscosity syndromes vary by pathology; including serum hyperviscosity, which may cause neurologic or ocular disorders; polycythemic hyperviscosity, which results in reduced blood flow or capillary perfusion and increased organ congestion; and syndromes of hyperviscosity, caused by reduced deformability of red blood cells, often evident in sickle cell anemia.
Cause
High cell counts are seen in conditions such as polycythemia (raised red blood cells) or leukemia (more white blood cells, especially in acute leukemic blast crises).
May occur with a white blood cell count greater than 100,000/mm3 (100×109/L).
Diagnosis
Although elevated whole blood viscosity is a better measure of hyperviscosity and more common and clinically important, serum viscosity and plasma viscosity are more frequently measured. Normal plasma viscosity is between 1.4 and 1.8 centipoise while symptoms from
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https://en.wikipedia.org/wiki/Monoclonal%20gammopathy
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Monoclonal gammopathy, also known as paraproteinemia, is the presence of excessive amounts of myeloma protein or monoclonal gamma globulin in the blood. It is usually due to an underlying immunoproliferative disorder or hematologic neoplasms, especially multiple myeloma. It is sometimes considered equivalent to plasma cell dyscrasia. The most common form of the disease is monoclonal gammopathy of undetermined significance.
Causes
Causes of paraproteinemia include the following:
Leukemias and lymphomas of various types, but usually B-cell non-Hodgkin lymphomas with a plasma cell component.
Myeloma
Plasmacytoma
Lymphoplasmacytic lymphoma
Idiopathic (no discernible cause): some of these will be revealed as leukemias or lymphomas over the years.
AL amyloidosis
Diagnosis
These are characterized by the presence of any abnormal protein that is involved in the immune system, which are most often immunoglobulins and are associated with the clonal proliferation of lymphocytes.
When a paraproteinemia is present in the blood, there will be a narrow band, or spike, in the serum protein electrophoresis because there will be an excess of production of one protein.
There are two large classes of blood proteins: albumin and globulin. They are generally equal in proportion, but albumin is much smaller than globulin, and slightly negatively charged, which leads to an accumulation at the end of the electrophoretic gel. The globulins separate out into three regions on the electrophore
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https://en.wikipedia.org/wiki/Macroglobulinemia
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Macroglobulinemia is the presence of increased levels of macroglobulins in the circulating blood.
It is a plasma cell dyscrasia, resembling leukemia, with cells of lymphocytic, plasmacytic, or intermediate morphology, which secrete a monoclonal immunoglobulin M component. There is diffuse infiltration by the malignant cells of the bone marrow and also, in many cases, of the spleen, liver, or lymph nodes. The circulating macroglobulin can produce symptoms of hyperviscosity syndrome: weakness, fatigue, bleeding disorders, and visual disturbances. Peak incidence of macroglobulinemia is in the sixth and seventh decades of life. (Dorland, 28th ed)
See also
Waldenström macroglobulinemia
Hematopoietic ulcer
References
External links
Blood disorders
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https://en.wikipedia.org/wiki/ZGS
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ZGS may refer to:
Zero Gradient Synchrotron – particle accelerator at Argonne National Laboratory, in operation 1964-79
Zimbabwe Geological Survey
ZGS Communications, a United States broadcasting company
Chinese Sign Language, from name in Mandarin, Zhōngguó Shǒuyǔ.
La Romaine Airport, with IATA code ZGS
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https://en.wikipedia.org/wiki/SBH
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SBH can refer to:
Stellar black hole or Supermassive black hole
Gustaf III Airport, Saint Barthélemy, IATA code
Sephardic Bikur Holim, a charity organisation
Sequencing by hybridization, DNA sequencing method
The Service Book and Hymnal of Lutheran churches
Singapore Badminton Hall
State Bank of Hyderabad
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https://en.wikipedia.org/wiki/VCM
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VCM may refer to:
Variable Cylinder Management, Honda's term for a variable-displacement technology
Variable Coding and Modulation, a technique for optimizing satellite broadcasts
Vermont City Marathon, a marathon in Burlington, Vermont
Vecima networks, a maker of telecommunications equipment
Victoria Conservatory of Music, a Canadian music school
Victoria Coren Mitchell, (Born 18 August 1972) an English writer, presenter and professional poker player
Vienna City Marathon, a marathon in Vienna, Austria
Vinyl chloride monomer, a compound used to produce polyvinyl chloride
Virtual Channel Memory, a memory architecture which was originally developed by NEC
Virtual Collection of Masterpieces, a search platform to a collection of Asian masterpieces
Voce del padrone-Columbia-Marconiphone, an Italian record label
Voice Coil Motor, an electric linear motor used to position hard drive heads.
Value Continuum Machine tbd.
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https://en.wikipedia.org/wiki/VMOS
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A VMOS () (vertical metal oxide semiconductor or V-groove MOS) transistor is a type of metal–oxide–semiconductor field-effect transistor (MOSFET). VMOS is also used to describe the V-groove shape vertically cut into the substrate material.
The "V" shape of the MOSFET's gate allows the device to deliver a higher amount of current from the source to the drain of the device. The shape of the depletion region creates a wider channel, allowing more current to flow through it.
During operation in blocking mode, the highest electric field occurs at the N+/p+ junction. The presence of a sharp corner at the bottom of the groove enhances the electric field at the edge of the channel in the depletion region, thus reducing the breakdown voltage of the device. This electric field launches electrons into the gate oxide and consequently, the trapped electrons shift the threshold voltage of the MOSFET. For this reason, the V-groove architecture is no longer used in commercial devices.
The device's use was a power device until more suitable geometries, like the UMOS (or Trench-Gate MOS) were introduced in order to lower the maximum electric field at the top of the V shape and thus leading to higher maximum voltages than in case of the VMOS.
History
The first MOSFET (without a V-groove) was invented by Mohamed Atalla and Dawon Kahng at Bell Labs in 1959. The V-groove construction was pioneered by Jun-ichi Nishizawa in 1969, initially for the static induction transistor (SIT), a type of jun
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https://en.wikipedia.org/wiki/Macroglobulin
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Macroglobulins are large globular proteins and are found in the blood and other body fluids. Various physiological processes, including immunity, coagulation, and chemical transport, rely on these proteins. A macroglobulin is a plasma globulin of high molecular weight. Elevated levels of macroglobulins (macroglobulinemia) may cause manifestations of excess blood viscosity (as is the case for IgM antibodies in Waldenström macroglobulinemia) and/or precipitate within blood vessels when temperature drops (as in cryoglobulinaemia). Other macroglobulins include α2-macroglobulin, which is elevated in nephrotic syndrome, diabetes, severe burns, and other conditions, while a deficiency is associated with chronic obstructive pulmonary disease.
Structure
Macroglobulins range in molecular weight from 400,000 to 720,000 Daltons. They are made up of four distinguishing subunits that each possess multiple domains. Disulfide bonds and non-covalent interactions allow the subunits to stay together. One zinc atom also occupies a position in each subunit, aiding to maintain the stability of tetramers. The macroglobulin tetramers can be irreversibly dissociated into dimers by metalscontraions as well as chaotropic substances like urea and guanidine hydrochloride. Despite being similar in structure to immunoglobulins (Ig), macroglobulins have a distinct Y-shaped conformation. A sequence of 16 amino acids at the C-terminus of each subunit provides a highly polar, hydrophobic, binding site that c
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https://en.wikipedia.org/wiki/George%20F.%20Pinder
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George Francis Pinder (born 1942) is an American environmental engineer who is Professor of Civil and Environmental Engineering with a secondary appointment in Mathematics and Statistics at the University of Vermont. He also served as a professional witness in various notable environmental cases including Love Canal and the Woburn groundwater contamination incident.
He was elected a member of the National Academy of Engineering in 2010 for leadership in groundwater modeling applied to diverse problems in water resources. He is founding editor of the journal "Advances in Water Resources", and he served as editor-in-chief of the journal Numerical Methods for Partial Differential Equations.
Pinder's principal research interest is in the development of numerical methods to solve complex problems pertaining to groundwater contamination and supply. He has published approximately one hundred and thirty five papers in refereed journals in the area of quantitative analysis of subsurface flow and transport, as well as twelve books.
In popular culture
Pinder was featured as a character in the movie A Civil Action, based on the Woburn toxic waste case and starring John Travolta. He was portrayed by British actor Stephen Fry. He and his wife Phyllis were also featured in the book on which the film is based.
References
External links
George Pinder at the University of Vermont
Official George Pinder Website
Environmental engineers
American civil engineers
Engineering educators
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https://en.wikipedia.org/wiki/Gian%20Carlo%20Wick
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Gian Carlo Wick (15 October 1909 – 20 April 1992) was an Italian theoretical physicist who made important contributions to quantum field theory. The Wick rotation, Wick contraction, Wick's theorem, and the Wick product are named after him.
Life
Gian Carlo Wick, first name "Gian Carlo", was born in Turin, Italy in 1909. Wick's father was a Latinist and Greekist, and his mother, Barbara Allason (1877–1968), was a well-known Italian writer and anti-fascist. His paternal grandfather had emigrated from Switzerland to Italy and his grandmother from Austria.
In 1930 Wick received his doctoral degree in Turin under G. Wataghin with a thesis on the electronic theory of metals. He then went to Göttingen and Leipzig to further his study of physics. One of the professors he got to know there was Werner Heisenberg. Heisenberg liked the young Italian theoretician—they shared a common interest in classical music—and treated him with an affection that Wick never forgot. Once a week, Heisenberg had invited Wick and other students to his home for spirited evenings of talk and Ping-Pong.
Wick became Enrico Fermi's assistant in Rome in 1932. In 1937 he became professor of theoretical physics in Palermo and then in Padua before returning to Rome in 1940 to become chair of theoretical physics. In 1946 he followed Fermi to the United States, first to the University of Notre Dame, then to Berkeley. Wick refused to subscribe a controversial oath during the McCarthy era, so he was fired at Ber
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https://en.wikipedia.org/wiki/City%20Slickers%20II%3A%20The%20Legend%20of%20Curly%27s%20Gold
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City Slickers II: The Legend of Curly's Gold is a 1994 American Western comedy film directed by Paul Weiland. It is the sequel to City Slickers (1991) and stars Billy Crystal, Daniel Stern, Jon Lovitz, and Jack Palance. Although a mild financial success, the film did not reach the popularity of the first, receiving generally negative responses from critics.
Plot
A year after the events of the first film, Mitch Robbins is a much happier and livelier man, having moved out of the city. He is the manager at the radio station, and has employed his best friend, Phil Berquist. However, he is plagued with nightmares about deceased trail boss, Curly, and believes he may still be alive. On his 40th birthday, Mitch sees a man resembling Curly on the train. Many things have changed; Phil is unexplainably single again and Mitch recognizes he's afraid of Curly still, plus Mitch's immature younger brother, Glen is plaguing the household with his antics. Mitch later finds a treasure map belonging to Lincoln Washburn hidden in Curly's old cowboy hat, albeit with a missing corner. He and Phil investigate the map's contents and learn that Lincoln was Curly's father and a train robber in the Old West. In 1908, he infamously stole and hid one million dollars in gold bullion in the deserts near Las Vegas. With an impending trip to Las Vegas for a convention, Mitch decides to search for the gold (now worth twenty million) along with Phil and Glen.
Several mishaps ensue, such as Glen accidentally
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https://en.wikipedia.org/wiki/Gibbs%20measure
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In mathematics, the Gibbs measure, named after Josiah Willard Gibbs, is a probability measure frequently seen in many problems of probability theory and statistical mechanics. It is a generalization of the canonical ensemble to infinite systems.
The canonical ensemble gives the probability of the system X being in state x (equivalently, of the random variable X having value x) as
Here, is a function from the space of states to the real numbers; in physics applications, is interpreted as the energy of the configuration x. The parameter is a free parameter; in physics, it is the inverse temperature. The normalizing constant is the partition function. However, in infinite systems, the total energy is no longer a finite number and cannot be used in the traditional construction of the probability distribution of a canonical ensemble. Traditional approaches in statistical physics studied the limit of intensive properties as the size of a finite system approaches infinity (the thermodynamic limit). When the energy function can be written as a sum of terms that each involve only variables from a finite subsystem, the notion of a Gibbs measure provides an alternative approach. Gibbs measures were proposed by probability theorists such as Dobrushin, Lanford, and Ruelle and provided a framework to directly study infinite systems, instead of taking the limit of finite systems.
A measure is a Gibbs measure if the conditional probabilities it induces on each finite subsystem satisfy
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https://en.wikipedia.org/wiki/KRP%20%28biochemistry%29
|
KRP stands for kinesin related proteins. bimC is a subfamily of KRPs and its function is to separate the duplicated centrosomes during mitosis.
Role in mitotic repair
Kinesin-13 MCAK (Mitotic Centromere-Associated Kinesin) is a KRP that is involved in resolving errors during mitosis involving kinetochore-microtubules. This process is associated with Aurora B Protein Kinase. When Aurora B's function is disrupted, MCAK ability to locate centromeres, which play a critical role in separation of chromosomes during mitosis, was suppressed. There are other environments in which MCAK's function is impaired, absent impact on its associated kinase. For example, alpha-tubulin detyrosination has been demonstrated to impact MCAK's mitotic repair capabilities, suggesting a potential cause of chromosomal instability.
References
Proteins
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https://en.wikipedia.org/wiki/Random%20self-reducibility
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Random self-reducibility (RSR) is the rule that a good algorithm for the average case implies a good algorithm for the worst case. RSR is the ability to solve all instances of a problem by solving a large fraction of the instances.
Definition
If for a function f evaluating any instance x can be reduced in polynomial time to the evaluation of f on one or more random instances yi, then it is self-reducible (this is also known as a non-adaptive uniform self-reduction). In a random self-reduction, an arbitrary worst-case instance x in the domain of f is mapped to a random set of instances y1, ..., yk. This is done so that f(x) can be computed in polynomial time, given the coin-toss sequence from the mapping, x, and f(y1), ..., f(yk). Therefore, taking the average with respect to the induced distribution on yi, the average-case complexity of f is the same (within polynomial factors) as the worst-case randomized complexity of f.
One special case of note is when each random instance yi is distributed uniformly over the entire set of elements in the domain of f that have a length of |x|. In this case f is as hard on average as it is in the worst case. This approach contains two key restrictions. First the generation of y1, ..., yk is performed non-adaptively. This means that y2 is picked before f(y1) is known. Second, it is not necessary that the points y1, ..., yk be uniformly distributed.
Application in cryptographic protocols
Problems that require some privacy in the
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https://en.wikipedia.org/wiki/Bit%20flipping
|
In computing, bit flipping may refer to:
Bit manipulation, algorithmic manipulation of binary digits (bits)
Bitwise operation NOT, performing logical negation to a single bit, or each of several bits, switching state 0 to 1, and vice versa
Memory error or soft error, an unintentional state switch from 0 to 1, or vice versa, of a bit stored to random access memory or other medium
See also
Bit-flipping attack
Single-event upset
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https://en.wikipedia.org/wiki/Approximation%20in%20algebraic%20groups
|
In algebraic group theory, approximation theorems are an extension of the Chinese remainder theorem to algebraic groups G over global fields k.
History
proved strong approximation for some classical groups.
Strong approximation was established in the 1960s and 1970s, for semisimple simply-connected algebraic groups over global fields. The results for number fields are due to and ; the function field case, over finite fields, is due to and . In the number field case Platonov also proved a related result over local fields called the Kneser–Tits conjecture.
Formal definitions and properties
Let G be a linear algebraic group over a global field k, and A the adele ring of k. If S is a non-empty finite set of places of k, then we write AS for the ring of S-adeles and AS for the product of the completions ks, for s in the finite set S. For any choice of S, G(k) embeds in G(AS) and G(AS).
The question asked in weak approximation is whether the embedding of G(k) in G(AS) has dense image. If the group G is connected and k-rational, then it satisfies weak approximation with respect to any set S . More generally, for any connected group G, there is a finite set T of finite places of k such that G satisfies weak approximation with respect to any set S that is disjoint with T . In particular, if k is an algebraic number field then any connected group G satisfies weak approximation with respect to the set S = S∞ of infinite places.
The question asked in strong approximation is whethe
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https://en.wikipedia.org/wiki/Scalar%20theories%20of%20gravitation
|
Scalar theories of gravitation are field theories of gravitation in which the gravitational field is described using a scalar field, which is required to satisfy some field equation.
Note: This article focuses on relativistic classical field theories of gravitation. The best known relativistic classical field theory of gravitation, general relativity, is a tensor theory, in which the gravitational interaction is described using a tensor field.
Newtonian gravity
The prototypical scalar theory of gravitation is Newtonian gravitation. In this theory, the gravitational interaction is completely described by the potential , which is required to satisfy the Poisson equation (with the mass density acting as the source of the field). To wit:
, where
G is the gravitational constant and
is the mass density.
This field theory formulation leads directly to the familiar law of universal gravitation, .
Nordström's theories of gravitation
The first attempts to present a relativistic (classical) field theory of gravitation were also scalar theories. Gunnar Nordström created two such theories.
Nordström's first idea (1912) was to simply replace the divergence operator in the field equation of Newtonian gravity with the d'Alembertian operator . This gives the field equation
.
However, several theoretical difficulties with this theory quickly arose, and Nordström dropped it.
A year later, Nordström tried again, presenting the field equation
,
where is the trace of the st
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https://en.wikipedia.org/wiki/Turbulence%20modeling
|
In fluid dynamics, turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real-life scenarios, including the flow of blood through the cardiovascular system, the airflow over an aircraft wing, the re-entry of space vehicles, besides others. In spite of decades of research, there is no analytical theory to predict the evolution of these turbulent flows. The equations governing turbulent flows can only be solved directly for simple cases of flow. For most real-life turbulent flows, CFD simulations use turbulent models to predict the evolution of turbulence. These turbulence models are simplified constitutive equations that predict the statistical evolution of turbulent flows.
Closure problem
The Navier–Stokes equations govern the velocity and pressure of a fluid flow. In a turbulent flow, each of these quantities may be decomposed into a mean part and a fluctuating part. Averaging the equations gives the Reynolds-averaged Navier–Stokes (RANS) equations, which govern the mean flow. However, the nonlinearity of the Navier–Stokes equations means that the velocity fluctuations still appear in the RANS equations, in the nonlinear term from the convective acceleration. This term is known as the Reynolds stress, . Its effect on the mean flow is like that of a stress term, such as from pressure or viscosity.
To obtain equations containing only the mean velocity and pressure, we need to cl
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https://en.wikipedia.org/wiki/Radio%20Campus%20Paris
|
Radio Campus Paris is a student radio station in Paris. Created in 1998 as an internet radio station, it established a half-frequency on 93.9 FM in the Paris region in 2004 that it shares with Vivre FM, maintaining their online broadcast 24 hours a day. A member of the Radio Campus France network, the station prides itself on youth culture and eclecticism, hosting around 80 different programs in the 2017–18 season.
History
Radio Campus Paris was founded in 1998 with the aim of creating a new alternative media for all students in the Paris region. In 2003, the station set up its studios at the , in the 3rd arrondissement, broadcasting 24/7 as a strictly web-radio station.
The assigned a half-frequency to Radio Campus Paris on the Parisian FM band on September 23, 2004, and since then, the station emits from 5:30 pm to 5:30 am on the 93.9 FM frequency in the Paris region.
Since June 2014 Radio Campus Paris also broadcasts on digital radio on multiplex 4 in Paris.
References
External links
Radio website
Campus, college, student and university radio stations
Radio stations in France
Radio in Paris
Radio stations established in 1998
1998 establishments in France
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https://en.wikipedia.org/wiki/Casado
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A casado (Spanish, "married man") is a Costa Rican meal using rice, black beans, plantains, salad, a tortilla, and an optional protein source such as chicken, beef, pork, fish, and so on.
The term may have originated when restaurant customers asked to be treated as casados, since married men ate such meals at home. Another theory is that the rice and beans and/or the grouping of dishes are married, since they are always together.
References
Costa Rican cuisine
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https://en.wikipedia.org/wiki/List%20of%20complex%20and%20algebraic%20surfaces
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This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification.
Kodaira dimension −∞
Rational surfaces
Projective plane
Quadric surfaces
Cone (geometry)
Cylinder
Ellipsoid
Hyperboloid
Paraboloid
Sphere
Spheroid
Rational cubic surfaces
Cayley nodal cubic surface, a certain cubic surface with 4 nodes
Cayley's ruled cubic surface
Clebsch surface or Klein icosahedral surface
Fermat cubic
Monkey saddle
Parabolic conoid
Plücker's conoid
Whitney umbrella
Rational quartic surfaces
Châtelet surfaces
Dupin cyclides, inversions of a cylinder, torus, or double cone in a sphere
Gabriel's horn
Right circular conoid
Roman surface or Steiner surface, a realization of the real projective plane in real affine space
Tori, surfaces of revolution generated by a circle about a coplanar axis
Other rational surfaces in space
Boy's surface, a sextic realization of the real projective plane in real affine space
Enneper surface, a nonic minimal surface
Henneberg surface, a minimal surface of degree 15
Bour's minimal surface, a surface of degree 16
Richmond surfaces, a family of minimal surfaces of variable degree
Other families of rational surfaces
Coble surfaces
Del Pezzo surfaces, surfaces with an ample anticanonical divisor
Hirzebruch surfaces, rational ruled surfaces
Segre surfaces, intersections of two quadrics in projective 4-space
Unirational su
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https://en.wikipedia.org/wiki/Bit%20cell
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A bit cell is the length of tape, the area of disc surface, or the part of an integrated circuit in which a single bit is recorded. The smaller the bit cells are, the greater the storage density of the medium is.
In magnetic storage, the magnetic flux or magnetization doesn't necessarily change at the boundaries of bit cells to indicate bit states. For example, the presence of a magnetic transition within a bit cell might record state 1, and the lack of such a transition might record state 0. Other encodings are also possible.
See also
Computer data storage
References
Software Preservation Society glossary entry for bit cell
Hitachi research page on patterned magnetic media
Computer data storage
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https://en.wikipedia.org/wiki/A-League%20Men%20records%20and%20statistics
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The A-League Men is an Australian professional league for association football clubs. At the top of the Australian soccer league system, it is the country's primary soccer competition and is contested by 12 clubs. The competition was formed in April 2004, following a number of issues including financial problems in the National Soccer League. Those records and statistics of the A-League Men are listed below. All updated as of 6 March 2023.
Team records
Titles
Most Premiership titles: 4, Sydney FC
Most Championship titles: 5, Sydney FC
Most consecutive Premiership title wins: 2, Sydney FC (2016–17, 2017–18); Melbourne City (2020–21, 2021–22)
Most consecutive Championship title wins: 2, Brisbane Roar (2011, 2012), Sydney FC (2019, 2020)
Biggest Premiership title winning margin: 17 points, 2016–17; Sydney FC (66 points) over Melbourne Victory (49 points)
Smallest Premiership title winning margin: 0 points and same goal difference, 2008–09; Melbourne Victory over Adelaide United through more goals scored.
Points
Most points in a season: 66, Sydney FC (2016–17)
Most home points in a season: 33, Brisbane Roar (2010–11, 2013–14)
Most away points in a season: 34, Sydney FC (2014–15)
Fewest points in a season: 6, New Zealand Knights (2005–06)
Fewest home points in a season: 2, New Zealand Knights (2005–06)
Fewest away points in a season: 4, New Zealand Knights (2005–06)
Most points in a season without winning the league: 57, Central Coast Mariners (2010–11)
Fewest points in a seas
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https://en.wikipedia.org/wiki/Standard%20normal%20table
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In statistics, a standard normal table, also called the unit normal table or Z table, is a mathematical table for the values of , the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution. Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal (known as a z-score) and then use the standard normal table to find probabilities.
Normal and standard normal distribution
Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data. The standard normal distribution, represented by , is the normal distribution having a mean of 0 and a standard deviation of 1.
Conversion
If is a random variable from a normal distribution with mean and standard deviation , its Z-score may be calculated from by subtracting and dividing by the standard deviation:
If is the mean of a sample of size from some population in which the mean is and the standard deviation is , the standard error is
If is the total of a sample of size from some population in which the mean is and the standard deviation is , the expected total is and the standard error is
Reading a Z table
Formatting / layout
tables are typically composed a
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https://en.wikipedia.org/wiki/Pentacene
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Pentacene () is a polycyclic aromatic hydrocarbon consisting of five linearly-fused benzene () rings. This highly conjugated compound is an organic semiconductor. The compound generates excitons upon absorption of ultra-violet (UV) or visible light; this makes it very sensitive to oxidation. For this reason, this compound, which is a purple powder, slowly degrades upon exposure to air and light.
Structurally, pentacene is one of the linear acenes, the previous one being tetracene (four fused benzene rings) and the next one being hexacene (six fused benzene rings). In August 2009, a group of researchers from IBM published experimental results of imaging a single molecule of pentacene using an atomic force microscope. In July 2011, they used a modification of scanning tunneling microscopy to experimentally determine the shapes of the highest occupied and lowest unoccupied molecular orbitals.
In 2012, pentacene-doped p-terphenyl was shown to be effective as the amplifier medium for a room-temperature maser.
Synthesis
Pentacene was first synthesized in 1912 by British chemists William Hobson Mills and Mildred May Gostling. A classic method for pentacene synthesis is by the Elbs reaction.
Pentacenes can also be prepared by extrusion of a small volatile component (carbon monoxide) from a suitable precursor at 150 °C.
The precursor itself is prepared in three steps from two molecules of α,α,α',α'-tetrabromo-o-xylene with a 7-tert-butoxybicyclo[2.2.1]hepta-2,5-diene by first h
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https://en.wikipedia.org/wiki/Acnode
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An acnode is an isolated point in the solution set of a polynomial equation in two real variables. Equivalent terms are isolated point and hermit point.
For example the equation
has an acnode at the origin, because it is equivalent to
and is non-negative only when ≥ 1 or . Thus, over the real numbers the equation has no solutions for except for (0, 0).
In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist. In fact, the complex solution set of a polynomial equation in two complex variables can never have an isolated point.
An acnode is a critical point, or singularity, of the defining polynomial function, in the sense that both partial derivatives and vanish. Further the Hessian matrix of second derivatives will be positive definite or negative definite, since the function must have a local minimum or a local maximum at the singularity.
See also
Singular point of a curve
Crunode
Cusp
Tacnode
References
Curves
Algebraic curves
Singularity theory
es:Punto singular de una curva#Acnodos
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https://en.wikipedia.org/wiki/Trovafloxacin
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Trovafloxacin (sold as Trovan by Pfizer and Turvel by Laboratorios Almirall) is a broad spectrum antibiotic that inhibits the uncoiling of supercoiled DNA in various bacteria by blocking the activity of DNA gyrase and topoisomerase IV. It was withdrawn from the market due to the risk of hepatotoxicity. It had better Gram-positive bacterial coverage but less Gram-negative coverage than the previous fluoroquinolones.
Adverse reactions
Trovafloxacin use is significantly restricted due to its high potential for inducing serious and sometimes fatal liver damage. Currently, the drug is not approved for use in the U.S. or the European Union due to association with cases of acute liver failure and death.
Manufacturing
The key reaction in building the ring consists of 1,3-Dipolar cycloaddition of ethyl diazoacetate to N-Cbz-3-pyrroline to afford the pyrrazolidine (3). Pyrolysis results in loss of nitrogen and formation of the cyclopropylpyrrolidine ring. The stereochemistry of the ring simply reflects the thermodynamics, since cis ring fusion is by far the most stable arrangement, as is the cis configuration of the ester group. The ester is then saponified to the corresponding carboxylic acid (5). The acid undergoes a version of the Curtius rearrangement when treated with diphenylphosphoryl azide (DPPA) to afford the transient isocyanate (6). The reactive function adds t-BuOH from the reaction medium to afford the product as its tert-Butyloxycarbonyl protecting group derivative (7)
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https://en.wikipedia.org/wiki/Mylonite
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Mylonite is a fine-grained, compact metamorphic rock produced by dynamic recrystallization of the constituent minerals resulting in a reduction of the grain size of the rock. Mylonites can have many different mineralogical compositions; it is a classification based on the textural appearance of the rock.
Formation
Mylonites are ductilely deformed rocks formed by the accumulation of large shear strain, in ductile fault zones. There are many different views on the formation of mylonites, but it is generally agreed that crystal-plastic deformation must have occurred, and that fracturing and cataclastic flow are secondary processes in the formation of mylonites. Mechanical abrasion of grains by milling does not occur, although this was originally thought to be the process that formed mylonites, which were named from the Greek μύλος mylos, meaning mill. Mylonites form at depths of no less than 4 km.
There are many different mechanisms that accommodate crystal-plastic deformation. In crustal rocks the most important processes are dislocation creep and diffusion creep. Dislocation generation acts to increase the internal energy of crystals. This effect is compensated through grain-boundary-migration recrystallization which reduces the internal energy by increasing the grain boundary area and reducing the grain volume, storing energy at the mineral grain surface. This process tends to organize dislocations into subgrain boundaries. As more dislocations are added to subgrain boun
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https://en.wikipedia.org/wiki/Lagrange%27s%20formula
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Lagrange's formula may refer to a number of results named after Joseph Louis Lagrange:
Lagrange interpolation formula
Lagrange–Bürmann formula
Triple product expansion
Mean value theorem
Euler–Lagrange equation
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https://en.wikipedia.org/wiki/Proofs%20of%20quadratic%20reciprocity
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In number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusually large number of proofs. Several hundred proofs of the law of quadratic reciprocity have been published.
Proof synopsis
Of the elementary combinatorial proofs, there are two which apply types of double counting. One by Gotthold Eisenstein counts lattice points. Another applies Zolotarev's lemma to , expressed by the Chinese remainder theorem as and calculates the signature of a permutation. The shortest known proof also uses a simplified version of double counting, namely double counting modulo a fixed prime.
Eisenstein's proof
Eisenstein's proof of quadratic reciprocity is a simplification of Gauss's third proof. It is more geometrically intuitive and requires less technical manipulation.
The point of departure is "Eisenstein's lemma", which states that for distinct odd primes p, q,
where denotes the floor function (the largest integer less than or equal to x), and where the sum is taken over the even integers u = 2, 4, 6, ..., p−1. For example,
This result is very similar to Gauss's lemma, and can be proved in a similar fashion (proof given below).
Using this representation of (q/p), the main argument is quite elegant. The sum counts the number of lattice points with even x-coordinate in the interior of the triangle ABC in the following diagram:
Because each column has an even number of points (namely q−1 points), the number of such lattice points
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https://en.wikipedia.org/wiki/Davson%E2%80%93Danielli%20model
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The Davson–Danielli model (or paucimolecular model) was a model of the plasma membrane of a cell, proposed in 1935 by Hugh Davson and James Danielli. The model describes a phospholipid bilayer that lies between two layers of globular proteins, which is both trilaminar and lipoprotinious. The phospholipid bilayer had already been proposed by Gorter and Grendel in 1925; however, the flanking proteinaceous layers in the Davson–Danielli model were novel and intended to explain Danielli's observations on the surface tension of lipid bi-layers (It is now known that the phospholipid head groups are sufficient to explain the measured surface tension).
Evidence for the model included electron microscopy, in which high-resolution micrographs showed three distinct layers within a cell membrane, with an inner white core and two flanking dark layers. Since proteins usually appear dark and phospholipids white, the micrographs were interpreted as a phospholipid bilayer sandwiched between two protein layers. The model proposed an explanation for the ability for certain molecules to permeate the cell membrane while other molecules could not, while also accounting for the thinness of cell membranes.
Despite the Davson–Danielli model being scientifically accepted, the model made assumptions, such as assuming that all membranes had the same structure, thickness and lipid-protein ratio, contradicting the observation that membranes could have specialized functions. Furthermore, the Davson–
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https://en.wikipedia.org/wiki/Bell%20P-76
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The Bell P-76 was the proposed designation for a production model derivative of the XP-39E, a single-engine American fighter aircraft prototype of World War II.
Design and development
On 26 February 1941 the United States Army Air Corps (USAAC) placed a contract with Bell allowing for the purchase of two XP-39Es (41-19501 and 41-19502) which were envisaged to be a major improvement on the P-39D series. Because of the number of changes proposed the production model was to be called the Bell P-76.
The Bell P-76 was proposed to address the poor high-altitude performance of the P-39 Airacobra by incorporating a new and thicker wing with a symmetrical airfoil; the section chosen was NACA 0018 at the wing-root tapering to an NACA 23009 at the tip. Although the new wing has often been referred to as a laminar flow type, this was not the case. The wing span was increased to 35 ft 10 in (10.9 m) and the area to 236 ft² (21.9 m²), the thicker wing allowing an increase in the fuel capacity to 150 US gallons (568 L).
Design of a new Allison V-1710-E9 was also underway. This version, which had the military designation of V-1710-47, used a two-stage mechanical supercharger to increase the engine power at altitude. However, this engine went through so many design changes that it ended up being almost identical to the later V-1710-93 which was fitted in the XP-63A.
Another change was the engine bay was modified to accept a more powerful engine in lieu of the V-1710. Its origins lie in th
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https://en.wikipedia.org/wiki/Niut%20Range
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The Niut Range is 3600 km2 (c. 1390 sq mi) in area. It is a subrange of the Pacific Ranges of the Coast Mountains of British Columbia, although in some classifications it is considered part of the Chilcotin Ranges (which in some classifications are themselves part of the Pacific Ranges). The Niut is located in the angle of the Homathko River and its main west fork, Mosley Creek. It is isolated, island-like, by those rivers from its neighbour ranges, as both streams have their source on the Chilcotin Plateau in behind the range. Razorback Mountain is its highest peak.
Northwest across Mosley Creek is the Pantheon Range and due west is the Waddington Range and south of that is the Whitemantle Range; further northwest is the Klinaklini Icefield, beyond the river of the same name. To the southeast across the great Grand Canyon of the Homathko is the Homathko Icefield, east of which beyond the area of Mount Queen Bess is Tsy'los Provincial Park.
History
Just below the confluence of Mosley Creek and the Homathko River, at the southern foot of the Niut Range, the bullying of a party of Tsilhqot'in First Nations warriors hired to help build an enterprise known as Waddington's Road led to their massacre of the road company's workers and the opening of hostilities between a faction of the Chilcotin people and the colonial government of British Columbia.
This was the opening round of the Chilcotin War of 1864. The land-surveyed townsite of Port Waddington on today's maps is a
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https://en.wikipedia.org/wiki/EOM
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Eom or EOM may refer to:
People
Eom (Korean surname)
Science and technology
Electro-optic modulator
End of message
Enterprise output management
Equations of motion
Ensemble optimization method; see Biological small-angle scattering
Other uses
Employee of the month (program)
Encyclopedia of Mathematics
Encyclopedia of Mormonism
English-only movement, a political movement in the United States
Estatuto Orgânico de Macau, an organic statute of Portuguese Macau
End Of Month
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https://en.wikipedia.org/wiki/Jind%C5%99ich%20Ba%C4%8Dkovsk%C3%BD
|
Jindřich Bačkovský (; May 4, 1912 – 2000) was an eminent Czechoslovak physicist whose work focused on X-ray spectroscopy, the structure of crystals, vacuum techniques, radiometry and the physics of high pressures. Many of his findings are used in industry, especially in the manufacture of semiconductor parts and synthetic diamonds.
External links
Czech archives
Short Biography (Czech)
Czechoslovak physicists
1912 births
2000 deaths
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https://en.wikipedia.org/wiki/Castelnuovo%E2%80%93de%20Franchis%20theorem
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In mathematics, the Castelnuovo–de Franchis theorem is a classical result on complex algebraic surfaces. Let X be such a surface, projective and non-singular, and let
ω1 and ω2
be two differentials of the first kind on X which are linearly independent but with wedge product 0. Then this data can be represented as a pullback of an algebraic curve: there is a non-singular algebraic curve C, a morphism
φ: X → C,
and differentials of the first kind ω1 and ω2 on C such that
φ*(1) = ω1 and φ*(2) = ω2.
This result is due to Guido Castelnuovo and Michele de Franchis (1875–1946).
The converse, that two such pullbacks would have wedge 0, is immediate.
See also
de Franchis theorem
References
.
Algebraic surfaces
Theorems in geometry
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https://en.wikipedia.org/wiki/De%20Franchis%20theorem
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In mathematics, the de Franchis theorem is one of a number of closely related statements applying to compact Riemann surfaces, or, more generally, algebraic curves, X and Y, in the case of genus g > 1. The simplest is that the automorphism group of X is finite (see though Hurwitz's automorphisms theorem). More generally,
the set of non-constant morphisms from X to Y is finite;
fixing X, for all but a finite number of such Y, there is no non-constant morphism from X to Y.
These results are named for (1875–1946). It is sometimes referenced as the De Franchis-Severi theorem. It was used in an important way by Gerd Faltings to prove the Mordell conjecture.
See also
Castelnuovo–de Franchis theorem
References
M. De Franchis: Un teorema sulle involuzioni irrazionali, Rend. Circ. Mat Palermo 36 (1913), 368
Algebraic curves
Riemann surfaces
Theorems in algebraic geometry
Theorems in algebraic topology
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https://en.wikipedia.org/wiki/Vascular%20tissue
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Vascular tissue is a complex conducting tissue, formed of more than one cell type, found in vascular plants. The primary components of vascular tissue are the xylem and phloem. These two tissues transport fluid and nutrients internally. There are also two meristems associated with vascular tissue: the vascular cambium and the cork cambium. All the vascular tissues within a particular plant together constitute the vascular tissue system of that plant.
The cells in vascular tissue are typically long and slender. Since the xylem and phloem function in the conduction of water, minerals, and nutrients throughout the plant, it is not surprising that their form should be similar to pipes. The individual cells of phloem are connected end-to-end, just as the sections of a pipe might be. As the plant grows, new vascular tissue differentiates in the growing tips of the plant. The new tissue is aligned with existing vascular tissue, maintaining its connection throughout the plant. The vascular tissue in plants is arranged in long, discrete strands called vascular bundles. These bundles include both xylem and phloem, as well as supporting and protective cells. In stems and roots, the xylem typically lies closer to the interior of the stem with phloem towards the exterior of the stem. In the stems of some Asterales dicots, there may be phloem located inwardly from the xylem as well.
Between the xylem and phloem is a meristem called the vascular cambium. This tissue divides off cells th
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https://en.wikipedia.org/wiki/Noether%27s%20theorem%20on%20rationality%20for%20surfaces
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In mathematics, Noether's theorem on rationality for surfaces is a classical result of Max Noether on complex algebraic surfaces, giving a criterion for a rational surface. Let S be an algebraic surface that is non-singular and projective. Suppose there is a morphism φ from S to the projective line, with general fibre also a projective line. Then the theorem states that S is rational.
See also
Hirzebruch surface
List of complex and algebraic surfaces
References
Castelnuovo’s Theorem
Notes
Algebraic surfaces
Theorems in algebraic geometry
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https://en.wikipedia.org/wiki/Walter%20Plecker
|
Walter Ashby Plecker (April 2, 1861 – August 2, 1947) was an American physician and public health advocate who was the first registrar of Virginia's Bureau of Vital Statistics, serving from 1912 to 1946. He was a leader of the Anglo-Saxon Clubs of America, a white supremacist organization founded in Richmond, Virginia, in 1922. A eugenicist and proponent of scientific racism, Plecker drafted and lobbied for the passage of the Racial Integrity Act of 1924 by the Virginia legislature; it institutionalized the one-drop rule.
Plecker was killed after being struck by a car in 1947.
Early life and education
Plecker was born in Augusta County, the son of a returned Confederate veteran. Sent to Staunton as a boy, he graduated from Hoover Military Academy in 1880 and obtained a medical degree from the University of Maryland in 1885. He was a devout Presbyterian, and throughout his life he supported the denomination's fundamentalist Southern branch, funding missionaries who believed, as he later would, that God had destroyed Sodom and Gomorrah as punishment for racial intermixing.
Career
Plecker settled in Hampton, Virginia, in 1892, and before his mother's death in 1915, he worked with women of all races and became known for his active interest in obstetrics and public health issues. Plecker educated midwives, invented a home incubator, and prescribed home remedies for infants. Plecker became the public health officer for Elizabeth City County in 1902.
In 1912, Plecker became the
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https://en.wikipedia.org/wiki/Axiality%20and%20rhombicity
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In physics and mathematics, axiality and rhombicity are two characteristics of a symmetric second-rank tensor in three-dimensional Euclidean space, describing its directional asymmetry.
Let A denote a second-rank tensor in R3, which can be represented by a 3-by-3 matrix. We assume that A is symmetric. This implies that A has three real eigenvalues, which we denote by , and . We assume that they are ordered such that
The axiality of A is defined by
The rhombicity is the difference between the smallest and the second-smallest eigenvalue:
Other definitions of axiality and rhombicity differ from the ones given above by constant factors which depend on the context. For example, when using them as parameters in the irreducible spherical tensor expansion, it is most convenient to divide the above definition of axiality by and that of rhombicity by .
Applications
The description of physical interactions in terms of axiality and rhombicity is frequently encountered in spin dynamics and, in particular, in spin relaxation theory, where many traceless bilinear interaction Hamiltonians, having the (eigenframe) form
(hats denote spin projection operators) may be conveniently rotated using rank 2 irreducible spherical tensor operators:
where are Wigner functions, are Euler angles, and the expressions for the rank 2 irreducible spherical tensor operators are:
Defining Hamiltonian rotations in this way (axiality, rhombicity, three angles) significantly simplifies calculations, si
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https://en.wikipedia.org/wiki/HDC
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HDC may refer to:
Computing
Hyperdimensional computing, or computation that uses very long vectors
Handle of Device Context, part of the GDI API
High-Definition Coding, an audio compression codec
; Unix-like ATA device file
Organizations
Halal Industry Development Corporation, Malaysia
Health and Disability Commissioner, New Zealand
Health Data Consortium, US
Historic Districts Council, New York City, US
Honeysuckle Development Corporation, NSW, Australia
HDC Hyundai Development Company, South Korea
Transportation
Haldia Dock Complex, of the Port of Kolkata, India
Hammond Northshore Regional Airport (FAA LID code), Louisiana, US
Hill descent control system, of an automobile
Other uses
Heavyweight Dub Champion, an American electronic music group
Herräng Dance Camp, Sweden
Histidine decarboxylase, an enzyme
Holder in due course, a concept in commercial law
Home Detention Curfew, in the UK
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https://en.wikipedia.org/wiki/Grim%27s%20Ditch
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Grim's Ditch, Grim's Dyke (also Grimsdyke or Grimes Dike in derivative names) or Grim's Bank is a name shared by a number of prehistoric bank and ditch linear earthworks across England. They are of different dates and may have had different functions.
Purpose
The purpose of these earthworks remains a mystery, but as they are too small for military use they may have served to demarcate territory. Some of the Grims Ditches may have had multiple functions.
Etymology
The name "Grim's Ditch" is Old English in origin. The Anglo-Saxon word dīc was pronounced "deek" in northern England and "deetch" in the south. The method of building this type of earthwork involved digging a trench and forming the upcast soil into a bank alongside it. This practice has resulted in the name dīc being given to either the trench or the bank, and this evolved into two words, ditch and dyke in modern British English.
The origin of the name Grim is shrouded in mystery, but there are several theories as to its origin. Many ancient earthworks of this name exist across England and Wales, pre-dating the Anglo Saxon settlement of Britain. It was common for the Anglo Saxons to name features of unexplained or mysterious origin Grim.
Danish Vikings
The name Grim was a common Old Danish personal-name during the Viking Age.
Many English place names are derived from the name, especially in those areas where people of Scandinavian origin settled.
The place name Grimston is particularly common.
The name was
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https://en.wikipedia.org/wiki/Human%20taxonomy
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Human taxonomy is the classification of the human species (systematic name Homo sapiens, Latin: "wise man") within zoological taxonomy. The systematic genus, Homo, is designed to include both anatomically modern humans and extinct varieties of archaic humans. Current humans have been designated as subspecies Homo sapiens sapiens, differentiated, according to some, from the direct ancestor, Homo sapiens idaltu (with some other research instead classifying idaltu and current humans as belonging to the same subspecies).
Since the introduction of systematic names in the 18th century, knowledge of human evolution has increased drastically, and a number of intermediate taxa have been proposed in the 20th and early 21st centuries. The most widely accepted taxonomy grouping takes the genus Homo as originating between two and three million years ago, divided into at least two species, archaic Homo erectus and modern Homo sapiens, with about a dozen further suggestions for species without universal recognition.
The genus Homo is placed in the tribe Hominini alongside Pan (chimpanzees). The two genera are estimated to have diverged over an extended time of hybridization, spanning roughly 10 to 6 million years ago, with possible admixture as late as 4 million years ago. A subtribe of uncertain validity, grouping archaic "pre-human" or "para-human" species younger than the Homo-Pan split, is Australopithecina (proposed in 1939).
A proposal by Wood and Richmond (2000) would introduce Ho
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https://en.wikipedia.org/wiki/Amphotropism
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Amphotropism or amphotropic indicates that a pathogen like a virus or a bacterium has a wide host range and can infect more than one species or cell culture line.
See also
Tropism, a list of tropisms
Ecotropism, indicating a narrow host range
Ecology terminology
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https://en.wikipedia.org/wiki/Block-matching%20algorithm
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A Block Matching Algorithm is a way of locating matching macroblocks in a sequence of digital video frames for the purposes of motion estimation. The underlying supposition behind motion estimation is that the patterns corresponding to objects and background in a frame of video sequence move within the frame to form corresponding objects on the subsequent frame. This can be used to discover temporal redundancy in the video sequence, increasing the effectiveness of inter-frame video compression by defining the contents of a macroblock by reference to the contents of a known macroblock which is minimally different.
A block matching algorithm involves dividing the current frame of a video into macroblocks and comparing each of the macroblocks with a corresponding block and its adjacent neighbors in a nearby frame of the video (sometimes just the previous one). A vector is created that models the movement of a macroblock from one location to another. This movement, calculated for all the macroblocks comprising a frame, constitutes the motion estimated in a frame.
The search area for a good macroblock match is decided by the ‘search parameter’, p, where p is the number of pixels on all four sides of the corresponding macro-block in the previous frame. The search parameter is a measure of motion. The larger the value of p, larger is the potential motion and the possibility for finding a good match. A full search of all potential blocks however is a computationally expensive task.
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https://en.wikipedia.org/wiki/Microsoft%20Video%201
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Microsoft Video 1 or MS-CRAM is an early lossy video compression and decompression algorithm (codec) that was released with version 1.0 of Microsoft's Video for Windows in November 1992. It is based on MotiVE, a vector quantization codec which Microsoft licensed from Media Vision. In 1993, Media Vision marketed the Pro Movie Spectrum, an ISA board that captured video in both raw and MSV1 formats (the MSV1 processing was done in hardware on the board).
Compression algorithm
Microsoft Video 1 operates either in an 8-bit palettized color space or in a 15-bit RGB color space. Each frame is split into 4×4 pixel blocks. Each 4×4 pixel block can be coded in one of three modes: skip, 2-color or 8-color. In skip mode, the content from the previous frame is copied to the current frame in a conditional replenishment fashion. In 2-color mode, two colors per 4×4 block are transmitted, and 1 bit per pixel is used to select between the two colors. In 8-color mode, the same scheme applies with 2 colors per 2×2 block. This can be interpreted as a 2-color palette which is locally adapted on either a 4×4 block basis or a 2×2 block basis. Interpreted as vector quantization, vectors with components red, green, and blue are quantized using a forward adaptive codebook with two entries.
Use in NetShow Encoder
The codec was available in Microsoft NetShow Encoder, which was later renamed Windows Media Encoder, and made available via the SDK. The NetShow encoder allowed the user to select a 2 pass
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https://en.wikipedia.org/wiki/Blum%E2%80%93Goldwasser%20cryptosystem
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The Blum–Goldwasser (BG) cryptosystem is an asymmetric key encryption algorithm proposed by Manuel Blum and Shafi Goldwasser in 1984. Blum–Goldwasser is a probabilistic, semantically secure cryptosystem with a constant-size ciphertext expansion. The encryption algorithm implements an XOR-based stream cipher using the Blum-Blum-Shub (BBS) pseudo-random number generator to generate the keystream. Decryption is accomplished by manipulating the final state of the BBS generator using the private key, in order to find the initial seed and reconstruct the keystream.
The BG cryptosystem is semantically secure based on the assumed intractability of integer factorization; specifically, factoring a composite value where are large primes. BG has multiple advantages over earlier probabilistic encryption schemes such as the Goldwasser–Micali cryptosystem. First, its semantic security reduces solely to integer factorization, without requiring any additional assumptions (e.g., hardness of the quadratic residuosity problem or the RSA problem). Secondly, BG is efficient in terms of storage, inducing a constant-size ciphertext expansion regardless of message length. BG is also relatively efficient in terms of computation, and fares well even in comparison with cryptosystems such as RSA (depending on message length and exponent choices). However, BG is highly vulnerable to adaptive chosen ciphertext attacks (see below).
Because encryption is performed using a probabilistic algorithm, a
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https://en.wikipedia.org/wiki/Comparison%20of%20raster-to-vector%20conversion%20software
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The following tables contain general and technical information about publicly available raster-to-vector conversion software.
General information
Basic features
CAD features
Raster editing features
Vector editing features
Discontinued software
Adobe Freehand (1988-2003)
Adobe Streamline (1989-2001)
Magic Tracer
Xara Xtreme for Linux – 2006 open source fork of Xara Photo & Graphic Designer
References
raster to vector software
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https://en.wikipedia.org/wiki/Ostwald%E2%80%93Freundlich%20equation
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The Ostwald–Freundlich equation governs boundaries between two phases; specifically, it relates the surface tension of the boundary to its curvature, the ambient temperature, and the vapor pressure or chemical potential in the two phases.
The Ostwald–Freundlich equation for a droplet or particle with radius is:
= atomic volume
= Boltzmann constant
= surface tension (J m−2)
= equilibrium partial pressure (or chemical potential or concentration)
= partial pressure (or chemical potential or concentration)
= absolute temperature
One consequence of this relation is that small liquid droplets (i.e., particles with a high surface curvature) exhibit a higher effective vapor pressure, since the surface is larger in comparison to the volume.
Another notable example of this relation is Ostwald ripening, in which surface tension causes small precipitates to dissolve and larger ones to grow. Ostwald ripening is thought to occur in the formation of orthoclase megacrysts in granites as a consequence of subsolidus growth. See rock microstructure for more.
History
In 1871, Lord Kelvin (William Thomson) obtained the following relation governing a liquid-vapor interface:
where:
= vapor pressure at a curved interface of radius
= vapor pressure at flat interface () =
= surface tension
= density of vapor
= density of liquid
, = radii of curvature along the principal sections of the curved interface.
In his dissertation of 1885, Robert von Helmholtz (son of the
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https://en.wikipedia.org/wiki/Protein%20poisoning
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Protein poisoning (also referred to colloquially as rabbit starvation, mal de caribou, or fat starvation) is an acute form of malnutrition caused by a diet deficient in fat and carbohydrates, where almost all bioavailable calories come from the protein in lean meat. The concept is discussed in the context of paleoanthropological investigations into the diet of ancient humans, especially during the Last Glacial Maximum and at high latitude regions.
The term rabbit starvation originates from the fact that rabbit meat is very low in fat, with almost all of its caloric content from the amino acids digested out of skeletal muscle protein, and therefore is a food which, if consumed exclusively, would cause protein poisoning. The reported symptoms include initial nausea and fatigue, followed by diarrhea and ultimately death.
Observations
In Appian's Roman History, Volume I, Book VI: The Wars in Spain, Chapter IX, page 223, the author notes a multitude of Roman soldiers dying of severe diarrhea after eating mostly rabbits while besieging the city Intercatia in approx 150 B.C. Appian wrote:
The explorer Vilhjalmur Stefansson is said to have lived for years exclusively on game meat and fish, with no ill effects. The same is true for his fellow explorer Karsten Anderson. As part of his promotion of meat-only diet modeled on Inuit cuisine, and to demonstrate the effects, in New York City beginning in February 1928, Stefansson and Anderson "lived and ate in the metabolism ward of Rus
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https://en.wikipedia.org/wiki/Aerodynamic%20force
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In fluid mechanics, an aerodynamic force is a force exerted on a body by the air (or other gas) in which the body is immersed, and is due to the relative motion between the body and the gas.
Force
There are two causes of aerodynamic force:
the normal force due to the pressure on the surface of the body
the shear force due to the viscosity of the gas, also known as skin friction.
Pressure acts normal to the surface, and shear force acts parallel to the surface. Both forces act locally. The net aerodynamic force on the body is equal to the pressure and shear forces integrated over the body's total exposed area.
When an airfoil moves relative to the air, it generates an aerodynamic force determined by the velocity of relative motion, and the angle of attack. This aerodynamic force is commonly resolved into two components, both acting through the center of pressure:
drag is the force component parallel to the direction of relative motion,
lift is the force component perpendicular to the direction of relative motion.
In addition to these two forces, the body may experience an aerodynamic moment.
The force created by propellers and jet engines is called thrust, and is also an aerodynamic force (since it acts on the surrounding air). The aerodynamic force on a powered airplane is commonly represented by three vectors: thrust, lift and drag.
The other force acting on an aircraft during flight is its weight, which is a body force and not an aerodynamic force.
See also
Flu
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https://en.wikipedia.org/wiki/Ore%27s%20theorem
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Ore's theorem is a result in graph theory proved in 1960 by Norwegian mathematician Øystein Ore. It gives a sufficient condition for a graph to be Hamiltonian, essentially stating that a graph with sufficiently many edges must contain a Hamilton cycle. Specifically, the theorem considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.
Formal statement
Let be a (finite and simple) graph with vertices. We denote by the degree of a vertex in , i.e. the number of incident edges in to . Then, Ore's theorem states that if
then is Hamiltonian.
Proof
It is equivalent to show that every non-Hamiltonian graph does not obey condition (∗). Accordingly, let be a graph on vertices that is not Hamiltonian, and let be formed from by adding edges one at a time that do not create a Hamiltonian cycle, until no more edges can be added. Let and be any two non-adjacent vertices in . Then adding edge to would create at least one new Hamiltonian cycle, and the edges other than in such a cycle must form a Hamiltonian path in with and . For each index in the range , consider the two possible edges in from to and from to . At most one of these two edges can be present in , for otherwise the cycle would be a Hamiltonian cycle. Thus, the total number of edges incident to either or is at most equal to the number of choices of , which is . Ther
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https://en.wikipedia.org/wiki/Rakesh%20Saxena
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Rakesh Saxena (born 13 July 1952, at Indore, Madhya Pradesh, India) is an Indian convicted criminal, financier and trader in the derivatives market. He is accused of embezzlement in the 1990s from his work as treasury adviser to the Bangkok Bank of Commerce (BBC) and is widely reputed to have been engaged in dozens of high risk ventures and deals throughout the world over the previous three decades.
In October 2009, he was deported to Thailand after fighting the longest extradition battle in Canadian history, which lasted 13 years. In June 2012 Saxena was jailed for 10 years by Bangkok South Criminal Court, and ordered to pay US$41 million in fines and compensation, after being convicted five counts of securities fraud between 1992 and 1995.
Early years
Rakesh Saxena was born 13 July 1952 in Indore, Madhya Pradesh, India. As a child he studied in England, because his mother was an international lawyer. He later lived in New Delhi, India and studied at St Columba's School, and St. Stephen's College. While in university he developed strong Marxist political leanings and by 1974 he graduated with a Master of Arts degree in English.
He worked in a foreign exchange and money market brokerage company, where he concentrated on complex financial transactions and foreign exchange speculation, first in Delhi, Bombay, Sri Lanka and Singapore, and then for the Oriental Bank of Commerce in Delhi, made many fraud deals and put the bank to around 4 crore loss before the Indian government
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https://en.wikipedia.org/wiki/Vector%20fields%20on%20spheres
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In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification of division algebras.
Specifically, the question is how many linearly independent smooth nowhere-zero vector fields can be constructed on a sphere in -dimensional Euclidean space. A definitive answer was provided in 1962 by Frank Adams. It was already known, by direct construction using Clifford algebras, that there were at least such fields (see definition below). Adams applied homotopy theory and topological K-theory to prove that no more independent vector fields could be found. Hence is the exact number of pointwise linearly independent vector fields that exist on an ()-dimensional sphere.
Technical details
In detail, the question applies to the 'round spheres' and to their tangent bundles: in fact since all exotic spheres have isomorphic tangent bundles, the Radon–Hurwitz numbers determine the maximum number of linearly independent sections of the tangent bundle of any homotopy sphere. The case of odd is taken care of by the Poincaré–Hopf index theorem (see hairy ball theorem), so the case even is an extension of that. Adams showed that the maximum number of continuous (smooth would be no different here) pointwise linearly-independent vector fields on the ()-sphere is exactly .
The construction of the fields is related to the real Clifford algebras, which is a theory with a perio
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https://en.wikipedia.org/wiki/Superior%20longitudinal%20muscle%20of%20tongue
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The superior longitudinal muscle of tongue or superior lingualis is a thin layer of oblique and longitudinal fibers immediately underlying the mucous membrane on the dorsum of the tongue.
Structure
The superior longitudinal muscle of the tongue is one of the intrinsic muscles of the tongue. It arises from the submucous fibrous layer close to the epiglottis and from the median fibrous septum, and runs forward to the edges of the tongue.
Nerve supply
The superior longitudinal muscle of the tongue is supplied by the hypoglossal nerve (CN XII).
Function
The superior longitudinal muscle of the tongue works with the other intrinsic muscles to move the tongue.
References
Muscles of the head and neck
Tongue
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https://en.wikipedia.org/wiki/Tensor%20veli%20palatini%20muscle
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The tensor veli palatini muscle (tensor palati or tensor muscle of the velum palatinum) is a thin, triangular muscle of the head that tenses the soft palate and opens the Eustachian tube to equalise pressure in the middle ear.
Structure
The tensor veli palatini muscle is thin and triangular in shape.
Origin
It arises from the scaphoid fossa of the pterygoid process of the sphenoid anteriorly, the (medial aspect of the) spine of sphenoid boneposteriorly, and - between the aforementioned anterior and posterior attachments - from the anterolateral aspect of the membranous wall of the petrotympanic tube.
At the muscle's origin, some of its muscle fibres may be continuous with those of the tensor tympani muscle.
Insertion
Inferiorly, the muscle converges to form a tendon of attachment. This tendon winds medially around the pterygoid hamulus (with a small bursa interposed between the two) to insert into the palatine aponeurosis and into the bony surface posterior to the palatine crest of the horizontal plate of palatine bone.
Dilator tubae component
Some of the muscle's fibres insert onto the lateral lamina of the cartilaginous part of pharyngotympanic tube and adjacent connective tissue, and the Ostmann's fat pad.
The portion of the muscle with these attachments is sometimes called the dilator tubae.
Innervation
The tensor veli palatini muscle receives motor innervation from the mandibular nerve (CN V3) (a branch of the trigeminal nerve (CN V)) via the nerve to medial
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https://en.wikipedia.org/wiki/Code%3A%3ABlocks
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Code::Blocks is a free, open-source cross-platform IDE that supports multiple compilers including GCC, Clang and Visual C++. It is developed in C++ using wxWidgets as the GUI toolkit. Using a plugin architecture, its capabilities and features are defined by the provided plugins.
Currently, Code::Blocks is oriented towards C, C++, and Fortran. It has a custom build system and optional Make support.
Code::Blocks is being developed for Windows and Linux and has been ported to FreeBSD, OpenBSD and Solaris. The latest binary provided for macOS version is 13.12 released on 2013/12/26 (compatible with Mac OS X 10.6 and later), but more recent versions can be compiled and MacPorts supplies version 17.12.
History
After releasing two release candidate versions, 1.0rc1 on July 25, 2005 and 1.0rc2 on October 25, 2005, instead of making a final release, the project developers started adding many new features, with the final release being repeatedly postponed. Instead, there were nightly builds of the latest SVN version made available on a daily basis.
The first stable release was on February 28, 2008, with the version number changed to 8.02. The versioning scheme was changed to that of Ubuntu, with the major and minor number representing the year and month of the release. Version 20.03 is the latest stable release; however for the most up-to-date version the user can download the relatively stable nightly build or download the source code from SVN.
In April 2020, a critical software
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https://en.wikipedia.org/wiki/Stationary%20ergodic%20process
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In probability theory, a stationary ergodic process is a stochastic process which exhibits both stationarity and ergodicity. In essence this implies that the random process will not change its statistical properties with time and that its statistical properties (such as the theoretical mean and variance of the process) can be deduced from a single, sufficiently long sample (realization) of the process.
Stationarity is the property of a random process which guarantees that its statistical properties, such as the mean value, its moments and variance, will not change over time. A stationary process is one whose probability distribution is the same at all times. For more information see stationary process.
An ergodic process is one which conforms to the ergodic theorem. The theorem allows the time average of a conforming process to equal the ensemble average. In practice this means that statistical sampling can be performed at one instant across a group of identical processes or sampled over time on a single process with no change in the measured result.
A simple example of a violation of ergodicity is a measured process which is the superposition of two underlying processes,
each with its own statistical properties. Although the measured process may be stationary in the long term, it is not appropriate to consider the sampled distribution to be the reflection of a single (ergodic) process: The ensemble average is meaningless. Also see ergodic theory and ergodic process.
See
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https://en.wikipedia.org/wiki/Horrocks%E2%80%93Mumford%20bundle
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In algebraic geometry, the Horrocks–Mumford bundle is an indecomposable rank 2 vector bundle on 4-dimensional projective space P4 introduced by . It is the only such bundle known, although a generalized construction involving Paley graphs produces other rank 2 sheaves (Sasukara et al. 1993). The zero sets of sections of the Horrocks–Mumford bundle are abelian surfaces of degree 10, called Horrocks–Mumford surfaces.
By computing Chern classes one sees that the second exterior power of the Horrocks–Mumford bundle F is the line bundle O(5) on P4. Therefore, the zero set V of a general section of this bundle is a quintic threefold called a Horrocks–Mumford quintic. Such a V has exactly 100 nodes; there exists a small resolution V′ which is a Calabi–Yau threefold fibered by Horrocks–Mumford surfaces.
See also
List of algebraic surfaces
References
Algebraic varieties
Vector bundles
Projective geometry of elliptic curves - contains chapter on constructions of the bundle
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https://en.wikipedia.org/wiki/Eco-cities
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An eco-city or ecocity is "a human settlement modeled on the self-sustaining resilient structure and function of natural ecosystems", as defined by Ecocity Builders (a non-profit organization started by Richard Register, who first coined the term). Simply put, an eco-city is an ecologically healthy city. The World Bank defines eco-cities as "cities that enhance the well-being of citizens and society through integrated urban planning and management that harness the benefits of ecological systems and protect and nurture these assets for future generations". Although there is no universally accepted definition of an 'eco-city', among available definitions, there is some consensus on the basic features of an eco-city.
The world's population is continuously increasing, which puts a tremendous amount of pressure on cities due to the need for new urban development. There is an urgent need for cities around the world to adapt ecologically based urban development to work towards sustainability. The dimensions of an ecocity provide solutions to improve the living conditions in cities by solving our current unsustainable practices.
The cities around the world that face the most severe challenges associated with the world's urban population are those in developing countries. Eco-cities are commonly found to focus on new-build developments, especially in developing nations such as China, wherein foundations are being laid for new eco-cities catering to 500,000 or more inhabitants.
Hist
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https://en.wikipedia.org/wiki/Vector%20area
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In 3-dimensional geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an oriented area in three dimensions.
Every bounded surface in three dimensions can be associated with a unique area vector called its vector area. It is equal to the surface integral of the surface normal, and distinct from the usual (scalar) surface area.
Vector area can be seen as the three dimensional generalization of signed area in two dimensions.
Definition
For a finite planar surface of scalar area and unit normal , the vector area is defined as the unit normal scaled by the area:
For an orientable surface composed of a set of flat facet areas, the vector area of the surface is given by
where is the unit normal vector to the area .
For bounded, oriented curved surfaces that are sufficiently well-behaved, we can still define vector area. First, we split the surface into infinitesimal elements, each of which is effectively flat. For each infinitesimal element of area, we have an area vector, also infinitesimal.
where is the local unit vector perpendicular to . Integrating gives the vector area for the surface.
Properties
The vector area of a surface can be interpreted as the (signed) projected area or "shadow" of the surface in the plane in which it is greatest; its direction is given by that plane's normal.
For a curved or faceted (i.e. non-planar) surface, the vector area is smaller in magnitude than the actual su
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https://en.wikipedia.org/wiki/Contiguity
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Contiguity or contiguous may refer to:
Contiguous data storage, in computer science
Contiguity (probability theory)
Contiguity (psychology)
Contiguous distribution of species, in biogeography
Geographic contiguity of territorial land
Contiguous zone in territorial waters
See also
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https://en.wikipedia.org/wiki/Evolved%20antenna
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In radio communications, an evolved antenna is an antenna designed fully or substantially by an automatic computer design program that uses an evolutionary algorithm that mimics Darwinian evolution. This procedure has been used since the early 2000s to design antennas for mission-critical applications involving stringent, conflicting, or unusual design requirements, such as unusual radiation patterns, for which none of the many existing antenna types are adequate.
Process
The computer program starts with simple antenna shapes, then adds or modifies elements in a semirandom manner to create a number of new candidate antenna shapes. These are then evaluated to determine how well they fulfill the design requirements, and a numerical score is computed for each. Then, in a step similar to natural selection, a portion of the candidate antennas with the worst scores are discarded, leaving a smaller population of the highest-scoring designs. Using these antennas, the computer repeats the procedure, generating a successive population (using operators such as mutation, crossover, and selection) from which the higher-scoring designs are selected. After a number of iterations, the population of antennas is evaluated and the highest-scoring design is chosen. The resulting antenna often outperforms the best manual designs, because it has a complicated asymmetric shape that could not have been found with traditional manual design methods.
The first evolved antenna designs appeared in the
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https://en.wikipedia.org/wiki/The%20Secret%20of%20Convict%20Lake
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The Secret of Convict Lake is a 1951 American Western film directed by Michael Gordon and starring Glenn Ford, Gene Tierney, Ethel Barrymore and Zachary Scott. The film was a critical and commercial success. The story is fiction, based on legends of Convict Lake, located in the Sierra Nevada mountain ranges of northern California. and a short story by Anna Hunger and Jack Pollexfen. The film is the final role for Ann Dvorak before her retirement from the screen.
Plot
The film opens with the narrator (Dale Robertson in an early, uncredited role) laying the foundation of the story.
In 1871, six convicts escape from a Carson City prison. One of them freezes to death during a blizzard. The others—Canfield, Greer, Cockerell, Anderson and Maxwell—make it to Lake Monte Diablo, where eight women live in a settlement while their men are away prospecting. Granny is the elder, watching over Marcia, Rachel, Barbara, Susan, Harriet, Mary, and Millie.
Frightened, the women reluctantly permit them to use an empty cabin. Granny hides all the guns except one when they realize that the men are escaped convicts. Canfield has returned here for a reason; the other convicts think that he has money hidden somewhere nearby. Canfield was convicted of killing a mine owner, and $40,000 is missing.
Canfield learns that Marcia, to whom he is attracted, is engaged to be married to a man named Rudy Schaeffer. Canfield claims Rudy took the $40,000 and committed perjury to get Canfield convicted and sent
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https://en.wikipedia.org/wiki/Aleurone
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Aleurone (from Greek aleuron, flour) is a protein found in protein granules of maturing seeds and tubers. The term also describes one of the two major cell types of the endosperm, the aleurone layer. The aleurone layer is the outermost layer of the endosperm, followed by the inner starchy endosperm. This layer of cells is sometimes referred to as the peripheral endosperm. It lies between the pericarp and the hyaline layer of the endosperm. Unlike the cells of the starchy endosperm, aleurone cells remain alive at maturity. The ploidy of the aleurone is (3n) [as a result of double fertilization].
Description
The aleurone layer surrounds the endosperm tissue of grass seeds and is morphologically and biochemically distinct from it. Starchy endosperm cells are large, irregularly shaped cells and contain starch grains while aleurone cells are cuboidal in shape and contain aleurone grains. In most cultivated cereals (wheat species, rye, oats, rice and maize) the aleurone is single-layered, whereas barley has a multicellular aleurone layer. Thick primary cell walls enclose and protect the aleurone cells.
The aleurone layer is important for both the developing seed and the mature plant. The aleurone tissue accumulates large quantities of oils and lipids that are useful during seed development. It is also a site of mineral storage and in some species, functions in seed dormancy. The aleurone may also express several pathogen-protective proteins including PR-4. Aleurone also serves
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https://en.wikipedia.org/wiki/Rankine%20vortex
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The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine.
The vortices observed in nature are usually modelled with an irrotational (potential or free) vortex. However, in potential vortex, the velocity becomes infinite at the vortex center. In reality, very close to the origin, the motion resembles a solid body rotation. The Rankine vortex model assumes a solid-body rotation inside a cylinder of radius and a potential vortex outside the cylinder. The radius is referred to as the vortex-core radius. The velocity components of the Rankine vortex, expressed in terms of the cylindrical-coordinate system are given by
where is the circulation strength of the Rankine vortex. Since solid-body rotation is characterized by an azimuthal velocity , where is the constant angular velocity, one can also use the parameter to characterize the vortex.
The vorticity field associated with the Rankine vortex is
At all points inside the core of the Rankine vortex, the vorticity is uniform at twice the angular velocity of the core; whereas vorticity is zero at all points outside the core because the flow there is irrotational.
In reality, vortex cores are not always circular; and vorticity is not exactly uniform throughout the vortex core.
See also
Kaufmann (Scully) vortex – an alternative mathematical simplification for a vortex, with a smoother transition.
Lamb–Oseen vortex – the exact solut
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https://en.wikipedia.org/wiki/Temporal%20theory%20%28hearing%29
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The temporal theory of hearing, also called frequency theory or timing theory, states that human perception of sound depends on temporal patterns with which neurons respond to sound in the cochlea. Therefore, in this theory, the pitch of a pure tone is determined by the period of neuron firing patterns—either of single neurons, or groups as described by the volley theory. Temporal theory competes with the place theory of hearing, which instead states that pitch is signaled according to the locations of vibrations along the basilar membrane.
Temporal theory was first suggested by August Seebeck.
Description
As the basilar membrane vibrates, each clump of hair cells along its length is deflected in time with the sound components as filtered by basilar membrane tuning for its position. The more intense this vibration is, the more the hair cells are deflected and the more likely they are to cause cochlear nerve firings. Temporal theory supposes that the consistent timing patterns, whether at high or low average firing rate, code for a consistent pitch percept.
High amplitudes
At high sounds levels, nerve fibers whose characteristic frequencies do not exactly match the stimulus still respond, because of the motion induced in larger areas of the basilar membrane by loud sounds. Temporal theory can help explain how we maintain this discrimination. Even when a larger group of nerve fibers are all firing, there is a periodicity to this firing, which corresponds to the periodicity
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https://en.wikipedia.org/wiki/Chromium%28III%29%20fluoride
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Chromium(III) fluoride is an inorganic compound with the chemical formula . It forms several hydrates. The compound is a green crystalline solid that is insoluble in common solvents, but the hydrates (violet) and (green) are soluble in water. The anhydrous form sublimes at 1100–1200 °C.
Structures
Like almost all compounds of chromium(III), these compounds feature octahedral Cr centres. In the anhydrous form, the six coordination sites are occupied by fluoride ligands that bridge to adjacent Cr centres. In the hydrates, some or all of the fluoride ligands are replaced by water.
Production
Chromium(III) fluoride is produced from the reaction of chromium(III) oxide and hydrofluoric acid:
The anhydrous form is produced from hydrogen fluoride and chromic chloride:
Another method of synthesis of involves thermal decomposition of (ammonium hexafluorochromate(III)):
A mixed valence compound (chromium(II,III) fluoride) is also known.
Uses
Chromium(III) fluoride finds some applications as a mordant in textiles and as a corrosion inhibitor. Chromium(III) fluoride catalyzes the fluorination of chlorocarbons by HF.
References
Fluorides
Metal halides
Chromium(III) compounds
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https://en.wikipedia.org/wiki/Daum%20%28studio%29
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Daum is a crystal studio based in Nancy, France, founded in 1878 by Jean Daum (1825–1885). His sons, Auguste Daum (1853–1909) and Antonin Daum (1864–1931), oversaw its growth during the burgeoning Art Nouveau period. Daum is one of the only crystal manufacturers toe employ the pâte de verre (glass paste) process for art glass and crystal sculptures, a technique in which crushed glass is packed into a refractory mould and then fused in a kiln.
History
The Daum family worked at the beginning of the Art Nouveau era and created one of France's most prominent glassworks. Established at the end of the 19th century, Daum’s renown was originally linked to the École de Nancy and the art of pâte-de-cristal, a major contributing factor in terms of its worldwide reputation.
During the Universal Exhibition of 1900 Daum was awarded a ‘Grand Prix’ medal. Daum glass became more elaborate. Acid etching (by Jacques Grüber) was often combined with carving, enamelling, and engraving on a single piece of glass to produce creative glass masterpieces. The most complicated creations also featured applied glass elements, such as handles and ornamental motifs in naturalistic forms. The Daum brothers soon became a major force in the Art Nouveau movement, seriously rivalling Gallé, so much so that when Émile Gallé died in 1904 they became the leaders in the field of decorative glass.
In 1906 Daum revived pâte de verre (glass paste), an ancient Egyptian method of glass casting, developing the metho
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https://en.wikipedia.org/wiki/Parallelizable%20manifold
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In mathematics, a differentiable manifold of dimension n is called parallelizable if there exist smooth vector fields
on the manifold, such that at every point of the tangent vectors
provide a basis of the tangent space at . Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a global section on
A particular choice of such a basis of vector fields on is called a parallelization (or an absolute parallelism) of .
Examples
An example with is the circle: we can take V1 to be the unit tangent vector field, say pointing in the anti-clockwise direction. The torus of dimension is also parallelizable, as can be seen by expressing it as a cartesian product of circles. For example, take and construct a torus from a square of graph paper with opposite edges glued together, to get an idea of the two tangent directions at each point. More generally, every Lie group G is parallelizable, since a basis for the tangent space at the identity element can be moved around by the action of the translation group of G on G (every translation is a diffeomorphism and therefore these translations induce linear isomorphisms between tangent spaces of points in G).
A classical problem was to determine which of the spheres Sn are parallelizable. The zero-dimensional case S0 is trivially parallelizable. The case S1 is the circle, which is parallelizable as has already been explained. The hairy ball theorem shows that S2 is not paral
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https://en.wikipedia.org/wiki/Neurogenic%20inflammation
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Neurogenic inflammation is inflammation arising from the local release by afferent neurons of inflammatory mediators such as Substance P, Calcitonin Gene-Related Peptide (CGRP), neurokinin A (NKA), and endothelin-3 (ET-3). In such neurons, release of these pro-inflammatory mediators is thought to be triggered by the activation of ion channels that are the principal detectors of noxious environmental stimuli. In particular, the heat/capsaicin receptor TRPV1 and the irritant/wasabi receptor TRPA1. TRPA1 channels stimulated by lipopolysaccharide (LPS) may also cause acute neurogenic inflammation.
Once released, these neuropeptides induce the release of histamine from adjacent mast cells. In turn, histamine evokes the release of substance P and calcitonin gene-related peptide; thus, a bidirectional link between histamine and neuropeptides in neurogenic inflammation is established.
Neurogenic inflammation appears to play an important role in the pathogenesis of numerous diseases including migraine, psoriasis, asthma, vasomotor rhinitis, fibromyalgia, eczema, rosacea, dystonia, and multiple chemical sensitivity.
In migraine, stimulation of the trigeminal nerve causes neurogenic inflammation via release of neuropeptides including Substance P, nitric oxide, vasoactive intestinal polypeptide, 5-HT, Neurokinin A and CGRP. leading to a "sterile neurogenic inflammation."
Prevention
Magnesium deficiency causes neurogenic inflammation in a rat model. Researchers have theorized that
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https://en.wikipedia.org/wiki/Sam%20Togwell
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Samuel James Togwell (born 14 October 1984) is an English former professional footballer who plays as a defensive midfielder for club Beaconsfield Town.
He began his career with Crystal Palace in 2002, where he was loaned out to Oxford United, Northampton Town, and Port Vale. In July 2006 he transferred to Barnsley, before he joined Scunthorpe United in August 2008. He helped the "Iron" to win promotion out of the League One play-offs in 2009. He signed with Chesterfield in July 2012, and became a key player in the 2012–13 season. He lost his first team place the following season and was loaned out to Wycombe Wanderers. He helped Chesterfield to win the League Two title in 2013–14. He signed with Barnet in August 2014, and helped the club to the Conference title in the 2014–15 season. He was sold on to Eastleigh in December 2016, before joining Slough Town in June 2018. He retired in May 2021, having made a total of 606 appearances in all competitions, scoring 23 goals. He came out of retirement the following year to play for Beaconsfield Town.
Career
Crystal Palace
Togwell started out in the Crystal Palace youth set-up at the age of ten, before making his senior debut as a seventeen-year-old substitute on 22 December 2002 at Millmoor. Palace beat Rotherham United 3–1, returning to London with three First Division points.
He did not get another game in the 2002–03 or 2003–04 seasons, mainly due to a broken leg he sustained in a reserve team match in February 2003. He ret
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https://en.wikipedia.org/wiki/Jim%20Cannon%20%28footballer%2C%20born%201953%29
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James Cannon (born 2 October 1953) is a Scottish retired footballer.
Along with several other promising young Scottish players he was signed as an apprentice for Crystal Palace in October 1970, by then manager Bert Head, having previously had a trial with Manchester City. He made a goalscoring debut on 31 March 1973 against Chelsea and went on to make 660 appearances for the club, beating Terry Long's record in the 1984–85 season.
A cultured centre half who could also play at left back or in midfield, he eventually left the club at the end of the 1987–88 season (15 seasons after his debut), having been captain for the previous ten seasons, and initially joined Croydon F.C. and then in November 1988, Dartford. He also had a short spell with Bristol Rovers before finishing his football career in 1994 after three seasons at Dulwich Hamlet. In retirement he owned a building company ICS Builders in the Croydon area, and managed Chipstead during the 2003–04 season.
At the start of 2005–06 season onwards, he made a return to Palace, in the hospitality department, hosting the executive boxes at Selhurst Park on matchdays. In 2005, Cannon was voted into Palace's Centenary XI, and was only just pipped to "The Player of The Century" award by Ian Wright. Wright would later claim that Cannon had bullied him and Kung fu kicked him in the back, Cannon disputed that account but admitted to giving Wright “a little slap”.
References
External links
1953 births
Scottish men's footballer
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https://en.wikipedia.org/wiki/Statgraphics
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Statgraphics is a statistics package that performs and explains basic and advanced statistical functions.
History
The software was created in 1980 by Dr. Neil W. Polhemus while on the faculty at the Princeton University School of Engineering and Applied Science for use as a teaching tool for his statistics students. It was made available to the public in 1982, becoming and early example of data science software designed for use on the PC.
Software
The flagship version of Statgraphics is Statgraphics Centurion, a Windows desktop application with capabilities for regression analysis, ANOVA, multivariate statistics, Design of Experiments, statistical process control, life data analysis, machine learning, and data visualization. The data analysis procedures include descriptive statistics, hypothesis testing, regression analysis, analysis of variance, survival analysis, time series analysis and forecasting, sample size determination, multivariate methods, machine learning and Monte Carlo techniques. The SPC menu includes many procedures for quality assessment, capability analysis, control charts, measurement systems analysis, and acceptance sampling. The program also features a DOE Wizard that creates and analyzes statistically designed experiments.
Applications
Statgraphics is frequently used for Six Sigma process improvement. The program has also been used in various health and nutrition-related studies. The software is heavily used in manufacturing chemicals, pharmaceut
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https://en.wikipedia.org/wiki/Crystal%20Warriors
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is a turn-based strategy video game developed and published by Sega for the Game Gear in Japan in 1991 and in Europe and North America in 1992. It was re-released for Virtual Console in 2013. A Japan-only sequel Royal Stone was published in 1995.
Gameplay
The gameplay of Crystal Warriors is similar to both the Fire Emblem and Shining Force series. The player forms a party of up to nine units to fight in each level. The player starts on one side of the map and an enemy force of up to nine units occupies a castle on the opposite side. The player must defeat the enemy force or move a unit on to the enemy castle entrance to complete each level.
Each level has terrain features which form bottlenecks or change the speed of units. The player controls specialized units belonging to a particular elemental group and most of the strategy revolves around the element of a given unit, its speciality and positioning. Each element is weak to one and strong versus another in a rock-paper-scissors system. Fire elemental units are strong against wind elemental units, while wind units are strong against water, and in turn water units are strong against fire. Earth-based units have no particular strengths or weaknesses to other elements. However, with the exception of the Princess(s) and Emperor Jyn the Earth-based units are all mages or healers and have a low base defence, making them vulnerable to combat units, unless they reach level 9 in which case they become the strongest unit in the game
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https://en.wikipedia.org/wiki/Zirconium%20hydride
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Zirconium hydride describes an alloy made by combining zirconium and hydrogen. Hydrogen acts as a hardening agent, preventing dislocations in the zirconium atom crystal lattice from sliding past one another. Varying the amount of hydrogen and the form of its presence in the zirconium hydride (precipitated phase) controls qualities such as the hardness, ductility, and tensile strength of the resulting zirconium hydride. Zirconium hydride with increased hydrogen content can be made harder and stronger than zirconium, but such zirconium hydride is also less ductile than zirconium.
Material properties
Zirconium is found in the Earth's crust only in the form of an ore, usually a zirconium silicate, such as zircon. Zirconium is extracted from zirconium ore by removing the oxygen and silica. This process, known as the Kroll process, was first applied to titanium. The Kroll process results in an alloy containing hafnium. The hafnium and other impurities are removed in a subsequent step. Zirconium hydride is created by combining refined zirconium with hydrogen. Like titanium, solid zirconium dissolves hydrogen quite readily.
The density of zirconium hydride varies based the hydrogen and ranges between 5.56 and 6.52 g cm−3.
Even in the narrow range of concentrations which make up zirconium hydride, mixtures of hydrogen and zirconium can form a number of different structures, with very different properties. Understanding such properties is essential to making quality zirconium hydrid
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https://en.wikipedia.org/wiki/Catabolite%20activator%20protein
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Catabolite activator protein (CAP; also known as cAMP receptor protein, CRP) is a trans-acting transcriptional activator that exists as a homodimer in solution. Each subunit of CAP is composed of a ligand-binding domain at the N-terminus (CAPN, residues 1–138) and a DNA-binding domain at the C-terminus (DBD, residues 139–209). Two cAMP (cyclic AMP) molecules bind dimeric CAP with negative cooperativity. Cyclic AMP functions as an allosteric effector by increasing CAP's affinity for DNA. CAP binds a DNA region upstream from the DNA binding site of RNA Polymerase. CAP activates transcription through protein-protein interactions with the α-subunit of RNA Polymerase. This protein-protein interaction is responsible for (i) catalyzing the formation of the RNAP-promoter closed complex; and (ii) isomerization of the RNAP-promoter complex to the open conformation. CAP's interaction with RNA polymerase causes bending of the DNA near the transcription start site, thus effectively catalyzing the transcription initiation process. CAP's name is derived from its ability to affect transcription of genes involved in many catabolic pathways. For example, when the amount of glucose transported into the cell is low, a cascade of events results in the increase of cytosolic cAMP levels. This increase in cAMP levels is sensed by CAP, which goes on to activate the transcription of many other catabolic genes.
CAP has a characteristic helix-turn-helix motif structure that allows it to bind to success
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https://en.wikipedia.org/wiki/Plate%20heat%20exchanger
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A plate heat exchanger is a type of heat exchanger that uses metal plates to transfer heat between two fluids. This has a major advantage over a conventional heat exchanger in that the fluids are exposed to a much larger surface area because the fluids are spread out over the plates. This facilitates the transfer of heat, and greatly increases the speed of the temperature change. Plate heat exchangers are now common and very small brazed versions are used in the hot-water sections of millions of combination boilers. The high heat transfer efficiency for such a small physical size has increased the domestic hot water (DHW) flowrate of combination boilers. The small plate heat exchanger has made a great impact in domestic heating and hot-water. Larger commercial versions use gaskets between the plates, whereas smaller versions tend to be brazed.
The concept behind a heat exchanger is the use of pipes or other containment vessels to heat or cool one fluid by transferring heat between it and another fluid. In most cases, the exchanger consists of a coiled pipe containing one fluid that passes through a chamber containing another fluid. The walls of the pipe are usually made of metal, or another substance with a high thermal conductivity, to facilitate the interchange, whereas the outer casing of the larger chamber is made of a plastic or coated with thermal insulation, to discourage heat from escaping from the exchanger.
The world's first commercially viable plate heat exch
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https://en.wikipedia.org/wiki/DCDC2
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Doublecortin domain-containing protein 2 is a protein that in humans is encoded by the DCDC2 gene.
Function
This gene encodes a protein with two doublecortin peptide domains. This domain has been demonstrated to bind tubulin and enhance microtubule polymerization.
Clinical significance
Mutations in this gene have been associated with reading disability (RD), also referred to as developmental dyslexia. But this is controverse since a recent study proposed that there is a "low likelihood of a direct deletion effect on reading skills."
Changes in the DCDC2 gene are frequently found among dyslexics. Altered alleles often occur among children with reading and writing difficulties. The gene appears to have a strong linkage with the processing of speech information when writing.
References
Further reading
Dyslexia research
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https://en.wikipedia.org/wiki/Crystal%20violet%20lactone
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Crystal violet lactone (CVL) is a leuco dye, a lactone derivate of crystal violet 10B. In pure state it is a slightly yellowish crystalline powder, soluble in nonpolar or slightly polar organic solvents.
The central carbon in the leuco form is in a tetrahedral configuration, with four covalent bonds.
In an acidic environment, the lactone ring is broken, with the oxygen detaching from the central carbon. This now-trivalent position is a planar carbocation that is resonance stabilized, interconnecting the π systems of the aromatic rings and the amino functional groups. This single large conjugated system is a chromophore with strong absorption in visible spectrum, giving this compound its distinctive color. This chemical is usually drawn in the resonance structure with the cation on nitrogen.
It was the first dye used in carbonless copy papers, and it is still widely used in this application. It is also the leuco dye component in some thermochromic dyes, e.g. in the Hypercolor line of clothing. One of its novel uses is a security marker for fuels.
Its limitations as a fuel marker have to be carefully contemplated by users, as Crystal Violet Lactone (leuco) readily transforms to the colored species in >10% Ethanol Containing Gasoline, imparting a strong color. Crystal violet lactone as a fuel marker was covered by the BASF patent DE4422336A1 until June 2014.
It may cause allergic contact dermatitis in people handling the carbonless copy paper.
References
Triarylmethane dye
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https://en.wikipedia.org/wiki/1%2C4-Benzoquinone
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1,4-Benzoquinone, commonly known as para-quinone, is a chemical compound with the formula C6H4O2. In a pure state, it forms bright-yellow crystals with a characteristic irritating odor, resembling that of chlorine, bleach, and hot plastic or formaldehyde. This six-membered ring compound is the oxidized derivative of 1,4-hydroquinone. The molecule is multifunctional: it exhibits properties of a ketone, being able to form oximes; an oxidant, forming the dihydroxy derivative; and an alkene, undergoing addition reactions, especially those typical for α,β-unsaturated ketones. 1,4-Benzoquinone is sensitive toward both strong mineral acids and alkali, which cause condensation and decomposition of the compound.
Preparation
1,4-Benzoquinone is prepared industrially by oxidation of hydroquinone, which can be obtained by several routes. One route involves oxidation of diisopropylbenzene and the Hock rearrangement. The net reaction can be represented as follows:
C6H4(CHMe2)2 + 3 O2 → C6H4O2 + 2 OCMe2 + H2O
The reaction proceeds via the bis(hydroperoxide) and the hydroquinone. Acetone is a coproduct.
Another major process involves the direct hydroxylation of phenol by acidic hydrogen peroxide:
C6H5OH + H2O2 → C6H4(OH)2 + H2O
Both hydroquinone and catechol are produced. Subsequent oxidation of the hydroquinone gives the quinone.
Quinone was originally prepared industrially by oxidation of aniline, for example by manganese dioxide. This method is mainly practiced in
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https://en.wikipedia.org/wiki/Vector%20calculus%20identities
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The following are important identities involving derivatives and integrals in vector calculus.
Operator notation
Gradient
For a function in three-dimensional Cartesian coordinate variables, the gradient is the vector field:
where i, j, k are the standard unit vectors for the x, y, z-axes. More generally, for a function of n variables , also called a scalar field, the gradient is the vector field:
where are orthogonal unit vectors in arbitrary directions.
As the name implies, the gradient is proportional to and points in the direction of the function's most rapid (positive) change.
For a vector field , also called a tensor field of order 1, the gradient or total derivative is the n × n Jacobian matrix:
For a tensor field of any order k, the gradient is a tensor field of order k + 1.
For a tensor field of order k > 0, the tensor field of order k + 1 is defined by the recursive relation
where is an arbitrary constant vector.
Divergence
In Cartesian coordinates, the divergence of a continuously differentiable vector field is the scalar-valued function:
As the name implies the divergence is a measure of how much vectors are diverging.
The divergence of a tensor field of non-zero order k is written as , a contraction to a tensor field of order k − 1. Specifically, the divergence of a vector is a scalar. The divergence of a higher order tensor field may be found by decomposing the tensor field into a sum of outer products and using the identity,
where is
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https://en.wikipedia.org/wiki/Cobalt%28II%29%20fluoride
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Cobalt(II) fluoride is a chemical compound with the formula (CoF2). It is a pink crystalline solid compound which is antiferromagnetic at low temperatures (TN=37.7 K) The formula is given for both the red tetragonal crystal, (CoF2), and the tetrahydrate red orthogonal crystal, (CoF2·4H2O). CoF2 is used in oxygen-sensitive fields, namely metal production. In low concentrations, it has public health uses.
CoF2 is sparingly soluble in water. The compound can be dissolved in warm mineral acid, and will decompose in boiling water. Yet the hydrate is water-soluble, especially the di-hydrate CoF2·2H2O and tri-hydrate CoF2·3H2O forms of the compound. The hydrate will also decompose with heat.
Like some other metal difluorides, CoF2 crystallizes in the rutile structure, which features octahedral Co centers and planar fluorides.
Preparation
Cobalt(II) fluoride can be prepared from anhydrous cobalt(II) chloride or cobalt(II) oxide in a stream of hydrogen fluoride:
CoCl2 + 2HF → CoF2 + 2HCl
CoO + 2HF → CoF2 + H2O
It is produced in the reaction of cobalt (III) fluoride with water.
The tetrahydrate cobalt(II) fluoride is formed by dissolving cobalt(II) in hydrofluoric acid. The anhydrous fluoride can be extracted from this by dehydration. Other synthesis can occur at higher temperatures. It has been shown that at 500 °C fluorine will combine with cobalt producing a mixture of CoF2 and CoF3.
Uses
Cobalt(II) fluoride can be used as a catalyst to alloy metals. It is also used for
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https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Szekeres%20theorem
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In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 1) + 1 contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s. The proof appeared in the same 1935 paper that mentions the Happy Ending problem.
It is a finitary result that makes precise one of the corollaries of Ramsey's theorem. While Ramsey's theorem makes it easy to prove that every infinite sequence of distinct real numbers contains a monotonically increasing infinite subsequence or a monotonically decreasing infinite subsequence, the result proved by Paul Erdős and George Szekeres goes further.
Example
For r = 3 and s = 2, the formula tells us that any permutation of three numbers has an increasing subsequence of length three or a decreasing subsequence of length two. Among the six permutations of the numbers 1,2,3:
1,2,3 has an increasing subsequence consisting of all three numbers
1,3,2 has a decreasing subsequence 3,2
2,1,3 has a decreasing subsequence 2,1
2,3,1 has two decreasing subsequences, 2,1 and 3,1
3,1,2 has two decreasing subsequences, 3,1 and 3,2
3,2,1 has three decreasing length-2 subsequences, 3,2, 3,1, and 2,1.
Alternative interpretations
Geometric interpretation
One can interpret the positions of the numbers in a sequence as x-coordinates of points in the Euclidean plane, and the numbers themselves as y-coordinates; conversely, for any point s
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