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3,300 | ; Hey, A.J.G. (2004). Gauge Theories in Particle Physics: Non-Abelian Gauge Theories: QCD and electroweak theory. | Field equation | 0.831264 |
3,301 | Course of Theoretical Physics. Vol. 4 (2nd ed.). | Field equation | 0.831264 |
3,302 | Not every partial differential equation (PDE) in physics is automatically called a "field equation", even if fields are involved. They are extra equations to provide additional constraints for a given physical system. "Continuity equations" and "diffusion equations" describe transport phenomena, even though they may in... | Field equation | 0.831264 |
3,303 | Field equations are not ordinary differential equations since a field depends on space and time, which requires at least two variables. Whereas the "wave equation", the "diffusion equation", and the "continuity equation" all have standard forms (and various special cases or generalizations), there is no single, special... | Field equation | 0.831264 |
3,304 | In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, a... | Field equation | 0.831264 |
3,305 | In quantum field theory, particles are described by quantum fields which satisfy the Schrödinger equation. They are also creation and annihilation operators which satisfy commutation relations and are subject to the spin–statistics theorem. Particular cases of relativistic quantum field equations include the Klein–Gord... | Field equation | 0.831264 |
3,306 | G. Woan (2010). The Cambridge Handbook of Physics Formulas. Cambridge University Press. ISBN 978-0-521-57507-2. | Field equation | 0.831264 |
3,307 | Field equations can be classified in many ways: classical or quantum, nonrelativistic or relativistic, according to the spin or mass of the field, and the number of components the field has and how they change under coordinate transformations (e.g. scalar fields, vector fields, tensor fields, spinor fields, twistor fie... | Field equation | 0.831264 |
3,308 | Sexl, R. U.; Urbantke, H. K. (2001) . Relativity, Groups Particles. Special Relativity and Relativistic Symmetry in Field and Particle Physics. Springer. ISBN 978-3211834435. | Field equation | 0.831264 |
3,309 | Microfluidics is the study and design of the control or transport of small volumes of fluid flow through porous material or narrow channels for a variety of applications (e.g. mixing, separations). Capillary pressure is one of many geometry-related characteristics that can be altered in a microfluidic device to optimiz... | Capillary pressure | 0.831262 |
3,310 | The Sequence Read Archive (SRA, previously known as the Short Read Archive) is a bioinformatics database that provides a public repository for DNA sequencing data, especially the "short reads" generated by high-throughput sequencing, which are typically less than 1,000 base pairs in length. The archive is part of the I... | Sequence Read Archive | 0.831246 |
3,311 | In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magnetic charge". Modern interest in the concept stems from particle theories, not... | Magnetic charge | 0.831241 |
3,312 | Systematic exploration of chemical space is possible by creating in silico databases of virtual molecules, which can be visualized by projecting multidimensional property space of molecules in lower dimensions. Generation of chemical spaces may involve creating stoichiometric combinations of electrons and atomic nuclei... | Chemical space | 0.831209 |
3,313 | This number is often misquoted in subsequent publications to be the estimated size of the whole organic chemistry space, which would be much larger if including the halogens and other elements. In addition to the drug-like space and lead-like space that are, in part, defined by the Lipinski's rule of five, the concept ... | Chemical space | 0.831209 |
3,314 | In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of poin... | Homogeneous coordinates | 0.831196 |
3,315 | An autoencoder ANN was used in bioinformatics, to predict gene ontology annotations and gene-function relationships.In medical informatics, deep learning was used to predict sleep quality based on data from wearables and predictions of health complications from electronic health record data. | Deep neural networks | 0.831191 |
3,316 | More specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks. The probabilistic interpretation was introduced by researchers including Hopfield, Widro... | Deep neural networks | 0.831191 |
3,317 | Deep learning has attracted both criticism and comment, in some cases from outside the field of computer science. | Deep neural networks | 0.831191 |
3,318 | A comprehensive list of results on this set is available.Deep learning-based image recognition has become "superhuman", producing more accurate results than human contestants. This first occurred in 2011 in recognition of traffic signs, and in 2014, with recognition of human faces.Deep learning-trained vehicles now int... | Deep neural networks | 0.831191 |
3,319 | Some deep learning architectures display problematic behaviors, such as confidently classifying unrecognizable images as belonging to a familiar category of ordinary images (2014) and misclassifying minuscule perturbations of correctly classified images (2013). Goertzel hypothesized that these behaviors are due to limi... | Deep neural networks | 0.831191 |
3,320 | Image reconstruction is the reconstruction of the underlying images from the image-related measurements. Several works showed the better and superior performance of the deep learning methods compared to analytical methods for various applications, e.g., spectral imaging and ultrasound imaging. | Deep neural networks | 0.831191 |
3,321 | Deep TAMER used deep learning to provide a robot the ability to learn new tasks through observation. Using Deep TAMER, a robot learned a task with a human trainer, watching video streams or observing a human perform a task in-person. The robot later practiced the task with the help of some coaching from the trainer, wh... | Deep neural networks | 0.831191 |
3,322 | In 2017, Covariant.ai was launched, which focuses on integrating deep learning into factories.As of 2008, researchers at The University of Texas at Austin (UT) developed a machine learning framework called Training an Agent Manually via Evaluative Reinforcement, or TAMER, which proposed new methods for robots or comput... | Deep neural networks | 0.831191 |
3,323 | Facebook's AI lab performs tasks such as automatically tagging uploaded pictures with the names of the people in them.Google's DeepMind Technologies developed a system capable of learning how to play Atari video games using only pixels as data input. In 2015 they demonstrated their AlphaGo system, which learned the gam... | Deep neural networks | 0.831191 |
3,324 | Lu et al. proved that if the width of a deep neural network with ReLU activation is strictly larger than the input dimension, then the network can approximate any Lebesgue integrable function; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator. The probab... | Deep neural networks | 0.831191 |
3,325 | Deep neural networks are generally interpreted in terms of the universal approximation theorem or probabilistic inference.The classic universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions. In 1989, the first pro... | Deep neural networks | 0.831191 |
3,326 | One defense is reverse image search, in which a possible fake image is submitted to a site such as TinEye that can then find other instances of it. A refinement is to search using only parts of the image, to identify images from which that piece may have been taken.Another group showed that certain psychedelic spectacl... | Deep neural networks | 0.831191 |
3,327 | As deep learning moves from the lab into the world, research and experience show that artificial neural networks are vulnerable to hacks and deception. By identifying patterns that these systems use to function, attackers can modify inputs to ANNs in such a way that the ANN finds a match that human observers would not ... | Deep neural networks | 0.831191 |
3,328 | The United States Department of Defense applied deep learning to train robots in new tasks through observation. | Deep neural networks | 0.831191 |
3,329 | Neural networks have been used for implementing language models since the early 2000s. LSTM helped to improve machine translation and language modeling.Other key techniques in this field are negative sampling and word embedding. Word embedding, such as word2vec, can be thought of as a representational layer in a deep l... | Deep neural networks | 0.831191 |
3,330 | In theoretical computer science, a pointer machine is an atomistic abstract computational machine model akin to the random-access machine. A pointer algorithm could also be an algorithm restricted to the pointer machine model.Depending on the type, a pointer machine may be called a linking automaton, a KU-machine, an S... | Pointer machine | 0.831185 |
3,331 | In mathematics, in the area of abstract algebra known as group theory, a verbal subgroup is a subgroup of a group that is generated by all elements that can be formed by substituting group elements for variables in a given set of words. For example, given the word xy, the corresponding verbal subgroup is generated by t... | Verbal subgroup | 0.831185 |
3,332 | Lisp and Scheme support anonymous functions using the "lambda" construct, which is a reference to lambda calculus. Clojure supports anonymous functions with the "fn" special form and #() reader syntax. | Function constant | 0.831164 |
3,333 | Decision tree learning uses a decision tree as a predictive model to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modeling approaches used in statistics, data mining, and machine learning. Tree mode... | Machine learning algorithm | 0.831163 |
3,334 | The difference between optimization and machine learning arises from the goal of generalization: while optimization algorithms can minimize the loss on a training set, machine learning is concerned with minimizing the loss on unseen samples. Characterizing the generalization of various learning algorithms is an active ... | Machine learning algorithm | 0.831163 |
3,335 | Machine learning approaches are traditionally divided into three broad categories, which correspond to learning paradigms, depending on the nature of the "signal" or "feedback" available to the learning system: Supervised learning: The computer is presented with example inputs and their desired outputs, given by a "tea... | Machine learning algorithm | 0.831163 |
3,336 | In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be.Leo Breiman distinguished two statistical modeling paradigms: data model and algorithm... | Machine learning algorithm | 0.831163 |
3,337 | Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalizable predictive patterns. According to Michael I. Jordan, the ideas of machine learning, from methodological p... | Machine learning algorithm | 0.831163 |
3,338 | His website includes his College Basketball Ratings, a tempo based statistics system. Some statisticians have become very famous for having successful prediction systems. | Experimental prediction | 0.831162 |
3,339 | Brian Burke, a former Navy fighter pilot turned sports statistician, has published his results of using regression analysis to predict the outcome of NFL games. Ken Pomeroy is widely accepted as a leading authority on college basketball statistics. | Experimental prediction | 0.831162 |
3,340 | When these and/or related, generalized set of regression or machine learning methods are deployed in commercial usage, the field is known as predictive analytics.In many applications, such as time series analysis, it is possible to estimate the models that generate the observations. If models can be expressed as transf... | Experimental prediction | 0.831162 |
3,341 | In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one possible description of statistics is that it provides a means of tran... | Experimental prediction | 0.831162 |
3,342 | The Numbers Game is a reality television infotainment series premiered on April 22, 2013, on National Geographic Channel that explores the numbers and stats in life's major events- birth, death, marriage, money etc. Hosted by data scientist Jake Porway, the show uses data science to unveil hidden numbers through street... | The Numbers Game | 0.831148 |
3,343 | The term "open-notebook science" was first used in 2006 in a blog post by Jean-Claude Bradley, an Associate Professor of Chemistry at Drexel University at the time. Bradley described open-notebook science as follows: ... there is a URL to a laboratory notebook that is freely available and indexed on common search engin... | Open Notebook Science | 0.831122 |
3,344 | A public laboratory notebook makes it convenient to cite the exact instances of experiments used to support arguments in articles. For example, in a paper on the optimization of a Ugi reaction, three different batches of product are used in the characterization and each spectrum references the specific experiment where... | Open Notebook Science | 0.831122 |
3,345 | Junior Physics Lab (307L) at University of New Mexico | Open Notebook Science | 0.831122 |
3,346 | NVIDIA provides an SDK Toolkit for CUDA (Compute Unified Device Architecture) technology that offers both a low and high-level API to the GPU. For their GPUs, AMD offers a similar SDK, called Close to Metal (CTM), which provides a thin hardware interface. PhysX is an example of a physics engine that can use GPGPU based... | Physics engine | 0.831116 |
3,347 | Hardware acceleration for physics processing is now usually provided by graphics processing units that support more general computation, a concept known as general-purpose computing on graphics processing units (GPGPU). AMD and NVIDIA provide support for rigid body dynamics computations on their latest graphics cards. ... | Physics engine | 0.831116 |
3,348 | This requires more accurate physics so that, for example, the momentum of an object can knock over an obstacle or lift a sinking object. Physically-based character animation in the past only used rigid body dynamics because they are faster and easier to calculate, but modern games and movies are starting to use soft bo... | Physics engine | 0.831116 |
3,349 | In most computer games, speed of the processors and gameplay are more important than accuracy of simulation. This leads to designs for physics engines that produce results in real-time but that replicate real world physics only for simple cases and typically with some approximation. More often than not, the simulation ... | Physics engine | 0.831116 |
3,350 | A physics processing unit (PPU) is a dedicated microprocessor designed to handle the calculations of physics, especially in the physics engine of video games. Examples of calculations involving a PPU might include rigid body dynamics, soft body dynamics, collision detection, fluid dynamics, hair and clothing simulation... | Physics engine | 0.831116 |
3,351 | A physics engine is computer software that provides an approximate simulation of certain physical systems, such as rigid body dynamics (including collision detection), soft body dynamics, and fluid dynamics, of use in the domains of computer graphics, video games and film (CGI). Their main uses are in video games (typi... | Physics engine | 0.831116 |
3,352 | Thus, games may put objects to "sleep" by disabling the computation of physics on objects that have not moved a particular distance within a certain amount of time. For example, in the 3D virtual world Second Life, if an object is resting on the floor and the object does not move beyond a minimal distance in about two ... | Physics engine | 0.831116 |
3,353 | In the real world, physics is always active. There is a constant Brownian motion jitter to all particles in our universe as the forces push back and forth against each other. For a game physics engine, such constant active precision is unnecessarily wasting the limited CPU power, which can cause problems such as decrea... | Physics engine | 0.831116 |
3,354 | Phylogenetic profiling is a bioinformatics technique in which the joint presence or joint absence of two traits across large numbers of species is used to infer a meaningful biological connection, such as involvement of two different proteins in the same biological pathway. Along with examination of conserved synteny, ... | Phylogenetic profiling | 0.831116 |
3,355 | Ingestion of saxitoxin, usually through shellfish contaminated by toxic algal blooms, can result in paralytic shellfish poisoning.Saxitoxin has been used in molecular biology to establish the function of the sodium channel. It acts on the voltage-gated sodium channels of nerve cells, preventing normal cellular function... | Cyanobacterial bloom | 0.831102 |
3,356 | In the 1960s through the 1970s, Paul Boyer, a UCLA Professor, developed the binding change, or flip-flop, mechanism theory, which postulated that ATP synthesis is dependent on a conformational change in ATP synthase generated by rotation of the gamma subunit. The research group of John E. Walker, then at the MRC Labora... | ATP synthesis | 0.831088 |
3,357 | More precisely, one should consider algebraic curves C {\displaystyle C} of a given genus g {\displaystyle g} , and their Jacobians Jac ( C ) {\displaystyle \operatorname {Jac} (C)} . There is a moduli space M g {\displaystyle {\mathcal {M}}_{g}} of such curves, and a moduli space of abelian varieties, A g {\displays... | Schottky problem | 0.831076 |
3,358 | In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties. | Schottky problem | 0.831076 |
3,359 | The Faraday constant can be thought of as the conversion factor between the mole (used in chemistry) and the coulomb (used in physics and in practical electrical measurements), and is therefore of particular use in electrochemistry. Because 1 mole contains exactly 6.02214076×1023 entities, and 1 coulomb contains exactl... | Faraday constant | 0.831071 |
3,360 | Modern biotechnology is challenging traditional concepts of organisms and species. Cloning is the process of creating a new multicellular organism, genetically identical to another, with the potential of creating entirely new species of organisms. Cloning is the subject of much ethical debate. | Organism | 0.83107 |
3,361 | Protein A is a 42 kDa surface protein originally found in the cell wall of the bacteria Staphylococcus aureus. It is encoded by the spa gene and its regulation is controlled by DNA topology, cellular osmolarity, and a two-component system called ArlS-ArlR. It has found use in biochemical research because of its ability... | Protein A | 0.831056 |
3,362 | The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function. More precisely, the sample complexity is the number of training-samples that we need to supply to the algorithm, so that the function returned by the algorithm ... | Sample-complexity bounds | 0.831053 |
3,363 | This trade-off leads to the concept of regularization.It is a theorem from VC theory that the following three statements are equivalent for a hypothesis space H {\displaystyle {\mathcal {H}}}: H {\displaystyle {\mathcal {H}}} is PAC-learnable. The VC dimension of H {\displaystyle {\mathcal {H}}} is finite. H {\displays... | Sample-complexity bounds | 0.831053 |
3,364 | One can ask whether there exists a learning algorithm so that the sample complexity is finite in the strong sense, that is, there is a bound on the number of samples needed so that the algorithm can learn any distribution over the input-output space with a specified target error. More formally, one asks whether there e... | Sample-complexity bounds | 0.831053 |
3,365 | Under extremely high pressure, as in the cores of dead stars, ordinary matter undergoes a transition to a series of exotic states of matter collectively known as degenerate matter, which are supported mainly by quantum mechanical effects. In physics, "degenerate" refers to two states that have the same energy and are t... | States of matter | 0.831046 |
3,366 | In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, and some states only exist under extreme conditions, such as Bose–Einstein con... | States of matter | 0.831046 |
3,367 | NMR data HypNMR, WINEQNMR2 Archived 2019-07-14 at the Wayback MachineIn biochemistry, formation constants of adducts may be obtained from Isothermal titration calorimetry (ITC) measurements. This technique yields both the stability constant and the standard enthalpy change for the equilibrium. It is mostly limited, by ... | Formation constant | 0.831034 |
3,368 | In coordination chemistry, a stability constant (also called formation constant or binding constant) is an equilibrium constant for the formation of a complex in solution. It is a measure of the strength of the interaction between the reagents that come together to form the complex. There are two main kinds of complex:... | Formation constant | 0.831034 |
3,369 | Supramolecular complexes are held together by hydrogen bonding, hydrophobic forces, van der Waals forces, π-π interactions, and electrostatic effects, all of which can be described as noncovalent bonding. Applications include molecular recognition, host–guest chemistry and anion sensors. A typical application in molecu... | Formation constant | 0.831034 |
3,370 | Successive stepwise formation constants Kn in a series such as MLn (n = 1, 2, ...) usually decrease as n increases. Exceptions to this rule occur when the geometry of the MLn complexes is not the same for all members of the series. The classic example is the formation of the diamminesilver(I) complex + in aqueous solut... | Formation constant | 0.831034 |
3,371 | Tammann temperature was pioneered by German astronomer, solid-state chemistry, and physics professor Gustav Tammann in the first half of the 20th century. : 152 He had considered a lattice motion very important for the reactivity of matter and quantified his theory by calculating a ratio of the given material temperatu... | Tammann and Hüttig temperatures | 0.831026 |
3,372 | Algorithmic Geometry is a textbook on computational geometry. It was originally written in the French language by Jean-Daniel Boissonnat and Mariette Yvinec, and published as Géometrie algorithmique by Edusciences in 1995. It was translated into English by Hervé Brönnimann, with improvements to some proofs and addition... | Algorithmic Geometry | 0.831003 |
3,373 | The book covers the theoretical background and analysis of algorithms in computational geometry, their implementation details, and their applications. It is grouped into five sections, the first of which covers background material on the design and analysis of algorithms and data structures, including computational com... | Algorithmic Geometry | 0.831003 |
3,374 | The book can be used as a graduate textbook, or as a reference for computational geometry research. Reviewer Peter McMullen calls it "a welcome addition to the shelves of anyone interested in algorithmic geometry". == References == | Algorithmic Geometry | 0.831003 |
3,375 | Structure-Based Assignment (SBA) is a technique to accelerate the resonance assignment which is a key bottleneck of NMR (Nuclear magnetic resonance) structural biology. A homologous (similar) protein is used as a template to the target protein in SBA. This template protein provides prior structural information about th... | Structure-based assignment | 0.830997 |
3,376 | In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. The stack-sortable permutations are exactly the permutations that do not contain the permut... | Stack-sortable permutation | 0.830994 |
3,377 | In non-abelian gauge theories, the beta function can be negative, as first found by Frank Wilczek, David Politzer and David Gross. An example of this is the beta function for quantum chromodynamics (QCD), and as a result the QCD coupling decreases at high energies.Furthermore, the coupling decreases logarithmically, a ... | Strong coupling constant | 0.830972 |
3,378 | A fused multiply–add (FMA or fmadd) is a floating-point multiply–add operation performed in one step (fused operation), with a single rounding. That is, where an unfused multiply–add would compute the product b × c, round it to N significant bits, add the result to a, and round back to N significant bits, a fused multi... | Multiply add | 0.830969 |
3,379 | Protein Data Bank (PDB): repository for protein sequence and structural information UniProt: provides sequence and functional information Structural Classification of Proteins (SCOP Classifications): hierarchical-based approach Class, Architecture, Topology and Homologous superfamily (CATH): hierarchical-based approach | Structural genomics | 0.830968 |
3,380 | The National Standard Examination in Chemistry or NSEC is an examination in chemistry for higher secondary school students in India, usually conducted in the end of November. The examination is organized by the Indian Association of Chemistry Teachers. Over 30,000 students, mainly from Standard 12, sit for this examina... | National Standard Examination in Chemistry | 0.830958 |
3,381 | The NSEC contains only multiple choice questions. The questions include physical chemistry, organic chemistry, and inorganic chemistry. The stress on biochemistry is more in the NSEC than in the typical school syllabi. | National Standard Examination in Chemistry | 0.830958 |
3,382 | The top 1% students from this examination are selected to sit for the Indian National Chemistry Olympiad. The theory part of the examination is held in the last week of January. The top 30 among all students are selected for the Orientation-Cum-Selection-Camp (OCSC), Chemistry. | National Standard Examination in Chemistry | 0.830958 |
3,383 | In the early twentieth century, these ideas led Kristian Birkeland to build a terrella, or laboratory device which simulates the Earth's magnetic field in a vacuum chamber, and which uses a cathode ray tube to simulate the energetic particles which compose the solar wind. A theory began to be formulated about the inter... | Solar-terrestrial physics | 0.830936 |
3,384 | Space physics can be traced to the Chinese who discovered the principle of the compass, but did not understand how it worked. During the 16th century, in De Magnete, William Gilbert gave the first description of the Earth's magnetic field, showing that the Earth itself is a great magnet, which explained why a compass n... | Solar-terrestrial physics | 0.830936 |
3,385 | "Nobody can reproduce these conversations verbatim, but I believe that the spirit of what the people said, and how they did, is conserved," the author tries to explain in the preface. Many believe that the golden years of physics around 1925, when "even small people could do big things" are gone. But the people who had... | Physics and Beyond | 0.830935 |
3,386 | ', 'Yes, I see only whales, but I hope they are only big waves. '", is one of humorous scenes when the author, Bohr and other friends were sailing in a dark night. The book provides a first-hand account about how science is done and how quantum physics, especially the Copenhagen interpretation, emerged. | Physics and Beyond | 0.830935 |
3,387 | With chapters like "The first encounter with the science about atoms", "Quantum mechanics and conversations with Einstein", "Conversation about the relation between biology, physics and chemistry" or "Conversations about language" and "The behavior of an individual during a political disaster", dated 1937–1941, a reade... | Physics and Beyond | 0.830935 |
3,388 | Physics and Beyond (German: Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik) is a book by Werner Heisenberg, the German physicist who discovered the uncertainty principle. It tells, from his point of view, the history of exploring atomic science and quantum mechanics in the first half of the 20th century. A... | Physics and Beyond | 0.830935 |
3,389 | In Galois theory, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q {\displaystyle \mathbb {Q} } . This problem, first posed in the early 19th century, is unsolved. There are some permutation groups for which generic poly... | Inverse Galois problem | 0.830934 |
3,390 | Use the scaling (1 − n)x = ny to get y n − { s ( 1 − n n ) n − 1 } y − { s ( 1 − n n ) n } {\displaystyle y^{n}-\left\{s\left({\frac {1-n}{n}}\right)^{n-1}\right\}y-\left\{s\left({\frac {1-n}{n}}\right)^{n}\right\}} and with t = s ( 1 − n ) n − 1 n n , {\displaystyle t={\frac {s(1-n)^{n-1}}{n^{n}}},} we arrive at: g(y,... | Inverse Galois problem | 0.830934 |
3,391 | By taking appropriate sums of conjugates of μ, following the construction of Gaussian periods, one can find an element α of F that generates F over Q {\displaystyle \mathbb {Q} } , and compute its minimal polynomial. This method can be extended to cover all finite abelian groups, since every such group appears in fact ... | Inverse Galois problem | 0.830934 |
3,392 | It is possible, using classical results, to construct explicitly a polynomial whose Galois group over Q {\displaystyle \mathbb {Q} } is the cyclic group Z/nZ for any positive integer n. To do this, choose a prime p such that p ≡ 1 (mod n); this is possible by Dirichlet's theorem. Let Q(μ) be the cyclotomic extension of... | Inverse Galois problem | 0.830934 |
3,393 | Drugs already on the market, such as heparin, erythropoietin and a few anti-flu drugs, have proven effective and highlight the importance of glycans as a new class of drug. Additionally, the search for new anti-cancer drugs is opening up new possibilities in glycobiology. Anti-cancer drugs with new and varied action me... | Glycobiology | 0.830931 |
3,394 | Defined in the narrowest sense, glycobiology is the study of the structure, biosynthesis, and biology of saccharides (sugar chains or glycans) that are widely distributed in nature. Sugars or saccharides are essential components of all living things and aspects of the various roles they play in biology are researched i... | Glycobiology | 0.830931 |
3,395 | "Glycomics, analogous to genomics and proteomics, is the systematic study of all glycan structures of a given cell type or organism" and is a subset of glycobiology. | Glycobiology | 0.830931 |
3,396 | Glycobiology, in which recent developments have been made possible by the latest technological advances, helps provide a more specific and precise understanding of skin aging. It has now been clearly established that glycans are major constituents of the skin and play a decisive role in skin homeostasis. They play a cr... | Glycobiology | 0.830931 |
3,397 | According to Oxford English Dictionary the specific term glycobiology was coined in 1988 by Prof. Raymond Dwek to recognize the coming together of the traditional disciplines of carbohydrate chemistry and biochemistry. This coming together was as a result of a much greater understanding of the cellular and molecular bi... | Glycobiology | 0.830931 |
3,398 | Once the ore is mined, the metals must be extracted, usually by chemical or electrolytic reduction. Pyrometallurgy uses high temperatures to convert ore into raw metals, while hydrometallurgy employs aqueous chemistry for the same purpose. The methods used depend on the metal and their contaminants. | Metal ions | 0.83092 |
3,399 | The role of metallic elements in the evolution of cell biochemistry has been reviewed, including a detailed section on the role of calcium in redox enzymes.One or more of the elements iron, cobalt, nickel, copper, and zinc are essential to all higher forms of life. Cobalt is an essential component of vitamin B12. Compo... | Metal ions | 0.83092 |
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