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200 | Discrete probability theory deals with events that occur in countable sample spaces. Examples: Throwing dice, experiments with decks of cards, random walk, and tossing coins. Classical definition: Initially the probability of an event to occur was defined as the number of cases favorable for the event, over the number ... | Mathematical probability | 0.855788 |
201 | Common intuition suggests that if a fair coin is tossed many times, then roughly half of the time it will turn up heads, and the other half it will turn up tails. Furthermore, the more often the coin is tossed, the more likely it should be that the ratio of the number of heads to the number of tails will approach unity... | Mathematical probability | 0.855788 |
202 | Calcium ions (Ca2+) contribute to the physiology and biochemistry of organisms' cells. They play an important role in signal transduction pathways, where they act as a second messenger, in neurotransmitter release from neurons, in contraction of all muscle cell types, and in fertilization. Many enzymes require calcium ... | Calcium in biology | 0.855787 |
203 | In 1859, not knowing of Stewarts work, Gustav Robert Kirchhoff reported the coincidence of the wavelengths of spectrally resolved lines of absorption and of emission of visible light. Importantly for thermal physics, he also observed that bright lines or dark lines were apparent depending on the temperature difference ... | Black body spectrum | 0.855762 |
204 | These quanta were called photons and the blackbody cavity was thought of as containing a gas of photons. In addition, it led to the development of quantum probability distributions, called Fermi–Dirac statistics and Bose–Einstein statistics, each applicable to a different class of particles, fermions and bosons. The wa... | Black body spectrum | 0.855762 |
205 | Calculating the blackbody curve was a major challenge in theoretical physics during the late nineteenth century. The problem was solved in 1901 by Max Planck in the formalism now known as Planck's law of blackbody radiation. By making changes to Wien's radiation law (not to be confused with Wien's displacement law) con... | Black body spectrum | 0.855762 |
206 | According to the Classical Theory of Radiation, if each Fourier mode of the equilibrium radiation (in an otherwise empty cavity with perfectly reflective walls) is considered as a degree of freedom capable of exchanging energy, then, according to the equipartition theorem of classical physics, there would be an equal a... | Black body spectrum | 0.855762 |
207 | When flattened to a one-form, A can be decomposed via the Hodge decomposition theorem as the sum of an exact, a coexact, and a harmonic form, A = d α + δ β + γ {\displaystyle A=d\alpha +\delta \beta +\gamma } .There is gauge freedom in A in that of the three forms in this decomposition, only the coexact form has any ef... | Electromagnetic potential | 0.855622 |
208 | Beckmann's version of this story has been widely copied in several books and internet sites, usually without his reservations and sometimes with fanciful embellishments. Several attempts to find corroborating evidence for this story, or even for the existence of Valmes, have failed.The proof that four is the highest de... | Fourth-degree equation | 0.855622 |
209 | Lodovico Ferrari is credited with the discovery of the solution to the quartic in 1540, but since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found, it could not be published immediately. The solution of the quartic was published together with that of the cubic by ... | Fourth-degree equation | 0.855622 |
210 | Bioinformatics tools exist to assist with interpretation of mass spectra (see de novo peptide sequencing), to compare or analyze protein sequences (see sequence analysis), or search databases using peptide or protein sequences (see BLAST). | Protein sequencing | 0.855612 |
211 | To circumvent this problem, Biochemistry Online suggests heating separate samples for different times, analysing each resulting solution, and extrapolating back to zero hydrolysis time. Rastall suggests a variety of reagents to prevent or reduce degradation, such as thiol reagents or phenol to protect tryptophan and ty... | Protein sequencing | 0.855612 |
212 | Though it is now regarded as pseudoscience, belief in a mystical significance of numbers, known as numerology, permeated ancient and medieval thought. Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.Dur... | Numerical value | 0.855394 |
213 | Their study or usage is called arithmetic, a term which may also refer to number theory, the study of the properties of numbers. Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society, the number 13 is often regarded as unlucky, and "a million" may signify... | Numerical value | 0.855394 |
214 | The fundamental theorem of algebra asserts that the complex numbers form an algebraically closed field, meaning that every polynomial with complex coefficients has a root in the complex numbers. Like the reals, the complex numbers form a field, which is complete, but unlike the real numbers, it is not ordered. That is,... | Numerical value | 0.855394 |
215 | Secondary structure prediction is a set of techniques in bioinformatics that aim to predict the local secondary structures of proteins based only on knowledge of their amino acid sequence. For proteins, a prediction consists of assigning regions of the amino acid sequence as likely alpha helices, beta strands (often no... | Protein folding problem | 0.855157 |
216 | These groups can therefore interact in the protein structure. Proteins consist mostly of 20 different types of L-α-amino acids (the proteinogenic amino acids). These can be classified according to the chemistry of the side chain, which also plays an important structural role. | Protein folding problem | 0.855157 |
217 | These methods use rotamer libraries, which are collections of favorable conformations for each residue type in proteins. Rotamer libraries may contain information about the conformation, its frequency, and the standard deviations about mean dihedral angles, which can be used in sampling. Rotamer libraries are derived f... | Protein folding problem | 0.855157 |
218 | Accurate packing of the amino acid side chains represents a separate problem in protein structure prediction. Methods that specifically address the problem of predicting side-chain geometry include dead-end elimination and the self-consistent mean field methods. The side chain conformations with low energy are usually ... | Protein folding problem | 0.855157 |
219 | Ab initio- or de novo- protein modelling methods seek to build three-dimensional protein models "from scratch", i.e., based on physical principles rather than (directly) on previously solved structures. There are many possible procedures that either attempt to mimic protein folding or apply some stochastic method to se... | Protein folding problem | 0.855157 |
220 | As a counter-example, considering the non-square-free n=60, the greatest common divisor of 30 and its complement 2 would be 2, while it should be the bottom element 1. Other examples of Boolean algebras arise from topological spaces: if X is a topological space, then the collection of all subsets of X which are both op... | Boolean algebra (structure) | 0.855125 |
221 | This lattice is a Boolean algebra if and only if n is square-free. The bottom and the top element of this Boolean algebra is the natural number 1 and n, respectively. The complement of a is given by n/a. | Boolean algebra (structure) | 0.855125 |
222 | A truth assignment in propositional calculus is then a Boolean algebra homomorphism from this algebra to the two-element Boolean algebra. Given any linearly ordered set L with a least element, the interval algebra is the smallest algebra of subsets of L containing all of the half-open intervals [a, b) such that a is in... | Boolean algebra (structure) | 0.855125 |
223 | Starting with the propositional calculus with κ sentence symbols, form the Lindenbaum algebra (that is, the set of sentences in the propositional calculus modulo logical equivalence). This construction yields a Boolean algebra. It is in fact the free Boolean algebra on κ generators. | Boolean algebra (structure) | 0.855125 |
224 | This can for example be used to show that the following laws (Consensus theorems) are generally valid in all Boolean algebras: (a ∨ b) ∧ (¬a ∨ c) ∧ (b ∨ c) ≡ (a ∨ b) ∧ (¬a ∨ c) (a ∧ b) ∨ (¬a ∧ c) ∨ (b ∧ c) ≡ (a ∧ b) ∨ (¬a ∧ c)The power set (set of all subsets) of any given nonempty set S forms a Boolean algebra, an alg... | Boolean algebra (structure) | 0.855125 |
225 | The simplest non-trivial Boolean algebra, the two-element Boolean algebra, has only two elements, 0 and 1, and is defined by the rules:It has applications in logic, interpreting 0 as false, 1 as true, ∧ as and, ∨ as or, and ¬ as not. Expressions involving variables and the Boolean operations represent statement forms, ... | Boolean algebra (structure) | 0.855125 |
226 | A filter of the Boolean algebra A is a subset p such that for all x, y in p we have x ∧ y in p and for all a in A we have a ∨ x in p. The dual of a maximal (or prime) ideal in a Boolean algebra is ultrafilter. Ultrafilters can alternatively be described as 2-valued morphisms from A to the two-element Boolean algebra. T... | Boolean algebra (structure) | 0.855125 |
227 | An ideal of the Boolean algebra A is a subset I such that for all x, y in I we have x ∨ y in I and for all a in A we have a ∧ x in I. This notion of ideal coincides with the notion of ring ideal in the Boolean ring A. An ideal I of A is called prime if I ≠ A and if a ∧ b in I always implies a in I or b in I. Furthermor... | Boolean algebra (structure) | 0.855125 |
228 | It follows from the first five pairs of axioms that any complement is unique. The set of axioms is self-dual in the sense that if one exchanges ∨ with ∧ and 0 with 1 in an axiom, the result is again an axiom. Therefore, by applying this operation to a Boolean algebra (or Boolean lattice), one obtains another Boolean al... | Boolean algebra (structure) | 0.855125 |
229 | A Boolean algebra is a set A, equipped with two binary operations ∧ (called "meet" or "and"), ∨ (called "join" or "or"), a unary operation ¬ (called "complement" or "not") and two elements 0 and 1 in A (called "bottom" and "top", or "least" and "greatest" element, also denoted by the symbols ⊥ and ⊤, respectively), suc... | Boolean algebra (structure) | 0.855125 |
230 | In accelerator physics, a kinematically complete experiment is an experiment in which all kinematic parameters of all collision products are determined. If the final state of the collision involves n particles 3n momentum components (3 Cartesian coordinates for each particle) need to be determined. However, these compo... | Kinematically complete experiment | 0.855008 |
231 | As well as discrete metric spaces, there are more general discrete topological spaces, finite metric spaces, finite topological spaces. The time scale calculus is a unification of the theory of difference equations with that of differential equations, which has applications to fields requiring simultaneous modelling of... | Discrete math | 0.854955 |
232 | Many questions and methods concerning differential equations have counterparts for difference equations. For instance, where there are integral transforms in harmonic analysis for studying continuous functions or analogue signals, there are discrete transforms for discrete functions or digital signals. | Discrete math | 0.854955 |
233 | In discrete calculus and the calculus of finite differences, a function defined on an interval of the integers is usually called a sequence. A sequence could be a finite sequence from a data source or an infinite sequence from a discrete dynamical system. Such a discrete function could be defined explicitly by a list (... | Discrete math | 0.854955 |
234 | They can model many types of relations and process dynamics in physical, biological and social systems. In computer science, they can represent networks of communication, data organization, computational devices, the flow of computation, etc. In mathematics, they are useful in geometry and certain parts of topology, e.... | Discrete math | 0.854955 |
235 | Graph theory, the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous... | Discrete math | 0.854955 |
236 | In university curricula, discrete mathematics appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time. The curriculum has thereafter developed in conjunction with efforts by ACM and MAA into a course that is basically intended to develop mathematical matur... | Discrete math | 0.854955 |
237 | Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in appl... | Discrete math | 0.854955 |
238 | However, there is no exact definition of the term "discrete mathematics".The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business... | Discrete math | 0.854955 |
239 | Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, ... | Discrete math | 0.854955 |
240 | Number theory is concerned with the properties of numbers in general, particularly integers. It has applications to cryptography and cryptanalysis, particularly with regard to modular arithmetic, diophantine equations, linear and quadratic congruences, prime numbers and primality testing. Other discrete aspects of numb... | Discrete math | 0.854955 |
241 | Modern Molecular phylogenetics largely ignores morphological characters, relying on DNA sequences as data. Molecular analysis of DNA sequences from most families of flowering plants enabled the Angiosperm Phylogeny Group to publish in 1998 a phylogeny of flowering plants, answering many of the questions about relations... | Plant biology | 0.854866 |
242 | 20th century developments in plant biochemistry have been driven by modern techniques of organic chemical analysis, such as spectroscopy, chromatography and electrophoresis. With the rise of the related molecular-scale biological approaches of molecular biology, genomics, proteomics and metabolomics, the relationship b... | Plant biology | 0.854866 |
243 | Building on the extensive earlier work of Alphonse de Candolle, Nikolai Vavilov (1887–1943) produced accounts of the biogeography, centres of origin, and evolutionary history of economic plants.Particularly since the mid-1960s there have been advances in understanding of the physics of plant physiological processes suc... | Plant biology | 0.854866 |
244 | The discipline of plant ecology was pioneered in the late 19th century by botanists such as Eugenius Warming, who produced the hypothesis that plants form communities, and his mentor and successor Christen C. Raunkiær whose system for describing plant life forms is still in use today. The concept that the composition o... | Plant biology | 0.854866 |
245 | Building upon the gene-chromosome theory of heredity that originated with Gregor Mendel (1822–1884), August Weismann (1834–1914) proved that inheritance only takes place through gametes. No other cells can pass on inherited characters. The work of Katherine Esau (1898–1997) on plant anatomy is still a major foundation ... | Plant biology | 0.854866 |
246 | The single celled green alga Chlamydomonas reinhardtii, while not an embryophyte itself, contains a green-pigmented chloroplast related to that of land plants, making it useful for study. A red alga Cyanidioschyzon merolae has also been used to study some basic chloroplast functions. Spinach, peas, soybeans and a moss ... | Plant biology | 0.854866 |
247 | Model plants such as Arabidopsis thaliana are used for studying the molecular biology of plant cells and the chloroplast. Ideally, these organisms have small genomes that are well known or completely sequenced, small stature and short generation times. Corn has been used to study mechanisms of photosynthesis and phloem... | Plant biology | 0.854866 |
248 | A considerable amount of new knowledge about plant function comes from studies of the molecular genetics of model plants such as the Thale cress, Arabidopsis thaliana, a weedy species in the mustard family (Brassicaceae). The genome or hereditary information contained in the genes of this species is encoded by about 13... | Plant biology | 0.854866 |
249 | The finding in 1939 that plant callus could be maintained in culture containing IAA, followed by the observation in 1947 that it could be induced to form roots and shoots by controlling the concentration of growth hormones were key steps in the development of plant biotechnology and genetic modification. Cytokinins are... | Plant biology | 0.854866 |
250 | Plant responses to climate and other environmental changes can inform our understanding of how these changes affect ecosystem function and productivity. For example, plant phenology can be a useful proxy for temperature in historical climatology, and the biological impact of climate change and global warming. Palynolog... | Plant biology | 0.854866 |
251 | Plant biochemistry is the study of the chemical processes used by plants. Some of these processes are used in their primary metabolism like the photosynthetic Calvin cycle and crassulacean acid metabolism. Others make specialised materials like the cellulose and lignin used to build their bodies, and secondary products... | Plant biology | 0.854866 |
252 | Cell Calcium is a monthly peer-reviewed scientific journal published by Elsevier that covers the field of cell biology and focuses mainly on calcium signalling and metabolism in living organisms. | Cell Calcium | 0.854799 |
253 | In biochemistry, a hypothetical protein is a protein whose existence has been predicted, but for which there is a lack of experimental evidence that it is expressed in vivo. Sequencing of several genomes has resulted in numerous predicted open reading frames to which functions cannot be readily assigned. These proteins... | Hypothetical protein | 0.854764 |
254 | {\displaystyle s.} Since the signatures that arise in algebra often contain only function symbols, a signature with no relation symbols is called an algebraic signature. A structure with such a signature is also called an algebra; this should not be confused with the notion of an algebra over a field. | Structure (mathematical logic) | 0.85465 |
255 | These techniques allowed for the discovery and detailed analysis of many molecules and metabolic pathways of the cell, such as glycolysis and the Krebs cycle (citric acid cycle), and led to an understanding of biochemistry on a molecular level. Another significant historic event in biochemistry is the discovery of the ... | Biochemistry | 0.854551 |
256 | In 1828, Friedrich Wöhler published a paper on his serendipitous urea synthesis from potassium cyanate and ammonium sulfate; some regarded that as a direct overthrow of vitalism and the establishment of organic chemistry. However, the Wöhler synthesis has sparked controversy as some reject the death of vitalism at his ... | Biochemistry | 0.854551 |
257 | In 1877, Felix Hoppe-Seyler used the term (biochemie in German) as a synonym for physiological chemistry in the foreword to the first issue of Zeitschrift für Physiologische Chemie (Journal of Physiological Chemistry) where he argued for the setting up of institutes dedicated to this field of study. The German chemist ... | Biochemistry | 0.854551 |
258 | Some might also point as its beginning to the influential 1842 work by Justus von Liebig, Animal chemistry, or, Organic chemistry in its applications to physiology and pathology, which presented a chemical theory of metabolism, or even earlier to the 18th century studies on fermentation and respiration by Antoine Lavoi... | Biochemistry | 0.854551 |
259 | At its most comprehensive definition, biochemistry can be seen as a study of the components and composition of living things and how they come together to become life. In this sense, the history of biochemistry may therefore go back as far as the ancient Greeks. However, biochemistry as a specific scientific discipline... | Biochemistry | 0.854551 |
260 | The 4 main classes of molecules in biochemistry (often called biomolecules) are carbohydrates, lipids, proteins, and nucleic acids. Many biological molecules are polymers: in this terminology, monomers are relatively small macromolecules that are linked together to create large macromolecules known as polymers. When mo... | Biochemistry | 0.854551 |
261 | Nevertheless, composition of relations and manipulation of the operators according to Schröder rules, provides a calculus to work in the power set of A × B . {\displaystyle A\times B.} In contrast to homogeneous relations, the composition of relations operation is only a partial function. The necessity of matching rang... | Binary relations | 0.854406 |
262 | Developments in algebraic logic have facilitated usage of binary relations. The calculus of relations includes the algebra of sets, extended by composition of relations and the use of converse relations. The inclusion R ⊆ S , {\displaystyle R\subseteq S,} meaning that aRb implies aSb, sets the scene in a lattice of rel... | Binary relations | 0.854406 |
263 | Binary relations have been described through their induced concept lattices: A concept C ⊂ R satisfies two properties: (1) The logical matrix of C is the outer product of logical vectors C i j = u i v j , u , v {\displaystyle C_{ij}\ =\ u_{i}v_{j},\quad u,v} logical vectors. (2) C is maximal, not contained in any other... | Binary relations | 0.854406 |
264 | However, NMR experiments are able to provide information from which a subset of distances between pairs of atoms can be estimated, and the final possible conformations for a protein are determined by solving a distance geometry problem. Dual polarisation interferometry is a quantitative analytical method for measuring ... | Structural proteins | 0.854386 |
265 | A key question in molecular biology is how proteins evolve, i.e. how can mutations (or rather changes in amino acid sequence) lead to new structures and functions? Most amino acids in a protein can be changed without disrupting activity or function, as can be seen from numerous homologous proteins across species (as co... | Structural proteins | 0.854386 |
266 | Circuit theory deals with electrical networks where the fields are largely confined around current carrying conductors. In such circuits, even Maxwell's equations can be dispensed with and simpler formulations used. On the other hand, a quantum treatment of electromagnetism is important in chemistry. Chemical reactions... | Introduction to electromagnetism | 0.854357 |
267 | Classical physics is still an accurate approximation in most situations involving macroscopic objects. With few exceptions, quantum theory is only necessary at the atomic scale and a simpler classical treatment can be applied. Further simplifications of treatment are possible in limited situations. | Introduction to electromagnetism | 0.854357 |
268 | Albert Einstein showed that the magnetic field arises through the relativistic motion of the electric field and thus magnetism is merely a side effect of electricity. The modern theoretical treatment of electromagnetism is as a quantum field in quantum electrodynamics. In many situations of interest to electrical engin... | Introduction to electromagnetism | 0.854357 |
269 | The fundamental law that describes the gravitational force on a massive object in classical physics is Newton's law of gravity. Analogously, Coulomb's law is the fundamental law that describes the force that charged objects exert on one another. It is given by the formula F = k e q 1 q 2 r 2 {\displaystyle F=k_{\text{e... | Introduction to electromagnetism | 0.854357 |
270 | They are needed to convert high voltage mains electricity into low voltage electricity which can be safely used in homes. Maxwell's formulation of the law is given in the Maxwell–Faraday equation—the fourth and final of Maxwell's equations—which states that a time-varying magnetic field produces an electric field. Toge... | Introduction to electromagnetism | 0.854357 |
271 | In physics, fields are entities that interact with matter and can be described mathematically by assigning a value to each point in space and time. Vector fields are fields which are assigned both a numerical value and a direction at each point in space and time. Electric charges produce a vector field called the elect... | Introduction to electromagnetism | 0.854357 |
272 | The discovery that certain toxic chemicals administered in combination can cure certain cancers ranks as one of the greatest in modern medicine. Childhood ALL (Acute Lymphoblastic Leukemia), testicular cancer, and Hodgkins disease, previously universally fatal, are now generally curable diseases. They have also proved ... | Combination chemotherapy | 0.854107 |
273 | Molecular genetics has uncovered signalling networks that regulate cellular activities such as proliferation and survival. In a particular cancer, such a network may be radically altered, due to a chance somatic mutation. Targeted therapy inhibits the metabolic pathway that underlies that type of cancer's cell division... | Combination chemotherapy | 0.854107 |
274 | Binary GCD algorithm: Efficient way of calculating GCD. Booth's multiplication algorithm Chakravala method: a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation Discrete logarithm: Baby-step giant-step Index calculus algorithm Pollard's rho algorithm for logarithms Pohlig–Hellman alg... | Combinatorial algorithms | 0.854075 |
275 | Basic Local Alignment Search Tool also known as BLAST: an algorithm for comparing primary biological sequence information Kabsch algorithm: calculate the optimal alignment of two sets of points in order to compute the root mean squared deviation between two protein structures. Velvet: a set of algorithms manipulating d... | Combinatorial algorithms | 0.854075 |
276 | Closest pair problem: find the pair of points (from a set of points) with the smallest distance between them Collision detection algorithms: check for the collision or intersection of two given solids Cone algorithm: identify surface points Convex hull algorithms: determining the convex hull of a set of points Graham s... | Combinatorial algorithms | 0.854075 |
277 | Clock synchronization Berkeley algorithm Cristian's algorithm Intersection algorithm Marzullo's algorithm Consensus (computer science): agreeing on a single value or history among unreliable processors Chandra–Toueg consensus algorithm Paxos algorithm Raft (computer science) Detection of Process Termination Dijkstra-Sc... | Combinatorial algorithms | 0.854075 |
278 | The nearest neighbour search problem arises in numerous fields of application, including: Pattern recognition – in particular for optical character recognition Statistical classification – see k-nearest neighbor algorithm Computer vision – for point cloud registration Computational geometry – see Closest pair of points... | Nearest neighbor problem | 0.853979 |
279 | In the special case where the data is a dense 3D map of geometric points, the projection geometry of the sensing technique can be used to dramatically simplify the search problem. This approach requires that the 3D data is organized by a projection to a two-dimensional grid and assumes that the data is spatially smooth... | Nearest neighbor problem | 0.853979 |
280 | As an ensemble, the Bayes optimal classifier represents a hypothesis that is not necessarily in H {\displaystyle H} . The hypothesis represented by the Bayes optimal classifier, however, is the optimal hypothesis in ensemble space (the space of all possible ensembles consisting only of hypotheses in H {\displaystyle H}... | Ensemble Methods | 0.853971 |
281 | While speech recognition is mainly based on deep learning because most of the industry players in this field like Google, Microsoft and IBM reveal that the core technology of their speech recognition is based on this approach, speech-based emotion recognition can also have a satisfactory performance with ensemble learn... | Ensemble Methods | 0.853971 |
282 | The content within the book is written using a question and answer format. It contains some 250 questions, which The Science Teacher states each are answered with a "concise and well-formulated essay that is informative and readable." The Science Teacher review goes on to state that many of the answers given in the boo... | A Question and Answer Guide to Astronomy | 0.853933 |
283 | A Question and Answer Guide to Astronomy is a book about astronomy and cosmology, and is intended for a general audience. The book was written by Pierre-Yves Bely, Carol Christian, and Jean-Rene Roy, and published in English by Cambridge University Press in 2010. It was originally written in French. | A Question and Answer Guide to Astronomy | 0.853933 |
284 | The degree can be used to generalize Bézout's theorem in an expected way to intersections of n hypersurfaces in Pn. == Notes == | Degree (algebraic geometry) | 0.853915 |
285 | A generalization of Bézout's theorem asserts that, if an intersection of n projective hypersurfaces has codimension n, then the degree of the intersection is the product of the degrees of the hypersurfaces. The degree of a projective variety is the evaluation at 1 of the numerator of the Hilbert series of its coordinat... | Degree (algebraic geometry) | 0.853915 |
286 | This is a generalization of Bézout's theorem (For a proof, see Hilbert series and Hilbert polynomial § Degree of a projective variety and Bézout's theorem). The degree is not an intrinsic property of the variety, as it depends on a specific embedding of the variety in an affine or projective space. The degree of a hype... | Degree (algebraic geometry) | 0.853915 |
287 | In mathematics, the degree of an affine or projective variety of dimension n is the number of intersection points of the variety with n hyperplanes in general position. For an algebraic set, the intersection points must be counted with their intersection multiplicity, because of the possibility of multiple components. ... | Degree (algebraic geometry) | 0.853915 |
288 | Actin was first observed experimentally in 1887 by W.D. Halliburton, who extracted a protein from muscle that 'coagulated' preparations of myosin that he called "myosin-ferment". However, Halliburton was unable to further refine his findings, and the discovery of actin is credited instead to Brunó Ferenc Straub, a youn... | F actin | 0.853902 |
289 | It is possible that actin could be applied to nanotechnology as its dynamic ability has been harnessed in a number of experiments including those carried out in acellular systems. The underlying idea is to use the microfilaments as tracks to guide molecular motors that can transport a given load. That is actin could be... | F actin | 0.853902 |
290 | Actin is used in scientific and technological laboratories as a track for molecular motors such as myosin (either in muscle tissue or outside it) and as a necessary component for cellular functioning. It can also be used as a diagnostic tool, as several of its anomalous variants are related to the appearance of specifi... | F actin | 0.853902 |
291 | Actin can spontaneously acquire a large part of its tertiary structure. However, the way it acquires its fully functional form from its newly synthesized native form is special and almost unique in protein chemistry. The reason for this special route could be the need to avoid the presence of incorrectly folded actin m... | F actin | 0.853902 |
292 | A number of natural toxins that interfere with actin's dynamics are widely used in research to study actin's role in biology. Latrunculin – a toxin produced by sponges – binds to G-actin preventing it from joining microfilaments. Cytochalasin D – produced by certain fungi – serves as a capping factor, binding to the (+... | F actin | 0.853902 |
293 | For example, in medicine it can be used to identify, diagnose and potentially develop treatments for genetic diseases. Similarly, research into pathogens may lead to treatments for contagious diseases. Biotechnology is a burgeoning discipline, with the potential for many useful products and services. | Nucleic acid sequence | 0.853895 |
294 | The electric field strength at a specific point can be determined from the power delivered to the transmitting antenna, its geometry and radiation resistance. Consider the case of a center-fed half-wave dipole antenna in free space, where the total length L is equal to one half wavelength (λ/2). If constructed from thi... | Electric field strength | 0.853894 |
295 | Given any field extension L/K, we can consider its automorphism group Aut(L/K), consisting of all field automorphisms α: L → L with α(x) = x for all x in K. When the extension is Galois this automorphism group is called the Galois group of the extension. Extensions whose Galois group is abelian are called abelian exten... | Degree (field theory) | 0.853858 |
296 | An algebraic extension L/K is called normal if every irreducible polynomial in K that has a root in L completely factors into linear factors over L. Every algebraic extension F/K admits a normal closure L, which is an extension field of F such that L/K is normal and which is minimal with this property. An algebraic ext... | Degree (field theory) | 0.853858 |
297 | Given a field extension, one can "extend scalars" on associated algebraic objects. For example, given a real vector space, one can produce a complex vector space via complexification. In addition to vector spaces, one can perform extension of scalars for associative algebras defined over the field, such as polynomials ... | Degree (field theory) | 0.853857 |
298 | This is the topic of the scientific field of structural biology, which employs techniques such as X-ray crystallography, NMR spectroscopy, cryo-electron microscopy (cryo-EM) and dual polarisation interferometry, to determine the structure of proteins. Protein structures range in size from tens to several thousand amino... | Protein Structure | 0.853837 |
299 | Testosterone was identified as 17β-hydroxyandrost-4-en-3-one (C19H28O2), a solid polycyclic alcohol with a hydroxyl group at the 17th carbon atom. This also made it obvious that additional modifications on the synthesized testosterone could be made, i.e., esterification and alkylation. The partial synthesis in the 1930... | Testosterone | 0.853807 |
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