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12,500 | Knowledge retrieval can draw results from the following related theories and technologies: Theory of knowledge: knowledge acquisition, knowledge organization, knowledge representation, knowledge validation, knowledge management. Cognitive science: cognitive psychology, cognitive neuroscience, cognitive informatics, con... | Knowledge retrieval | 0.816952 |
12,501 | In the field of retrieval systems, established approaches include: Data retrieval systems, such as database management systems, are well suitable for the storage and retrieval of structured data. Information retrieval systems, such as web search engines, are very effective in finding the relevant documents or web pages... | Knowledge retrieval | 0.816952 |
12,502 | The composition f {\displaystyle f} of H {\displaystyle H} and g {\displaystyle g} is a continuous function mapping the Cantor set onto the entire unit square. (Alternatively, we could use the theorem that every compact metric space is a continuous image of the Cantor set to get the function f {\displaystyle f} .) Fina... | Plane-filling curve | 0.816951 |
12,503 | The commutation relations of creation and annihilation operators in a multiple-boson system are, where {\displaystyle } is the commutator and δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. For fermions, the commutator is replaced by the anticommutator { ⋅ , ⋅ } {\displaystyle \{\cdot ,\cdot \}} , Therefore... | Creation and annihilation operator | 0.81695 |
12,504 | In common usage, "environmental science" and "ecology" are often used interchangeably, but technically, ecology refers only to the study of organisms and their interactions with each other as well as how they interrelate with environment. Ecology could be considered a subset of environmental science, which also could i... | Environmental Biology | 0.816949 |
12,505 | The resulting digital imagery is used to create increasingly accurate models of environmental processes, climate change, and much more. Advancements to remote sensing technology are particularly useful in locating the nonpoint sources of pollution and analyzing ecosystem health through image analysis across the electro... | Environmental Biology | 0.816949 |
12,506 | Another technological development, blockchain technology, monitors and regulates global fisheries. By tracking the path of fish through global markets, environmental scientists can observe whether certain species are being overharvested to the point of extinction. Additionally, remote sensing allows for the detection o... | Environmental Biology | 0.816949 |
12,507 | The algorithm has been criticized for presenting biased or inaccurate information, usually because of sourcing information from websites with high search engine optimization. It had been noted in 2014 that while there was a Knowledge Graph for most major historical or pseudo-historical religious figures such as Moses, ... | Knowledge Graph | 0.816949 |
12,508 | Eskergian believed this book serves as a bridge to modern physics.Writing for The Mathematical Gazette on the first edition, L. Rosenhead congratulated Goldstein for a lucid account of classical mechanics leading to modern theoretical physics, which he believed would stand the test of time alongside acknowledged classi... | Classical Mechanics (Goldstein) | 0.816941 |
12,509 | Scattering is treated in the same chapter as central forces and the two-body problem. Unlike most other books on mechanics, this one elaborates upon the virial theorem. The discussion of canonical and contact transformations, the Hamilton-Jacobi theory, and action-angle coordinates is followed by a presentation of geom... | Classical Mechanics (Goldstein) | 0.816941 |
12,510 | Quimby pointed out that although this book is suitable for students preparing for quantum mechanics, it is not helpful for those interested in analytical mechanics because its treatment omits too much. Quimby praised the quality of printing and binding which make the book attractive.In the Journal of the Franklin Insti... | Classical Mechanics (Goldstein) | 0.816941 |
12,511 | S.L. Quimby of Columbia University noted that the first half of the first edition of the book is dedicated to the development of Lagrangian mechanics with the treatment of velocity-dependent potentials, which are important in electromagnetism, and the use of the Cayley-Klein parameters and matrix algebra for rigid-body... | Classical Mechanics (Goldstein) | 0.816941 |
12,512 | There is an appendix on group theory. New to the third edition include a chapter on nonlinear dynamics and chaos, a section on the exact solutions to the three-body problem obtained by Euler and Lagrange, a discussion of the damped driven pendulum that explains the Josephson junctions. This is counterbalanced by the re... | Classical Mechanics (Goldstein) | 0.816941 |
12,513 | In multivariate statistics, if ε {\displaystyle \varepsilon } is a vector of n {\displaystyle n} random variables, and Λ {\displaystyle \Lambda } is an n {\displaystyle n} -dimensional symmetric matrix, then the scalar quantity ε T Λ ε {\displaystyle \varepsilon ^{T}\Lambda \varepsilon } is known as a quadratic form in... | Quadratic form (statistics) | 0.816941 |
12,514 | Twersky said that Goldstein's Classical Mechanics is more suitable for physicists compared to the much older treatise Analytical Dynamics by E.T. Whittaker, which he deemed more appropriate for mathematicians.E. W. Banhagel, an instructor from Detroit, Michigan, observed that despite requiring no more than multivariabl... | Classical Mechanics (Goldstein) | 0.81694 |
12,515 | Concerning the second printing of the first edition, Vic Twersky of the Mathematical Research Group at New York University considered the book to be of pedagogical merit because it explains things in a clear and simple manner, and its humor is not forced. Published in the 1950s, this book replaced the outdated and frag... | Classical Mechanics (Goldstein) | 0.81694 |
12,516 | In all, Addison believed that this book remains a classic text on the eighteenth- and nineteenth-century approaches to theoretical mechanics; those interested in a more modern approach – expressed in the language of differential geometry and Lie groups – should refer to Mathematical Methods of Classical Mechanics by Vl... | Classical Mechanics (Goldstein) | 0.81694 |
12,517 | Stephen R. Addison from the University of Central Arkansas commented that while the first edition of Classical Mechanics was essentially a treatise with exercises, the third has become less scholarly and more of a textbook. This book is most useful for students who are interested in learning the necessary material in p... | Classical Mechanics (Goldstein) | 0.81694 |
12,518 | In the second edition, Goldstein corrected all the errors that had been pointed out, added a new chapter on perturbation theory, a new section on Bertrand's theorem, and another on Noether's theorem. Other arguments and proofs were simplified and supplemented.Before the death of its primary author in 2005, a new (third... | Classical Mechanics (Goldstein) | 0.81694 |
12,519 | While trigonometry and exponential functions were systematized and unified by the eighteenth century, the search for a complete and unified theory of special functions has continued since the nineteenth century. The high point of special function theory in 1800–1900 was the theory of elliptic functions; treatises that ... | Special functions | 0.816938 |
12,520 | In number theory, certain special functions have traditionally been studied, such as particular Dirichlet series and modular forms. Almost all aspects of special function theory are reflected there, as well as some new ones, such as came out of the monstrous moonshine theory. | Special functions | 0.816938 |
12,521 | Many special functions appear as solutions of differential equations or integrals of elementary functions. Therefore, tables of integrals usually include descriptions of special functions, and tables of special functions include most important integrals; at least, the integral representation of special functions. Becau... | Special functions | 0.816938 |
12,522 | In order to analyse the length and strength of various interactions within the molecule, Richard Bader's "Atoms in molecules" theorem may be applied. Due to the complex description of the electron field provided by this aspherical model, it becomes possible to establish realistic bond paths between interacting atoms as... | Multipole density formalism | 0.816938 |
12,523 | The result of scientific investigation into these causes can lead to one of two insights into the underlying biology: Homology - the structure is similar between the two species because of shared ancestry and common genetics. Convergence - the structure is similar between the two species because of independent adaptati... | Plant morphology | 0.816937 |
12,524 | A plant morphologist makes comparisons between structures in many different plants of the same or different species. Making such comparisons between similar structures in different plants tackles the question of why the structures are similar. It is quite likely that similar underlying causes of genetics, physiology, o... | Plant morphology | 0.816937 |
12,525 | Thus, the structure/process dichotomy is overcome by "an enlargement of our concept of 'structure' so as to include and recognise that in the living organism it is not merely a question of spatial structure with an 'activity' as something over or against it, but that the concrete organism is a spatio-temporal structure... | Plant morphology | 0.816937 |
12,526 | Rutishauser and Isler emphasised that this approach is not only supported by many morphological data but also by evidence from molecular genetics. More recent evidence from molecular genetics provides further support for continuum morphology. James (2009) concluded that "it is now widely accepted that... radiality and... | Plant morphology | 0.816937 |
12,527 | Phytomorphology is the study of the physical form and external structure of plants. This is usually considered distinct from plant anatomy, which is the study of the internal structure of plants, especially at the microscopic level. Plant morphology is useful in the visual identification of plants. Recent studies in mo... | Plant morphology | 0.816937 |
12,528 | It is a well illustrated volume of 1305 pages in a very large format that presents a wealth of morphological data. Unfortunately, all of these data are only interpreted in terms of classical morphology and the qualitative homology concept, disregarding modern conceptional innovations. Including continuum and process mo... | Plant morphology | 0.816937 |
12,529 | The partial trace generalizes to operators on infinite dimensional Hilbert spaces. Suppose V, W are Hilbert spaces, and let { f i } i ∈ I {\displaystyle \{f_{i}\}_{i\in I}} be an orthonormal basis for W. Now there is an isometric isomorphism ⨁ ℓ ∈ I ( V ⊗ C f ℓ ) → V ⊗ W {\displaystyle \bigoplus _{\ell \in I}(V\otimes ... | Partial trace | 0.816936 |
12,530 | The partial trace map as given above induces a dual map Tr B ∗ {\displaystyle \operatorname {Tr} _{B}^{*}} between the C*-algebras of bounded operators on H A {\displaystyle \;H_{A}} and H A ⊗ H B {\displaystyle H_{A}\otimes H_{B}} given by Tr B ∗ ( A ) = A ⊗ I . {\displaystyle \operatorname {Tr} _{B}^{*}(A)=A\otimes... | Partial trace | 0.816936 |
12,531 | Let M be an observable on the subsystem A, then the corresponding observable on the composite system is M ⊗ I {\displaystyle M\otimes I} . However one chooses to define a reduced state ρ A {\displaystyle \rho ^{A}} , there should be consistency of measurement statistics. The expectation value of M after the subsystem A... | Partial trace | 0.816936 |
12,532 | In the case of finite dimensional Hilbert spaces, there is a useful way of looking at partial trace involving integration with respect to a suitably normalized Haar measure μ over the unitary group U(W) of W. Suitably normalized means that μ is taken to be a measure with total mass dim(W). Theorem. Suppose V, W are fin... | Partial trace | 0.816936 |
12,533 | In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement... | Partial trace | 0.816936 |
12,534 | Suppose instead of quantum mechanical systems, the two systems A and B are classical. The space of observables for each system are then abelian C*-algebras. These are of the form C(X) and C(Y) respectively for compact spaces X, Y. The state space of the composite system is simply C ( X ) ⊗ C ( Y ) = C ( X × Y ) . {\dis... | Partial trace | 0.816936 |
12,535 | Many concepts of Riemannian geometry can be applied. There is only one obvious notion of parallel transport and only one natural connection. The concept of holonomy is strikingly simple in this case. The restricted holonomy group is trivial, and so there is a homomorphism from the fundamental group onto the holonomy gr... | Polyhedral space | 0.816935 |
12,536 | In statistics, a unit of observation is the unit described by the data that one analyzes. A study may treat groups as a unit of observation with a country as the unit of analysis, drawing conclusions on group characteristics from data collected at the national level. For example, in a study of the demand for money, the... | Data points | 0.816935 |
12,537 | In software engineering and programming language theory, the abstraction principle (or the principle of abstraction) is a basic dictum that aims to reduce duplication of information in a program (usually with emphasis on code duplication) whenever practical by making use of abstractions provided by the programming lang... | Abstraction principle (computer programming) | 0.816933 |
12,538 | The company sells microturbine generators for electrical power generation, cogeneration, biogas-fueled renewable energy, and hybrid vehicle power. Capstone offers microturbines with output power ratings ranging from 30 to 1,000 kW (40 to 1,341 hp). Multiple turbines can be combined with Capstone's Advanced Power Server... | Capstone Turbine | 0.816933 |
12,539 | NAE3SAT remains NP-complete when all clauses are monotone (meaning that variables are never negated), by Schaefer's dichotomy theorem. Monotone NAE3SAT can also be interpreted as an instance of the set splitting problem, or as a generalization of graph bipartiteness testing to 3-uniform hypergraphs: it asks whether the... | Not-all-equal 3-satisfiability | 0.816933 |
12,540 | The rise of Systems Biology, seeking to comprehend biological processes as a whole, highlighted the need to not only develop corresponding quantitative models, but also to create standards allowing their exchange and integration. This concern drove the community to design common data formats, such as SBML and CellML. S... | Systems Biology Ontology | 0.81693 |
12,541 | The Systems Biology Pathway Exchange (SBPAX) allows SBO terms to be added to Biological Pathway Exchange (BioPAX). This links BioPAX to information useful for modelling, especially by adding quantitative descriptions described by SBO. | Systems Biology Ontology | 0.81693 |
12,542 | The Systems Biology Ontology (SBO) is a set of controlled, relational vocabularies of terms commonly used in systems biology, and in particular in computational modeling. | Systems Biology Ontology | 0.81693 |
12,543 | Since Level 2 Version 2 SBML provides a mechanism to annotate model components with SBO terms, therefore increasing the semantics of the model beyond the sole topology of interaction and mathematical expression. Modelling tools such as SBMLsqueezer interpret SBO terms to augment the mathematics in the SBML file. Simula... | Systems Biology Ontology | 0.81693 |
12,544 | SBO is built in collaboration by the Computational Neurobiology Group (Nicolas Le Novère, EMBL-EBI, United-Kingdom) and the SBMLTeam (Michael Hucka, Caltech, USA). | Systems Biology Ontology | 0.81693 |
12,545 | SBO has benefited from the funds of the European Molecular Biology Laboratory and the National Institute of General Medical Sciences. | Systems Biology Ontology | 0.81693 |
12,546 | To curate and maintain SBO, a dedicated resource has been developed and the public interface of the SBO browser can be accessed at http://www.ebi.ac.uk/sbo. A relational database management system (MySQL) at the back-end is accessed through a web interface based on Java Server Pages (JSP) and JavaBeans. Its content is ... | Systems Biology Ontology | 0.81693 |
12,547 | SBO is an attempt to provide the means of annotating models with terms that indicate the intended semantics of an important subset of models in common use in computational systems biology. The development of SBO was first discussed at the 9th SBML Forum Meeting in Heidelberg Oct. | Systems Biology Ontology | 0.81693 |
12,548 | The computational complexity of the problem is a subject of research in computer science. For unbounded polyhedra, the problem is known to be NP-hard, more precisely, there is no algorithm that runs in polynomial time in the combined input-output size, unless P=NP.A 1992 article by David Avis and Komei Fukuda presents ... | Vertex enumeration problem | 0.816929 |
12,549 | In mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the object's vertices given some formal representation of the object. A classical example is the problem of enumeration of the... | Vertex enumeration problem | 0.816929 |
12,550 | The library’s approximately 2,400 books, 750 dissertations, and 12,000 articles comprise the world’s largest collection of writings in the Whiteheadian-Hartshornean tradition of process thought. The library has thematic bibliographies to guide researchers to process scholarship in over 300 areas, such as aesthetics, bi... | Process Studies | 0.816928 |
12,551 | The Center organizes conferences, seminars, and lectures on topics ranging from physics, education, and ecology to Buddhist and Chinese philosophy; from gender, race, poverty, and human rights to hermeneutics and transpersonal psychology. These conferences are a central part of CPS's work as they demonstrate the releva... | Process Studies | 0.816928 |
12,552 | It seeks to offer an approach to the social, political, and economic order that brings issues of human justice together with a concern for ecology. Its range of interests also includes scientific, philosophical, multicultural, feminist, interreligious, political, and economic concerns; with a strong focus on ecology an... | Process Studies | 0.816928 |
12,553 | In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have th... | Mass properties | 0.816926 |
12,554 | Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless di... | Mass properties | 0.816926 |
12,555 | The two are related by the following equation: m r e l a t i v e = γ ( m r e s t ) {\displaystyle m_{\mathrm {relative} }=\gamma (m_{\mathrm {rest} })\!} where γ {\displaystyle \gamma } is the Lorentz factor: γ = 1 1 − v 2 / c 2 {\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}} The invariant mass of systems is... | Mass properties | 0.816926 |
12,556 | Statistics can help collecting empiric data of player behavior, success rates, etc., to identify unbalanced areas and make corrections. Ideally, a game gathers this data automatically. Statistics can only support a designers‘ abilities and intuition and are therefore only one part of making design decisions, together w... | Game balance | 0.816923 |
12,557 | Some obvious problems become clear through sheer observation of the game and player behavior. This includes mathematical superiority of game elements or strategies but also extremely high or low usage of those. In any case, statistics do not necessarily represent causalities and that there are typically multiple factor... | Game balance | 0.816923 |
12,558 | Biological computers use biologically derived molecules — such as DNA and/or proteins — to perform digital or real computations. The development of biocomputers has been made possible by the expanding new science of nanobiotechnology. The term nanobiotechnology can be defined in multiple ways; in a more general sense, ... | Biomolecular computing | 0.816916 |
12,559 | Thus, implementing nanobiotechnology to design and produce synthetically designed proteins—as well as the design and synthesis of artificial DNA molecules—can allow the construction of functional biocomputers (e.g. Computational Genes). Biocomputers can also be designed with cells as their basic components. Chemically ... | Biomolecular computing | 0.816916 |
12,560 | The behavior of biologically derived computational systems such as these relies on the particular molecules that make up the system, which are primarily proteins but may also include DNA molecules. Nanobiotechnology provides the means to synthesize the multiple chemical components necessary to create such a system. The... | Biomolecular computing | 0.816916 |
12,561 | Some problems which do not have a PTAS may admit a randomized algorithm with similar properties, a polynomial-time randomized approximation scheme or PRAS. A PRAS is an algorithm which takes an instance of an optimization or counting problem and a parameter ε > 0 and, in polynomial time, produces a solution that has a ... | Fully polynomial-time randomized approximation scheme | 0.816916 |
12,562 | In mathematics, the plus sign "+" almost invariably indicates an operation that satisfies the axioms assigned to addition in the type of algebraic structure that is known as a field. For boolean algebra, this means that the logical operation signified by "+" is not the same as the inclusive disjunction signified by "∨"... | Logical equality | 0.816911 |
12,563 | Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional arguments have the same logical value, and false if they are different. It is customary practice in various application... | Logical equality | 0.816911 |
12,564 | In quantum mechanics, there is a distinction between an elementary particle (also called "point particle") and a composite particle. An elementary particle, such as an electron, quark, or photon, is a particle with no known internal structure. Whereas a composite particle, such as a proton or neutron, has an internal s... | Point charge | 0.816903 |
12,565 | The third chapter brings in more modern concepts of algebraic geometry including the degree and genus of an algebraic curve, and rational mappings and birational equivalences between curves.Chapters four and five concern conic sections, and the theorem that when a conic has at least one rational point it has infinitely... | Diophantus and Diophantine Equations | 0.816903 |
12,566 | In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation (dispersion) of a given data set. Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total variation is called unexplain... | Explained variance | 0.816903 |
12,567 | This timeline of chemistry lists important works, discoveries, ideas, inventions, and experiments that significantly changed humanity's understanding of the modern science known as chemistry, defined as the scientific study of the composition of matter and of its interactions. Known as "the central science", the study ... | Timeline of chemistry | 0.816902 |
12,568 | These would later be named protons.1893 Alfred Werner discovers the octahedral structure of cobalt complexes, thus establishing the field of coordination chemistry.1894–1898 William Ramsay discovers the noble gases, which fill a large and unexpected gap in the periodic table and led to models of chemical bonding.1897 J... | Timeline of chemistry | 0.816902 |
12,569 | key structure in many biomolecules, which he later synthesized in 1898. Also begins work on the chemistry of glucose and related sugars.1884 Henry Louis Le Chatelier develops Le Chatelier's principle, which explains the response of dynamic chemical equilibria to external stresses.1885 Eugen Goldstein names the cathode ... | Timeline of chemistry | 0.816902 |
12,570 | This discovery formed the foundation of the modern plastics industry.1862 Alexandre-Emile Béguyer de Chancourtois publishes the telluric helix, an early, three-dimensional version of the periodic table of the elements.1864 John Newlands proposes the law of octaves, a precursor to the periodic law.1864 Lothar Meyer deve... | Timeline of chemistry | 0.816902 |
12,571 | 1310 Pseudo-Geber, an anonymous alchemist who wrote under the name of Geber (i.e., Jābir ibn Hayyān, see above), publishes the Summa perfectionis magisterii. This work contains experimental demonstrations of the corpuscular nature of matter that would still be used by seventeenth-century chemists such as Daniel Sennert... | Timeline of chemistry | 0.816902 |
12,572 | 360 BC Plato coins term ‘elements’ (stoicheia) and in his dialogue Timaeus, which includes a discussion of the composition of inorganic and organic bodies and is a rudimentary treatise on chemistry, assumes that the minute particle of each element had a special geometric shape: tetrahedron (fire), octahedron (air), ico... | Timeline of chemistry | 0.816902 |
12,573 | Prior to the acceptance of the scientific method and its application to the field of chemistry, it is somewhat controversial to consider many of the people listed below as "chemists" in the modern sense of the word. However, the ideas of certain great thinkers, either for their prescience, or for their wide and long-te... | Timeline of chemistry | 0.816902 |
12,574 | The Goldschmidt method can be used with factors that allow simplifications by the binomial theorem. Assume N / D {\displaystyle N/D} has been scaled by a power of two such that D ∈ ( 1 2 , 1 ] {\displaystyle D\in \left({\tfrac {1}{2}},1\right]} . We choose D = 1 − x {\displaystyle D=1-x} and F i = 1 + x 2 i {\displayst... | Non-restoring division | 0.8169 |
12,575 | {\displaystyle X_{0}={48 \over 17}-{32 \over 17}D.\,} The coefficients of the linear approximation are determined as follows. The absolute value of the error is | ε 0 | = | 1 − D ( T 1 + T 2 D ) | {\displaystyle |\varepsilon _{0}|=|1-D(T_{1}+T_{2}D)|} . The minimum of the maximum absolute value of the error is determin... | Non-restoring division | 0.8169 |
12,576 | In the field of computer vision, velocity moments are weighted averages of the intensities of pixels in a sequence of images, similar to image moments but in addition to describing an object's shape also describe its motion through the sequence of images. Velocity moments can be used to aid automated identification of ... | Velocity Moments | 0.816898 |
12,577 | in organic chemistry. Most training regimens also include a postdoctoral fellowship period of 2 or more years after receiving a Ph.D. in chemistry, making the total length of training range from 10 to 12 years of college education. | Medicinal chemist | 0.816892 |
12,578 | Medicinal chemistry is by nature an interdisciplinary science, and practitioners have a strong background in organic chemistry, which must eventually be coupled with a broad understanding of biological concepts related to cellular drug targets. Scientists in medicinal chemistry work are principally industrial scientist... | Medicinal chemist | 0.816892 |
12,579 | and post-doctoral positions, ibid.). In the medicinal chemistry specialty areas associated with the design and synthesis of chemical libraries or the execution of process chemistry aimed at viable commercial syntheses (areas generally with fewer opportunities), training paths are often much more varied (e.g., including... | Medicinal chemist | 0.816892 |
12,580 | However, the majority of working medicinal chemists have graduate degrees (MS, but especially Ph.D.) in organic chemistry, rather than medicinal chemistry, and the preponderance of positions are in research, where the net is necessarily cast widest, and most broad synthetic activity occurs. In research of small molecul... | Medicinal chemist | 0.816892 |
12,581 | However, employment opportunities at the Master's level also exist in the pharmaceutical industry, and at that and the Ph.D. level there are further opportunities for employment in academia and government. Graduate level programs in medicinal chemistry can be found in traditional medicinal chemistry or pharmaceutical s... | Medicinal chemist | 0.816892 |
12,582 | Algebraic groups over algebraically closed fields have finite Morley rank, equal to their dimension as algebraic sets. Sela (2006) showed that free groups, and more generally torsion-free hyperbolic groups, are stable. Free groups on more than one generator are not superstable. | Groups of finite Morley rank | 0.816886 |
12,583 | The Peano axioms are the most widely used axiomatization of first-order arithmetic. They are a set of axioms strong enough to prove many important facts about number theory and they allowed Gödel to establish his famous second incompleteness theorem.We have a language L N T = { 0 , S } {\displaystyle {\mathfrak {L}}_{N... | Logical axioms | 0.816885 |
12,584 | Probably the oldest, and most famous, list of axioms are the 4 + 1 Euclid's postulates of plane geometry. The axioms are referred to as "4 + 1" because for nearly two millennia the fifth (parallel) postulate ("through a point outside a line there is exactly one parallel") was suspected of being derivable from the first... | Logical axioms | 0.816885 |
12,585 | Equivalence: the symbol ≡ {\displaystyle \equiv } in Frege in 1879; ↔ {\displaystyle \leftrightarrow } in Becker in 1933 (not the first time and for this see the following); ⇔ {\displaystyle \Leftrightarrow } appeared in Bourbaki in 1954; other symbols appeared punctually in the history, such as ⊃⊂ {\displaystyle \sups... | Logical connective | 0.816883 |
12,586 | Negation: the symbol ¬ {\displaystyle \neg } appeared in Heyting in 1930 (compare to Frege's symbol ⫟ in his Begriffsschrift); the symbol ∼ {\displaystyle \sim } appeared in Russell in 1908; an alternative notation is to add a horizontal line on top of the formula, as in p ¯ {\displaystyle {\overline {p}}} ; another al... | Logical connective | 0.816883 |
12,587 | Three elements { ∨ , ↔ , ⊥ } {\displaystyle \{\lor ,\leftrightarrow ,\bot \}} , { ∨ , ↔ , ↮ } {\displaystyle \{\lor ,\leftrightarrow ,\nleftrightarrow \}} , { ∨ , ↮ , ⊤ } {\displaystyle \{\lor ,\nleftrightarrow ,\top \}} , { ∧ , ↔ , ⊥ } {\displaystyle \{\land ,\leftrightarrow ,\bot \}} , { ∧ , ↔ , ↮ } {\displaystyle \{... | Logical connective | 0.816883 |
12,588 | Ligand cone angles are measures of the size of ligands in coordination chemistry. It is defined as the solid angle formed with the metal at the vertex and the hydrogen atoms at the perimeter of the cone (see figure). | Steric shielding | 0.816876 |
12,589 | The National Science Advisory Board for Biosecurity (NSABB) is a panel of experts that reports to the Secretary of the United States Department of Health and Human Services. It is tasked with recommending policies on such questions as how to prevent published research in biotechnology from aiding terrorism, without slo... | National Science Advisory Board for Biosecurity | 0.816872 |
12,590 | Cone studied the role of resting potential in regulating cell differentiation and proliferation and subsequent work has identified specific regions of the resting potential spectrum that correspond to distinct cell states such as quiescent, stem, cancer, and terminally differentiated. Although this body of work generat... | Bioelectricity | 0.816872 |
12,591 | Developmental bioelectricity is a sub-discipline of biology, related to, but distinct from, neurophysiology and bioelectromagnetics. Developmental bioelectricity refers to the endogenous ion fluxes, transmembrane and transepithelial voltage gradients, and electric currents and fields produced and sustained in living ce... | Bioelectricity | 0.816872 |
12,592 | Progress in molecular biology over the last six decades has produced powerful tools that facilitate the dissection of biochemical and genetic signals; yet, they tend to not be well-suited for bioelectric studies in vivo. Prior work relied extensively on current applied directly by electrodes, reinvigorated by significa... | Bioelectricity | 0.816872 |
12,593 | Thus, the proximal mechanisms of bioelectric signaling within single cells are becoming well-understood, and advances in optogenetics and magnetogenetics continue to facilitate this research program. More challenging however is the integrative program of understanding how specific patterns of bioelectric dynamics help ... | Bioelectricity | 0.816872 |
12,594 | In developmental biology, bioelectricity refers to the regulation of cell, tissue, and organ-level patterning and behavior as the result of endogenous electrically mediated signalling. Cells and tissues of all types use ion fluxes to communicate electrically. The charge carrier in bioelectricity is the ion (charged ato... | Bioelectricity | 0.816871 |
12,595 | Hence, this is where Array DBMSs can make a particular contribution. Generally, Array DBMSs are an emerging technology. While operationally deployed systems exist, like Oracle GeoRaster, PostGIS 2.0 and rasdaman, there are still many open research questions, including query language design and formalization, query opti... | Array DBMS | 0.81687 |
12,596 | Seminal theoretical work has been accomplished by Libkin et al.; in their model, called NCRA, they extend a nested relational calculus with multidimensional arrays; among the results are important contributions on array query complexity analysis. A map algebra, suitable for 2-D and 3-D spatial raster data, has been pub... | Array DBMS | 0.81687 |
12,597 | This system offers the precursor of a 2-D array query language, albeit still procedural and without suitable storage support. A first declarative query language suitable for multiple dimensions and with an algebra-based semantics has been published by Baumann, together with a scalable architecture. Another array databa... | Array DBMS | 0.81687 |
12,598 | As iteration over an array is at the heart of array processing, declarativeness very much centers on this aspect. The requirement, then, is that conceptually all cells should be inspected simultaneously – in other words, the query does not enforce any explicit iteration sequence over the array cells during evaluation. ... | Array DBMS | 0.81687 |
12,599 | As an example for array query operators the rasdaman algebra and query language can serve, which establish an expression language over a minimal set of array primitives. We begin with the generic core operators and then present common special cases and shorthands. The marray operator creates an array over some given do... | Array DBMS | 0.81687 |
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