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3,100 | It is a vast and recently developed area of computer science. computer network Also data network. A digital telecommunications network which allows nodes to share resources. | Glossary of computer science | 0.831867 |
3,101 | computational physics Is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. computational science Also ... | Glossary of computer science | 0.831867 |
3,102 | computational model A mathematical model in computational science that requires extensive computational resources to study the behavior of a complex system by computer simulation. computational neuroscience Also theoretical neuroscience or mathematical neuroscience. A branch of neuroscience which employs mathematical m... | Glossary of computer science | 0.831867 |
3,103 | Computational biology is different from biological computing, which is a subfield of computer science and computer engineering using bioengineering and biology to build computers. computational chemistry A branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theor... | Glossary of computer science | 0.831867 |
3,104 | The study of computation is paramount to the discipline of computer science. computational biology Involves the development and application of data-analytical and theoretical methods, mathematical modelling and computational simulation techniques to the study of biological, ecological, behavioural, and social systems. ... | Glossary of computer science | 0.831867 |
3,105 | Compilers are a type of translator that support digital devices, primarily computers. The name compiler is primarily used for programs that translate source code from a high-level programming language to a lower-level language (e.g. assembly language, object code, or machine code) to create an executable program. compu... | Glossary of computer science | 0.831867 |
3,106 | Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of error... | Glossary of computer science | 0.831867 |
3,107 | cleanroom software engineering A software development process intended to produce software with a certifiable level of reliability. The cleanroom process was originally developed by Harlan Mills and several of his colleagues including Alan Hevner at IBM. | Glossary of computer science | 0.831867 |
3,108 | Contrary to elementary algebra, where the values of the variables are numbers and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction and (denoted as ∧), the disjunction or (denoted as ∨), and the negation not (denoted as ¬). It is thus a formalism for descri... | Glossary of computer science | 0.831867 |
3,109 | Boolean expression An expression used in a programming language that returns a Boolean value when evaluated, that is one of true or false. A Boolean expression may be composed of a combination of the Boolean constants true or false, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. Boolea... | Glossary of computer science | 0.831867 |
3,110 | A raster graphics image file format used to store bitmap digital images independently of the display device (such as a graphics adapter), used especially on Microsoft Windows and OS/2 operating systems. Boolean data type A data type that has one of two possible values (usually denoted true and false), intended to repre... | Glossary of computer science | 0.831867 |
3,111 | Some authors allow the binary tree to be the empty set as well. bioinformatics An interdisciplinary field that combines biology, computer science, information engineering, mathematics, and statistics to develop methods and software tools for analyzing and interpreting biological data. Bioinformatics is widely used for ... | Glossary of computer science | 0.831867 |
3,112 | artificial intelligence (AI) Also machine intelligence. Intelligence demonstrated by machines, in contrast to the natural intelligence displayed by humans and other animals. In computer science, AI research is defined as the study of "intelligent agents": devices capable of perceiving their environment and taking actio... | Glossary of computer science | 0.831867 |
3,113 | In software engineering and computer science, the process of removing physical, spatial, or temporal details or attributes in the study of objects or systems in order to more closely attend to other details of interest; it is also very similar in nature to the process of generalization. 2. | Glossary of computer science | 0.831867 |
3,114 | This glossary of computer science is a list of definitions of terms and concepts used in computer science, its sub-disciplines, and related fields, including terms relevant to software, data science, and computer programming. | Glossary of computer science | 0.831867 |
3,115 | In other words, "runtime" is the running phase of a program. run time error A runtime error is detected after or during the execution (running state) of a program, whereas a compile-time error is detected by the compiler before the program is ever executed. Type checking, register allocation, code generation, and code ... | Glossary of computer science | 0.831867 |
3,116 | reliability engineering A sub-discipline of systems engineering that emphasizes dependability in the lifecycle management of a product. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time. Reliability is closely related to availability, which is ... | Glossary of computer science | 0.831867 |
3,117 | relational database Is a digital database based on the relational model of data, as proposed by E. F. Codd in 1970. A software system used to maintain relational databases is a relational database management system (RDBMS). Many relational database systems have an option of using the SQL (Structured Query Language) for... | Glossary of computer science | 0.831867 |
3,118 | The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references can ... | Glossary of computer science | 0.831867 |
3,119 | The generic, umbrella term callable unit is sometimes used. symbolic computation In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expres... | Glossary of computer science | 0.831866 |
3,120 | Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6, ...). In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them in computer memo... | Glossary of computer science | 0.831866 |
3,121 | numerical analysis The study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). numerical method In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problem... | Glossary of computer science | 0.831866 |
3,122 | encryption In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decipher a ciphertext back to plaintext and access the original info... | Glossary of computer science | 0.831866 |
3,123 | It examines the nature, the tasks, and the functions of cognition (in a broad sense). Cognitive scientists study intelligence and behavior, with a focus on how nervous systems represent, process, and transform information. Mental faculties of concern to cognitive scientists include language, perception, memory, attenti... | Glossary of computer science | 0.831866 |
3,124 | The process of programming thus often requires expertise in several different subjects, including knowledge of the application domain, specialized algorithms, and formal logic. coding theory The study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression,... | Glossary of computer science | 0.831866 |
3,125 | cipher Also cypher. In cryptography, an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. class In object-oriented programming, an extensible program-code-template for creating objects, providing initial values for state (member variables) and implemen... | Glossary of computer science | 0.831866 |
3,126 | Operations associated with this data type allow:the addition of a pair to the collection the removal of a pair from the collection the modification of an existing pair the lookup of a value associated with a particular key automata theory The study of abstract machines and automata, as well as the computational problem... | Glossary of computer science | 0.831866 |
3,127 | Colloquially, the term "artificial intelligence" is applied when a machine mimics "cognitive" functions that humans associate with other human minds, such as "learning" and "problem solving". ASCII See American Standard Code for Information Interchange. assertion In computer programming, a statement that a predicate (B... | Glossary of computer science | 0.831866 |
3,128 | aggregate function In database management, a function in which the values of multiple rows are grouped together to form a single value of more significant meaning or measurement, such as a sum, count, or max. agile software development An approach to software development under which requirements and solutions evolve th... | Glossary of computer science | 0.831866 |
3,129 | routing table In computer networking a routing table, or routing information base (RIB), is a data table stored in a router or a network host that lists the routes to particular network destinations, and in some cases, metrics (distances) associated with those routes. The routing table contains information about the to... | Glossary of computer science | 0.831866 |
3,130 | The goal of robotics is to design intelligent machines that can help and assist humans in their day-to-day lives and keep everyone safe. round-off error Also rounding error. The difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-... | Glossary of computer science | 0.831866 |
3,131 | robotics An interdisciplinary branch of engineering and science that includes mechanical engineering, electronic engineering, information engineering, computer science, and others. Robotics involves design, construction, operation, and use of robots, as well as computer systems for their perception, control, sensory fe... | Glossary of computer science | 0.831866 |
3,132 | As regression test suites tend to grow with each found defect, test automation is frequently involved. Sometimes a change impact analysis is performed to determine an appropriate subset of tests (non-regression analysis). requirements analysis In systems engineering and software engineering, requirements analysis focus... | Glossary of computer science | 0.831866 |
3,133 | Both quarks and leptons are elementary particles, and were in 2004 seen by authors of an undergraduate text as being the fundamental constituents of matter.These quarks and leptons interact through four fundamental forces: gravity, electromagnetism, weak interactions, and strong interactions. The Standard Model of part... | Chemical matter | 0.831863 |
3,134 | In 1909 the famous physicist J. J. Thomson (1856–1940) wrote about the "constitution of matter" and was concerned with the possible connection between matter and electrical charge.In the late 19th century with the discovery of the electron, and in the early 20th century, with the Geiger–Marsden experiment discovery of ... | Chemical matter | 0.831863 |
3,135 | Baryons are strongly interacting fermions, and so are subject to Fermi–Dirac statistics. Amongst the baryons are the protons and neutrons, which occur in atomic nuclei, but many other unstable baryons exist as well. The term baryon usually refers to triquarks—particles made of three quarks. Also, "exotic" baryons made ... | Chemical matter | 0.831863 |
3,136 | Some of these ways are based on loose historical meanings, from a time when there was no reason to distinguish mass from simply a quantity of matter. As such, there is no single universally agreed scientific meaning of the word "matter". Scientifically, the term "mass" is well-defined, but "matter" can be defined in se... | Chemical matter | 0.831863 |
3,137 | Matter should not be confused with mass, as the two are not the same in modern physics. Matter is a general term describing any 'physical substance'. By contrast, mass is not a substance but rather a quantitative property of matter and other substances or systems; various types of mass are defined within physics – incl... | Chemical matter | 0.831863 |
3,138 | Orbital Mechanics for Engineering Students is an aerospace engineering textbook by Howard D. Curtis, in its fourth edition as of 2019. The book provides an introduction to orbital mechanics, while assuming an undergraduate-level background in physics, rigid body dynamics, differential equations, and linear algebra.Topi... | Orbital Mechanics for Engineering Students | 0.831859 |
3,139 | The notion of an arithmetic group is a vast generalisation based upon the fundamental example of S L d ( Z ) {\displaystyle \mathrm {SL} _{d}(\mathbb {Z} )} . In general, to give a definition one needs a semisimple algebraic group G {\displaystyle \mathbf {G} } defined over Q {\displaystyle \mathbb {Q} } and a faithful... | Non-congruence subgroup | 0.83185 |
3,140 | If n ⩾ 1 {\displaystyle n\geqslant 1} is an integer there is a homomorphism π n: S L 2 ( Z ) → S L 2 ( Z / n Z ) {\displaystyle \pi _{n}:\mathrm {SL} _{2}(\mathbb {Z} )\to \mathrm {SL} _{2}(\mathbb {Z} /n\mathbb {Z} )} induced by the reduction modulo n {\displaystyle n} morphism Z → Z / n Z {\displaystyle \mathbb {Z} \... | Non-congruence subgroup | 0.83185 |
3,141 | The congruence subgroups of the modular group and the associated Riemann surfaces are distinguished by some particularly nice geometric and topological properties. Here is a sample: There are only finitely many congruence covers of the modular surface which have genus zero; (Selberg's 3/16 theorem) If f {\displaystyle ... | Non-congruence subgroup | 0.83185 |
3,142 | Both are profinite groups and there is a natural surjective morphism Γ ^ → Γ ¯ {\displaystyle {\widehat {\Gamma }}\to {\overline {\Gamma }}} (intuitively, there are fewer conditions for a Cauchy sequence to comply with in the congruence topology than in the profinite topology). The congruence kernel C ( Γ ) {\displayst... | Non-congruence subgroup | 0.83185 |
3,143 | On the other hand, the work of Serre on S L 2 {\displaystyle \mathrm {SL} _{2}} over number fields shows that in some cases the answer to the naïve question is "no" while a slight relaxation of the problem has a positive answer.This new problem is better stated in terms of certain compact topological groups associated ... | Non-congruence subgroup | 0.83185 |
3,144 | One can ask the same question for any arithmetic group as for the modular group: Naïve congruence subgroup problem: Given an arithmetic group, are all of its finite-index subgroups congruence subgroups? This problem can have a positive solution: its origin is in the work of Hyman Bass, Jean-Pierre Serre and John Milnor... | Non-congruence subgroup | 0.83185 |
3,145 | If you apply a voltage across a capacitor, it 'charges up' by storing the electrical charge as an electrical field inside the device. This means that while the voltage across the capacitor remains initially small, a large current flows. Later, the current flow is smaller because the capacity is filled, and the voltage ... | Mathematical methods in electronics | 0.831846 |
3,146 | Electronics engineering careers usually include courses in calculus (single and multivariable), complex analysis, differential equations (both ordinary and partial), linear algebra and probability. Fourier analysis and Z-transforms are also subjects which are usually included in electrical engineering programs. Laplace... | Mathematical methods in electronics | 0.831846 |
3,147 | Ohm's law: the voltage across a resistor is the product of its resistance and the current flowing through it.at constant temperature. Norton's theorem: any two-terminal collection of voltage sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor. Thévenin's theore... | Mathematical methods in electronics | 0.831846 |
3,148 | Fourier analysis. Deconstructing a periodic waveform into its constituent frequencies; see also: Fourier theorem, Fourier transform. Nyquist–Shannon sampling theorem. Information theory. Sets fundamental limits on how information can be transmitted or processed by any system. | Mathematical methods in electronics | 0.831846 |
3,149 | Millman's theorem: the voltage on the ends of branches in parallel is equal to the sum of the currents flowing in every branch divided by the total equivalent conductance. See also Analysis of resistive circuits.Circuit analysis is the study of methods to solve linear systems for an unknown variable. Circuit analysis | Mathematical methods in electronics | 0.831846 |
3,150 | There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the Abel Prize, the Chern Medal, the Fields Medal, the Gauss Prize, the Nemmers Prize, the Balzan Prize, the Crafoord Prize, the Sh... | Applied mathematician | 0.831845 |
3,151 | Pure mathematics is mathematics that studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of navigation, astronomy, physics, economics... | Applied mathematician | 0.831845 |
3,152 | An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective o... | Applied mathematician | 0.831845 |
3,153 | A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham. | Applied mathematician | 0.831845 |
3,154 | He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582 – c. | Applied mathematician | 0.831845 |
3,155 | Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in a manner which will help ensure that the plans are maintained on a sound financial basis. As another example, mathematical finance will derive and extend the mathematical or numerical models... | Applied mathematician | 0.831845 |
3,156 | The philosopher of computing Bill Rapaport noted three Great Insights of Computer Science: Gottfried Wilhelm Leibniz's, George Boole's, Alan Turing's, Claude Shannon's, and Samuel Morse's insight: there are only two objects that a computer has to deal with in order to represent "anything".All the information about any ... | Computing science | 0.831837 |
3,157 | It has since been argued that computer science can be classified as an empirical science since it makes use of empirical testing to evaluate the correctness of programs, but a problem remains in defining the laws and theorems of computer science (if any exist) and defining the nature of experiments in computer science.... | Computing science | 0.831837 |
3,158 | Despite the word "science" in its name, there is debate over whether or not computer science is a discipline of science, mathematics, or engineering. Allen Newell and Herbert A. Simon argued in 1975, Computer science is an empirical discipline. We would have called it an experimental science, but like astronomy, econom... | Computing science | 0.831837 |
3,159 | Computer security is a branch of computer technology with the objective of protecting information from unauthorized access, disruption, or modification while maintaining the accessibility and usability of the system for its intended users. Historical cryptography is the art of writing and deciphering secret messages. M... | Computing science | 0.831837 |
3,160 | Artificial intelligence and machine learning aim to synthesize goal-orientated processes such as problem-solving, decision-making, environmental adaptation, planning and learning found in humans and animals. Within artificial intelligence, computer vision aims to understand and process image and video data, while natur... | Computing science | 0.831837 |
3,161 | Human–computer interaction investigates the interfaces through which humans and computers interact, and software engineering focuses on the design and principles behind developing software. Areas such as operating systems, networks and embedded systems investigate the principles and design behind complex systems. Compu... | Computing science | 0.831837 |
3,162 | The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and d... | Computing science | 0.831837 |
3,163 | Computer science is the study of computation, information, and automation. Computer science spans theoretical disciplines (such as algorithms, theory of computation, and information theory) to applied disciplines (including the design and implementation of hardware and software). Though more often considered an academi... | Computing science | 0.831837 |
3,164 | Computer Science, known by its near synonyms, Computing, Computer Studies, has been taught in UK schools since the days of batch processing, mark sensitive cards and paper tape but usually to a select few students. In 1981, the BBC produced a micro-computer and classroom network and Computer Studies became common for G... | Computing science | 0.831837 |
3,165 | Artificial intelligence (AI) aims to or is required to synthesize goal-orientated processes such as problem-solving, decision-making, environmental adaptation, learning, and communication found in humans and animals. From its origins in cybernetics and in the Dartmouth Conference (1956), artificial intelligence researc... | Computing science | 0.831837 |
3,166 | Computer science is considered by some to have a much closer relationship with mathematics than many scientific disciplines, with some observers saying that computing is a mathematical science. Early computer science was strongly influenced by the work of mathematicians such as Kurt Gödel, Alan Turing, John von Neumann... | Computing science | 0.831837 |
3,167 | For example, the study of computer hardware is usually considered part of computer engineering, while the study of commercial computer systems and their deployment is often called information technology or information systems. However, there has been exchange of ideas between the various computer-related disciplines. C... | Computing science | 0.831837 |
3,168 | "In the U.S., however, informatics is linked with applied computing, or computing in the context of another domain. "A folkloric quotation, often attributed to—but almost certainly not first formulated by—Edsger Dijkstra, states that "computer science is no more about computers than astronomy is about telescopes." The ... | Computing science | 0.831837 |
3,169 | An alternative term, also proposed by Naur, is data science; this is now used for a multi-disciplinary field of data analysis, including statistics and databases. In the early days of computing, a number of terms for the practitioners of the field of computing were suggested in the Communications of the ACM—turingineer... | Computing science | 0.831837 |
3,170 | Despite its name, a significant amount of computer science does not involve the study of computers themselves. Because of this, several alternative names have been proposed. Certain departments of major universities prefer the term computing science, to emphasize precisely that difference. | Computing science | 0.831837 |
3,171 | Although first proposed in 1956, the term "computer science" appears in a 1959 article in Communications of the ACM, in which Louis Fein argues for the creation of a Graduate School in Computer Sciences analogous to the creation of Harvard Business School in 1921. Louis justifies the name by arguing that, like manageme... | Computing science | 0.831837 |
3,172 | A number of computer scientists have argued for the distinction of three separate paradigms in computer science. Peter Wegner argued that those paradigms are science, technology, and mathematics. Peter Denning's working group argued that they are theory, abstraction (modeling), and design. Amnon H. Eden described them ... | Computing science | 0.831837 |
3,173 | For industrial use, tool support is required. However, the high cost of using formal methods means that they are usually only used in the development of high-integrity and life-critical systems, where safety or security is of utmost importance. Formal methods are best described as the application of a fairly broad vari... | Computing science | 0.831837 |
3,174 | The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design. They form an important theoretical underpinning for software engineering, espec... | Computing science | 0.831837 |
3,175 | Programming language theory is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of programming languages and their individual features. It falls within the discipline of computer science, both depending on and affecting mathematics, software enginee... | Computing science | 0.831837 |
3,176 | Cooperation between agents – in this case, algorithms and humans – depends on trust. If humans are to accept algorithmic prescriptions, they need to trust them. Incompleteness in formal trust criteria is a barrier to optimization. | Interpretability (machine learning) | 0.831812 |
3,177 | Scholars have suggested that explainability in AI should be considered a goal secondary to AI effectiveness, and that encouraging the exclusive development of XAI may limit the functionality of AI more broadly. Critiques of XAI rely on developed concepts of mechanistic and empiric reasoning from evidence-based medicine... | Interpretability (machine learning) | 0.831812 |
3,178 | Senator Robert Byrd, Democrat from West Virginia, joined critics of reform mathematics on the floor of the senate by dubbing Addison-Wesley Secondary Math: An Integrated Approach: Focus on Algebra the "Texas rainforest algebra book". It had received an "F" grade on a report card produced by Mathematically Correct, a ba... | Rainforest algebra | 0.831799 |
3,179 | The multidisciplinary nature of learning engineering creates challenges. The problems that learning engineering attempts to solve often require expertise in diverse fields such as software engineering, instructional design, domain knowledge, pedagogy/andragogy, psychometrics, learning sciences, data science, and system... | Learning engineering | 0.83179 |
3,180 | Herbert Simon, a cognitive psychologist and economist, first coined the term learning engineering in 1967. However, associations between the two terms learning and engineering began emerging earlier, in the 1940s and as early as the 1920s. Simon argued that the social sciences, including the field of education, should ... | Learning engineering | 0.83179 |
3,181 | In 2019, PBS partnered with Kaggle to create the 2019 Data Science Bowl. The DataScience Bowl sought machine learning insights from researchers and developers, specifically into how digital media can better facilitate early-childhood STEM learning outcomes. Datasets, like those hosted by Kaggle PBS and Carnegie Learnin... | Learning engineering | 0.83179 |
3,182 | Datasets provide the raw material that researchers use to formulate educational insights. For example, Carnegie Mellon University hosts a large volume of learning interaction data in LearnLab's DataShop. Their datasets range from sources like Intelligent Writing Tutors to Chinese tone studies to data from Carnegie Lear... | Learning engineering | 0.83179 |
3,183 | Learning engineering teams require expertise associated with the content that learners will learn, the targeted learners themselves, the venues in which learning is expected to happen, educational practice, software engineering, and sometimes even more. Learning engineering teams employ an iterative design process for ... | Learning engineering | 0.83179 |
3,184 | Mixtures are not limited in either their number of substances or the amounts of those substances, though in a homogeneous mixture the solute-to-solvent proportion can only reach a certain point before the mixture separates and becomes heterogeneous. A homogeneous mixture is characterized by uniform dispersion of its co... | Homogeneous and heterogeneous mixtures | 0.831783 |
3,185 | Target proteins are functional biomolecules that are addressed and controlled by biologically active compounds. They are used in the processes of transduction, transformation and conjugation. The identification of target proteins, the investigation of signal transduction processes and the understanding of their interac... | Target protein | 0.831765 |
3,186 | In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup H of a group G is a proper subgroup, such that no proper subgroup K contains H strictly. In other words, H is a maximal element of the partially ordered set of subgroups... | Maximal subgroup | 0.831765 |
3,187 | Similarly, a normal subgroup N of G is said to be a maximal normal subgroup (or maximal proper normal subgroup) of G if N < G and there is no normal subgroup K of G such that N < K < G. We have the following theorem: Theorem: A normal subgroup N of a group G is a maximal normal subgroup if and only if the quotient G/N ... | Maximal subgroup | 0.831765 |
3,188 | If an integer relation is found, this suggests a possible closed-form expression for the original series, product or integral. This conjecture can then be validated by formal algebraic methods. The higher the precision to which the inputs to the algorithm are known, the greater the level of confidence that any integer ... | Integer relation algorithm | 0.831753 |
3,189 | Integer relation algorithms have numerous applications. The first application is to determine whether a given real number x is likely to be algebraic, by searching for an integer relation between a set of powers of x {1, x, x2, ..., xn}. The second application is to search for an integer relation between a real number ... | Integer relation algorithm | 0.831753 |
3,190 | A Bertrand curve is a regular curve in R 3 {\displaystyle \mathbb {R} ^{3}} with the additional property that there is a second curve in R 3 {\displaystyle \mathbb {R} ^{3}} such that the principal normal vectors to these two curves are identical at each corresponding point. In other words, if γ1(t) and γ2(t) are two c... | Unit speed parametrization | 0.831745 |
3,191 | An axiomatization of propositional calculus is a set of tautologies called axioms and one or more inference rules for producing new tautologies from old. A proof in an axiom system A is a finite nonempty sequence of propositions each of which is either an instance of an axiom of A or follows by some rule of A from prop... | Boolean algebra (logic) | 0.831744 |
3,192 | Propositional calculus restricts attention to abstract propositions, those built up from propositional variables using Boolean operations. Instantiation is still possible within propositional calculus, but only by instantiating propositional variables by abstract propositions, such as instantiating Q by Q→P in P→(Q→P) ... | Boolean algebra (logic) | 0.831744 |
3,193 | One motivating application of propositional calculus is the analysis of propositions and deductive arguments in natural language. Whereas the proposition "if x = 3 then x+1 = 4" depends on the meanings of such symbols as + and 1, the proposition "if x = 3 then x = 3" does not; it is true merely by virtue of its structu... | Boolean algebra (logic) | 0.831744 |
3,194 | Therefore, it was concluded that clusters of these specific numbers of rare gas atoms dominate due to their exceptional stability. The concept was also successfully applied to explain the monodispersed occurrence of thiolate-protected gold clusters; here the outstanding stability of specific cluster sizes is connected ... | Magic number (chemistry) | 0.831739 |
3,195 | The concept of magic numbers in the field of chemistry refers to a specific property (such as stability) for only certain representatives among a distribution of structures. It was first recognized by inspecting the intensity of mass-spectrometric signals of rare gas cluster ions. In case a gas condenses into clusters ... | Magic number (chemistry) | 0.831739 |
3,196 | Stem cell genomics analyzes the genomes of stem cells. Currently, this field is rapidly expanding due to the dramatic decrease in the cost of sequencing genomes. The study of stem cell genomics has wide reaching implications in the study of stem cell biology and possible therapeutic usages of stem cells. Application of... | Stem cell genomics | 0.831739 |
3,197 | Molecules and Cells is a peer-reviewed open access scientific journal of molecular and cellular biology. It was established in 1990 as the official publication of the Korean Society for Molecular and Cellular Biology, and is currently edited by Rho Hyun Seong (Seoul National University). From 1992 to 2013, the journal ... | Molecules and Cells | 0.831732 |
3,198 | Permeability is a property of porous materials that is an indication of the ability for fluids (gas or liquid) to flow through them. Fluids can more easily flow through a material with high permeability than one with low permeability. The permeability of a medium is related to the porosity, but also to the shapes of th... | Soil permeability | 0.831729 |
3,199 | For example, Marshall Hall used the near-field of order 9 given above to produce a Hall plane, the first of a sequence of such planes based on Dickson near-fields of order the square of a prime. In 1971 T. G. Room and P.B. Kirkpatrick provided an alternative development.There are numerous other applications, mostly to ... | Near-field (mathematics) | 0.831728 |
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