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10,700 | Also known as factoring in automated theorem proving systems using resolution. Known as idempotency of entailment in classical logic. Exchange, where two members on the same side of a sequent may be swapped. | Rule of contraction | 0.818657 |
10,701 | Newton and Gottfried Leibniz both claimed priority in discovering calculus. Newton said that he wrote about calculus in the 1660s and 1670s, but did not publish until 1693. Leibniz published "Nova Methodus pro Maximis et Minimis", a treatise on calculus, in 1684. | Open Science | 0.818657 |
10,702 | Naboulsi requested Watanabe to upload his papers on ArXiv as he was not able to do so, because of his lack of an institutional affiliation. Later, the papers were realized to have been copied from the proceedings of a physics conference. Preprint servers are increasingly developing measures to circumvent this plagiaris... | Open Science | 0.818657 |
10,703 | According to the founders, this allows for greater transparency and minimal work on the authors' part.One criticism of pre-print servers is their potential to foster a culture of plagiarism. For example, the popular physics preprint server ArXiv had to withdraw 22 papers when it came to light that they were plagiarized... | Open Science | 0.818657 |
10,704 | Open research is often used quasi-synonymously to address the gap that the denotion of "science" might have regarding an inclusion of the Arts, Humanities and Social Sciences. The primary focus connecting all disciplines is the widespread uptake of new technologies and tools, and the underlying ecology of the productio... | Open Science | 0.818657 |
10,705 | The Researcher Index aims to establish a data-driven statistical metric for quantifying researcher impact. The Unique Researcher Identity is a blockchain technology based solution for creating a single unifying identity for each researcher, which is connected to the researcher's profile, research activities, and public... | Open Science | 0.818657 |
10,706 | In group theory, a group A {\displaystyle A\ } is algebraically closed if any finite set of equations and inequations that are applicable to A {\displaystyle A\ } have a solution in A {\displaystyle A\ } without needing a group extension. This notion will be made precise later in the article in § Formal definition. | Algebraically closed group | 0.818653 |
10,707 | However if we extend the group G {\displaystyle G\ } to the group H {\displaystyle H\ } with the adjacent multiplication table: Then the conditions have two solutions, namely x = b {\displaystyle x=b\ } and x = c {\displaystyle x=c\ } . Thus there are three possibilities regarding such conditions: They may be inconsist... | Algebraically closed group | 0.818653 |
10,708 | A finitely generated group has a solvable word problem if and only if it can be embedded in every algebraically closed group.The proofs of these results are in general very complex. However, a sketch of the proof that a countable group C {\displaystyle C\ } can be embedded in an algebraically closed group follows. Firs... | Algebraically closed group | 0.818653 |
10,709 | It is difficult to give concrete examples of algebraically closed groups as the following results indicate: Every countable group can be embedded in a countable algebraically closed group. Every algebraically closed group is simple. No algebraically closed group is finitely generated. An algebraically closed group cann... | Algebraically closed group | 0.818653 |
10,710 | Nomenclature of Organic Chemistry, commonly referred to by chemists as the Blue Book, is a collection of recommendations on organic chemical nomenclature published at irregular intervals by the International Union of Pure and Applied Chemistry (IUPAC). A full edition was published in 1979, an abridged and updated versi... | Nomenclature of Organic Chemistry | 0.818653 |
10,711 | MathJax is a cross-browser JavaScript library that displays mathematical notation in web browsers, using MathML, LaTeX and ASCIIMathML markup. MathJax is released as open-source software under the Apache License. The MathJax project started in 2009 as the successor to an earlier JavaScript mathematics formatting librar... | MathJax | 0.818652 |
10,712 | The Serine octamer cluster in physical chemistry is an unusually stable cluster consisting of eight serine molecules (Ser) implicated in the origin of homochirality. This cluster was first discovered in mass spectrometry experiments. Electrospray ionization of an aerosol of serine in methanol results in a mass spectrum... | Serine octamer cluster | 0.81865 |
10,713 | The expression for vector { X } {\displaystyle \{\ X\}} may be written as { X } = { X ′ } + { Δ X } {\displaystyle \{\ X\}=\{\ X'\}+\{\Delta \ X\}} The vector { X } {\displaystyle \{\ X\}} determination is related to minimization of the quadratic form Π {\displaystyle \ \Pi } by incremental vector { Δ X } {\displaystyl... | Stretched grid method | 0.818648 |
10,714 | However, as it is noted by some researchers it might sometimes be preferable to use the so-called ‘minimal surfaces’ in the design of tension structures. The physical meaning of SGM consists in convergence of the energy of an arbitrary grid structure embedded into rigid (or elastic) 3D contour to minimum that is equiva... | Stretched grid method | 0.818648 |
10,715 | Let us assume that two surfaces are parameterized so that their first quadratic forms may be written as follows I 1 = E 1 ( u , v ) d u 2 + 2 F 1 ( u , v ) d u d v + G 1 ( u , v ) d v 2 {\displaystyle I_{1}=E_{1}(u,v)\operatorname {d} u^{2}+2F_{1}(u,v)\operatorname {d} u\operatorname {d} v+G_{1}(u,v)\operatorna... | Stretched grid method | 0.818648 |
10,716 | The cutting pattern generation problem is actually subdivided into two independent formulations. These are the generation of a distortion-free plane form unfolding each cloth strip and flattening double-curved surfaces that cannot be simply unfolded. Studying the problem carefully one can notice that from the position ... | Stretched grid method | 0.818648 |
10,717 | As stated above, rotation hardly influences the molecular geometry. But, as a quantum mechanical motion, it is thermally excited at relatively (as compared to vibration) low temperatures. From a classical point of view it can be stated that at higher temperatures more molecules will rotate faster, which implies that th... | Molecular geometry | 0.818642 |
10,718 | The molecular vibrations are harmonic (at least to good approximation), and the atoms oscillate about their equilibrium positions, even at the absolute zero of temperature. At absolute zero all atoms are in their vibrational ground state and show zero point quantum mechanical motion, so that the wavefunction of a singl... | Molecular geometry | 0.818642 |
10,719 | Since the motions of the atoms in a molecule are determined by quantum mechanics, "motion" must be defined in a quantum mechanical way. The overall (external) quantum mechanical motions translation and rotation hardly change the geometry of the molecule. (To some extent rotation influences the geometry via Coriolis for... | Molecular geometry | 0.818642 |
10,720 | Discrete Mathematics and Theoretical Computer Science Information and Computation Theory of Computing (open access journal) Formal Aspects of Computing Journal of the ACM SIAM Journal on Computing (SICOMP) SIGACT News Theoretical Computer Science Theory of Computing Systems TheoretiCS (open access journal) Internationa... | Theoretical Computer Science | 0.818641 |
10,721 | Computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations. The best known problem in the field is integer factorization. | Theoretical Computer Science | 0.818641 |
10,722 | Annual ACM Symposium on Theory of Computing (STOC) Annual IEEE Symposium on Foundations of Computer Science (FOCS) Innovations in Theoretical Computer Science (ITCS) Mathematical Foundations of Computer Science (MFCS) International Computer Science Symposium in Russia (CSR) ACM–SIAM Symposium on Discrete Algorithms (SO... | Theoretical Computer Science | 0.818641 |
10,723 | Information-based complexity (IBC) studies optimal algorithms and computational complexity for continuous problems. IBC has studied continuous problems as path integration, partial differential equations, systems of ordinary differential equations, nonlinear equations, integral equations, fixed points, and very-high-di... | Theoretical Computer Science | 0.818641 |
10,724 | At times, it is not even clear which collection of axioms a proof appeals to. For example, a number-theoretic statement might be expressible in the language of arithmetic (i.e. the language of the Peano axioms) and a proof might be given that appeals to topology or complex analysis. It might not be immediately clear wh... | Axiomatic logic | 0.81864 |
10,725 | The result is that one will not know which propositions are theorems and the axiomatic method breaks down. An example of such a body of propositions is the theory of the natural numbers, which is only partially axiomatized by the Peano axioms (described below). In practice, not every proof is traced back to the axioms. | Axiomatic logic | 0.81864 |
10,726 | Not every consistent body of propositions can be captured by a describable collection of axioms. In recursion theory, a collection of axioms is called recursive if a computer program can recognize whether a given proposition in the language is a theorem. Gödel's first incompleteness theorem then tells us that there are... | Axiomatic logic | 0.81864 |
10,727 | {\displaystyle X.} A field of sets ( X , F ) {\displaystyle (X,{\mathcal {F}})} is called a σ-field of sets and the algebra F {\displaystyle {\mathcal {F}}} is called a σ-algebra if the following additional condition (4) is satisfied: Any/both of the following equivalent conditions hold: Closed under countable unions: ... | Field of sets | 0.818638 |
10,728 | Any/all of the following equivalent conditions hold: Closed under binary unions: Closed under binary intersections: Closed under finite unions: Closed under finite intersections: In other words, F {\displaystyle {\mathcal {F}}} forms a subalgebra of the power set Boolean algebra of X {\displaystyle X} (with the same id... | Field of sets | 0.818638 |
10,729 | A field of sets is a pair ( X , F ) {\displaystyle (X,{\mathcal {F}})} consisting of a set X {\displaystyle X} and a family F {\displaystyle {\mathcal {F}}} of subsets of X , {\displaystyle X,} called an algebra over X , {\displaystyle X,} that has the following properties: Closed under complementation in X {\displayst... | Field of sets | 0.818638 |
10,730 | In mathematics, a field of sets is a mathematical structure consisting of a pair ( X , F ) {\displaystyle (X,{\mathcal {F}})} consisting of a set X {\displaystyle X} and a family F {\displaystyle {\mathcal {F}}} of subsets of X {\displaystyle X} called an algebra over X {\displaystyle X} that contains the empty set as ... | Field of sets | 0.818638 |
10,731 | In 2005, the International Committee for Weights and Measures (CIPM) approved preparation of new definitions for the kilogram, the ampere, and the kelvin and it noted the possibility of a new definition of the mole based on the Avogadro constant. The 23rd CGPM (2007) decided to postpone any formal change until the next... | SI base units | 0.818634 |
10,732 | One of the basic tenets of Euclidean geometry is that two figures (usually considered as subsets) of the plane should be considered equivalent (congruent) if one can be transformed into the other by some sequence of translations, rotations and reflections (see below). In order to make all of this mathematically precise... | Euclidean space | 0.818615 |
10,733 | This article will follow this usage; that is ⟨ x , y ⟩ {\displaystyle \langle x,y\rangle } will be denoted x ⋅ y in the remainder of this article. The Euclidean norm of a vector x is The inner product and the norm allows expressing and proving metric and topological properties of Euclidean geometry. The next subsection... | Euclidean space | 0.818615 |
10,734 | Originally, projective spaces have been introduced by adding "points at infinity" to Euclidean spaces, and, more generally to affine spaces, in order to make true the assertion "two coplanar lines meet in exactly one point". Projective space share with Euclidean and affine spaces the property of being isotropic, that i... | Euclidean space | 0.818615 |
10,735 | In the study of geology, lithospheric flexure affects the thin lithospheric plates covering the surface of the Earth when a load or force is applied to them. On a geological timescale, the lithosphere behaves elastically (in first approach) and can therefore bend under loading by mountain chains, volcanoes and other he... | Flexural rigidity | 0.818614 |
10,736 | This problem can be found amongst the problems proposed by Paul Erdős in combinatorial number theory, known by English speakers as the Minimum overlap problem. It was first formulated in the 1955 article Some remarks on number theory (in Hebrew) in Riveon Lematematica, and has become one of the classical problems descr... | Minimum overlap problem | 0.818609 |
10,737 | In number theory and set theory, the minimum overlap problem is a problem proposed by Hungarian mathematician Paul Erdős in 1955. | Minimum overlap problem | 0.818609 |
10,738 | Multicritical points are special points in the parameter space of thermodynamic or other systems with a continuous phase transition. At least two thermodynamic or other parameters must be adjusted to reach a multicritical point. At a multicritical point the system belongs to a universality class different from the "nor... | Multicritical point | 0.818609 |
10,739 | This result paved the way for the celebrated PCP theorem, which can be considered to be a "scaled-down" version of this theorem. MIP also has the helpful property that zero-knowledge proofs for every language in NP can be described without the assumption of one-way functions that IP must make. This has bearing on the d... | Soundness (interactive proof) | 0.818607 |
10,740 | In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the... | Function evaluation | 0.818601 |
10,741 | Since |K| = |Pt|, the orders of H and K are relatively prime. Lagrange's Theorem implies the intersection of H and K is equal to 1. By definition,P1P2···Pt = HK, hence HK is isomorphic to H×K which is equal to P1×P2×···×Pt. | Nilpotency class | 0.818599 |
10,742 | The classic model vertebrate is currently the mouse (Mus musculus). Many inbred strains exist, as well as lines selected for particular traits, often of medical interest, e.g. body size, obesity, muscularity, and voluntary wheel-running behavior. The rat (Rattus norvegicus) is particularly useful as a toxicology model,... | Model organism | 0.818599 |
10,743 | Implicit interaction means that the flow of data between skeletons is completely defined by the skeleton composition, while explicit means that data can be generated or removed from the flow in a way not specified by the skeleton composition. For example, a skeleton that produces an output without ever receiving an inp... | Algorithmic skeleton | 0.818599 |
10,744 | Dictyostelium discoideum is used in molecular biology and genetics, and is studied as an example of cell communication, differentiation, and programmed cell death. Among invertebrates, the fruit fly Drosophila melanogaster is famous as the subject of genetics experiments by Thomas Hunt Morgan and others. They are easil... | Model organism | 0.818599 |
10,745 | For instance, many cell division genes that are critical for the development of cancer have been discovered in yeast. Chlamydomonas reinhardtii, a unicellular green alga with well-studied genetics, is used to study photosynthesis and motility. C. reinhardtii has many known and mapped mutants and expressed sequence tags... | Model organism | 0.818599 |
10,746 | Model organisms are drawn from all three domains of life, as well as viruses. The most widely studied prokaryotic model organism is Escherichia coli (E. coli), which has been intensively investigated for over 60 years. It is a common, gram-negative gut bacterium which can be grown and cultured easily and inexpensively ... | Model organism | 0.818599 |
10,747 | Nevertheless, many distributed applications require or produce large amounts of data during their computation. This is the case for astrophysics, particle physics, bio-informatics, etc. Thus, providing file transfer support that integrates with skeleton programming is a key concern which has been mostly overlooked. | Algorithmic skeleton | 0.818599 |
10,748 | The SkeTo project is a C++ library which achieves parallelization using MPI. SkeTo is different from other skeleton libraries because instead of providing nestable parallelism patterns, SkeTo provides parallel skeletons for parallel data structures such as: lists, trees, and matrices. The data structures are typed usin... | Algorithmic skeleton | 0.818599 |
10,749 | One of the interesting things about SKiPPER is that the skeleton program can be executed sequentially for debugging. Different approaches have been explored in SKiPPER for writing operational skeletons: static data-flow graphs, parametric process networks, hierarchical task graphs, and tagged-token data-flow graphs.QUA... | Algorithmic skeleton | 0.818599 |
10,750 | An extension of PAS labeled as SuperPas and later as EPAS addresses skeleton extensibility concerns. With the EPAS tool, new skeletons can be added to PAS. A Skeleton Description Language (SDL) is used to describe the skeleton pattern by specifying the topology with respect to a virtual processor grid. The SDL can then... | Algorithmic skeleton | 0.818599 |
10,751 | Additionally, several performance optimization are applied such as: skeleton rewriting techniques , task lookahead, and server-to-server lazy binding.At the implementation level, Lithium exploits macro-data flow to achieve parallelism. When the input stream receives a new parameter, the skeleton program is processed to... | Algorithmic skeleton | 0.818599 |
10,752 | Professionals in construction, civil engineering, chemical engineering, and other technical disciplines, especially in the United States, may use the so-called English Engineering units, that include the pound (lb = 0.45359237 kg) as the unit of mass, the degree Fahrenheit or Rankine (5/9K, about 0.55556 K) as the unit... | Molar specific heat | 0.818592 |
10,753 | The metallic state has historically been an important building block for studying properties of solids. The first theoretical description of metals was given by Paul Drude in 1900 with the Drude model, which explained electrical and thermal properties by describing a metal as an ideal gas of then-newly discovered elect... | Condensed matter theory | 0.818591 |
10,754 | In 1879, Edwin Herbert Hall working at the Johns Hopkins University discovered a voltage developed across conductors transverse to an electric current in the conductor and magnetic field perpendicular to the current. This phenomenon arising due to the nature of charge carriers in the conductor came to be termed the Hal... | Condensed matter theory | 0.818591 |
10,755 | Two years later, Bloch used quantum mechanics to describe the motion of an electron in a periodic lattice. : 366–368 The mathematics of crystal structures developed by Auguste Bravais, Yevgraf Fyodorov and others was used to classify crystals by their symmetry group, and tables of crystal structures were the basis for ... | Condensed matter theory | 0.818591 |
10,756 | Drude's classical model was augmented by Wolfgang Pauli, Arnold Sommerfeld, Felix Bloch and other physicists. Pauli realized that the free electrons in metal must obey the Fermi–Dirac statistics. Using this idea, he developed the theory of paramagnetism in 1926. Shortly after, Sommerfeld incorporated the Fermi–Dirac st... | Condensed matter theory | 0.818591 |
10,757 | The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of superconductivity and the Kondo effect. After World War II, several ideas fr... | Condensed matter theory | 0.818591 |
10,758 | Later in the 1930s, Douglas Hartree, Vladimir Fock and John Slater developed the so-called Hartree–Fock wavefunction as an improvement over the Thomas–Fermi model. The Hartree–Fock method accounted for exchange statistics of single particle electron wavefunctions. In general, it is very difficult to solve the Hartree–F... | Condensed matter theory | 0.818591 |
10,759 | : 101–103 In 1912, The structure of crystalline solids was studied by Max von Laue and Paul Knipping, when they observed the X-ray diffraction pattern of crystals, and concluded that crystals get their structure from periodic lattices of atoms. : 48 In 1928, Swiss physicist Felix Bloch provided a wave function solution... | Condensed matter theory | 0.818591 |
10,760 | At this workshop staff and students reviewed 33 experiments submitted by the different participating universities. After completing the activities there were debrief sessions in the evening. All those who completed experiments also completed surveys on the experiment and the documentation behind it. Another (smaller) w... | Advancing Chemistry by Enhancing Learning in the Laboratory | 0.818588 |
10,761 | Advancing Chemistry by Enhancing Learning in the Laboratory (ACELL) is a project for improving the teaching of Chemistry in the Laboratory. | Advancing Chemistry by Enhancing Learning in the Laboratory | 0.818588 |
10,762 | The educational analyses of experiments which completed this process were published in the Australian Journal of Education in Chemistry. Additional funding was received from the Department of Education, Science and Training (Australia) through its Higher Education Innovation Program (HEIP) to enable the project to be e... | Advancing Chemistry by Enhancing Learning in the Laboratory | 0.818588 |
10,763 | The current ACELL project began as APCELL (Australian Physical Chemistry Enhanced Laboratory Learning) in the late 1990s. Initially funded by the Australian Government through its Committee for University Teaching and Staff Development (CUTSD) program, the aim of APCELL was to build a database of tested, educationally-... | Advancing Chemistry by Enhancing Learning in the Laboratory | 0.818588 |
10,764 | Reliability engineering for "complex systems" requires a different, more elaborate systems approach than for non-complex systems. Reliability engineering may in that case involve: System availability and mission readiness analysis and related reliability and maintenance requirement allocation Functional system failure ... | Experimental reliability | 0.818585 |
10,765 | The Math Test – No Calculator section has 20 questions (15 multiple choice and 5 grid-in) and lasts 25 minutes. The Math Test – Calculator section has 38 questions (30 multiple choice and 8 grid-in) and lasts 55 minutes.Several scores are provided to the test taker for the math test. A subscore (on a scale of 1 to 15) ... | Scholastic aptitude test | 0.818583 |
10,766 | In 2010, physicists Stephen Hsu and James Schombert of the University of Oregon examined five years of student records at their school and discovered that the academic standing of students majoring in mathematics or physics (but not biology, English, sociology, or history) was strongly dependent on SAT mathematics scor... | Scholastic aptitude test | 0.818583 |
10,767 | A 2006 study led by psychometrician Robert Sternberg found that the ability of SAT scores and high-school GPAs to predict collegiate performance could further be enhanced by additional assessments of analytical, creative, and practical thinking.Experimental psychologist Meredith Frey noted that while advances in educat... | Scholastic aptitude test | 0.818583 |
10,768 | Furthermore, an admissions officer who failed to take average SAT scores into account would risk overestimating the future performance of a student from a low-scoring school and underestimating that of a student from a high-scoring school.Like other standardized tests such as the ACT or the GRE, the SAT is a traditiona... | Scholastic aptitude test | 0.818583 |
10,769 | By analyzing data from the National Center for Education Statistics, economists Ember Smith and Richard Reeves of the Brookings Institution deduced that the number of students taking the SAT increased at a rate faster than population and high-school graduation growth rates between 2000 and 2020. The increase was especi... | Scholastic aptitude test | 0.818583 |
10,770 | All scientific and most graphing calculators, including Computer Algebra System (CAS) calculators, are permitted on the SAT Math – Calculator section only. All four-function calculators are allowed as well; however, these devices are not recommended. All mobile phone and smartphone calculators, calculators with typewri... | Scholastic aptitude test | 0.818583 |
10,771 | One of the proposed partial explanations for the gap between Asian- and European-American students in educational achievement, as measured for example by the SAT, is the general tendency of Asians to come from stable two-parent households. In their 2018 analysis of data from the National Longitudinal Surveys of the Bur... | Scholastic aptitude test | 0.818583 |
10,772 | The evolutionary approach is key to much current research in biology that does not set out to study evolution per se, especially in organismal biology and ecology. For example, evolutionary thinking is key to life history theory. Annotation of genes and their function relies heavily on comparative, that is evolutionary... | Applications of evolution | 0.818579 |
10,773 | Evolutionary biology, in particular the understanding of how organisms evolve through natural selection, is an area of science with many practical applications. Creationists often claim that the theory of evolution lacks any practical applications; however, this claim has been refuted by scientists. | Applications of evolution | 0.818579 |
10,774 | As evolution can produce highly optimised processes and networks, it has many applications in computer science. Here, simulations of evolution using evolutionary algorithms and artificial life started with the work of Nils Aall Barricelli in the 1960s, and was extended by Alex Fraser, who published a series of papers o... | Applications of evolution | 0.818579 |
10,775 | A major technological application of evolution is artificial selection, which is the intentional selection of certain traits in a population of organisms. Humans have used artificial selection for thousands of years in the domestication of plants and animals. More recently, such selection has become a vital part of gen... | Applications of evolution | 0.818579 |
10,776 | A form of Lamarckism was revived in the Soviet Union of the 1930s when Trofim Lysenko promoted the ideologically driven research programme, Lysenkoism; this suited the ideological opposition of Joseph Stalin to genetics. Lysenkoism influenced Soviet agricultural policy which in turn was later blamed for crop failures. | Inheritance of acquired characters | 0.818578 |
10,777 | 2000 new experimental results in the fields of epigenetics, genetics, and somatic hypermutation proved the possibility of transgenerational epigenetic inheritance of traits acquired by the previous generation. These proved a limited validity of Lamarckism. The inheritance of the hologenome, consisting of the genomes of... | Inheritance of acquired characters | 0.818578 |
10,778 | However, Darwin's book On the Origin of Species gave credence to the idea of heritable effects of use and disuse, as Lamarck had done, and his own concept of pangenesis similarly implied soft inheritance.Many researchers from the 1860s onwards attempted to find evidence for Lamarckian inheritance, but these have all be... | Inheritance of acquired characters | 0.818578 |
10,779 | The historian of biology Peter J. Bowler noted in 1989 that other scientists had been unable to reproduce his results, and described the scientific consensus at the time: There is no feedback of information from the proteins to the DNA, and hence no route by which characteristics acquired in the body can be passed on t... | Inheritance of acquired characters | 0.818578 |
10,780 | Iran Bioinformatics Center (IBC) is the only academic center in Iran working on Bioinformatics. Although there are some independent research groups such as Bioinformatics and Biomathematics Unit in Mazandaran University of Medical Sciences working on Bioinformatics but IBC is a part of Institute of Biochemistry and Bio... | Iran Bioinformatics Center | 0.818568 |
10,781 | The mission statement of the Chemistry Literacy Project includes environmental and social justice. Technological literacy is defined in a three-dimensional coordinate space; on the knowledge axis, it is noted that technology can be risky, and that it "reflects the values and culture of society". Energy Literacy boasts ... | Scientific literacy | 0.818563 |
10,782 | Robin Wright, a writer for Cell Biology Education, laments "will misunderstandings or lack of knowledge about science imperil our democratic way of life and national security?" A discussion of physics literacy includes energy conservation, ozone depletion and global warming. | Scientific literacy | 0.818563 |
10,783 | Studies of college students' attitudes about learning physics suggest that these attitudes may be divided into categories of real world connections, personal connections, conceptual connections, student effort and problem-solving.The decision-making aspect of science literacy suggests further attitudes about the state ... | Scientific literacy | 0.818563 |
10,784 | Reforms in science education in the United States have often been driven by strategic challenges such as the launch of the Sputnik satellite in 1957 and the Japanese economic boom in the 1980s. By contrast, scientific literacy is now taken to mean that everyone should have a working knowledge of science and its role in... | Scientific literacy | 0.818563 |
10,785 | First, we write a proof using a natural-deduction like method: Q 1. hypothesis Q→R 2. hypothesis R 3. modus ponens 1,2 (Q→R)→R 4. deduction from 2 to 3Q→((Q→R)→R) 5. deduction from 1 to 4 QEDSecond, we convert the inner deduction to an axiomatic proof: (Q→R)→(Q→R) 1. theorem schema (A→A) ((Q→R)→(Q→R))→(((Q→R)→Q)→((Q→R)... | Deduction theorem | 0.81856 |
10,786 | Similarly, if A→S is outside the scope of H, apply axiom 1, (A→S)→(H→(A→S)), and modus ponens to get H→(A→S). It should not be necessary to do both of these, unless the modus ponens step is the conclusion, because if both are outside the scope, then the modus ponens should have been moved up before H and thus be outsid... | Deduction theorem | 0.81856 |
10,787 | From these axiom schemas one can quickly deduce the theorem schema P→P (reflexivity of implication), which is used below: (P→((Q→P)→P))→((P→(Q→P))→(P→P)) from axiom schema 2 with P, (Q→P), P P→((Q→P)→P) from axiom schema 1 with P, (Q→P) (P→(Q→P))→(P→P) from modus ponens applied to step 2 and step 1 P→(Q→P) from axiom s... | Deduction theorem | 0.81856 |
10,788 | In axiomatic versions of propositional logic, one usually has among the axiom schemas (where P, Q, and R are replaced by any propositions): Axiom 1 is: P→(Q→P) Axiom 2 is: (P→(Q→R))→((P→Q)→(P→R)) Modus ponens is: from P and P→Q infer QThese axiom schemas are chosen to enable one to derive the deduction theorem from the... | Deduction theorem | 0.81856 |
10,789 | If one intends to convert a complicated proof using the deduction theorem to a straight-line proof not using the deduction theorem, then it would probably be useful to prove these theorems once and for all at the beginning and then use them to help with the conversion: A → A {\displaystyle A\to A} helps convert the hyp... | Deduction theorem | 0.81856 |
10,790 | Then there is a formula C such that Δ ∪ { A } {\displaystyle \Delta \cup \{A\}} proves C {\displaystyle C} and C → B {\displaystyle C\to B} , and modus ponens is then used to prove B {\displaystyle B} . The proofs of C {\displaystyle C} and C → B {\displaystyle C\to B} are with at most n steps, and by the induction hyp... | Deduction theorem | 0.81856 |
10,791 | We prove the deduction theorem in a Hilbert-style deductive system of propositional calculus.Let Δ {\displaystyle \Delta } be a set of formulas and A {\displaystyle A} and B {\displaystyle B} formulas, such that Δ ∪ { A } ⊢ B {\displaystyle \Delta \cup \{A\}\vdash B} . We want to prove that Δ ⊢ A → B {\displaystyle \De... | Deduction theorem | 0.81856 |
10,792 | The deduction theorem holds for all first-order theories with the usual deductive systems for first-order logic. However, there are first-order systems in which new inference rules are added for which the deduction theorem fails. Most notably, the deduction theorem fails to hold in Birkhoff–von Neumann quantum logic, b... | Deduction theorem | 0.81856 |
10,793 | In the special case where Δ {\displaystyle \Delta } is the empty set, the deduction theorem claim can be more compactly written as: A ⊢ B {\displaystyle A\vdash B} implies ⊢ A → B {\displaystyle \vdash A\to B} . The deduction theorem for predicate logic is similar, but comes with some extra constraints (that would for ... | Deduction theorem | 0.81856 |
10,794 | In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis, i.e. to prove an implication A → B, it is sufficient to assume A as an hypothesis and then proceed to derive B. Deduction theorems exist for... | Deduction theorem | 0.81856 |
10,795 | Random sampling is a related, but distinct process. Random sampling is recruiting participants in a way that they represent a larger population. Because most basic statistical tests require the hypothesis of an independent randomly sampled population, random assignment is the desired assignment method because it provid... | Randomized assignment | 0.818556 |
10,796 | Consistency is one of the four guarantees that define ACID transactions; however, significant ambiguity exists about the nature of this guarantee. It is defined variously as: The guarantee that database constraints are not violated, particularly once a transaction commits. The guarantee that any transactions started in... | Data inconsistency | 0.818555 |
10,797 | The CAP theorem is based on three trade-offs, one of which is "atomic consistency" (shortened to "consistency" for the acronym), about which the authors note, "Discussing atomic consistency is somewhat different than talking about an ACID database, as database consistency refers to transactions, while atomic consistenc... | Data inconsistency | 0.818555 |
10,798 | Experts frequently describe five basic nonresidential learning community models: Linked courses: Students take two connected courses, usually one disciplinary course such as history or biology and one skills course such as writing, speech, or information literacy. Learning clusters: Students take three or more connecte... | Group learning | 0.818552 |
10,799 | Viral capsid are often composed of protomers. Examples in chemistry include tyrosine and 4-aminobenzoic acid. The former may be deprotonated to form the carboxylate and phenoxide anions, and the later may be protonated at the amino or carboxyl groups. | Protomer | 0.81855 |
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