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900 | The d electron count or number of d electrons is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes. The formal... | D electron count | 0.845863 |
901 | The concepts of plant perception, communication, and intelligence have parallels in other biological organisms for which such phenomena appear foreign to or incompatible with traditional understandings of biology, or have otherwise proven difficult to study or interpret. Similar mechanisms exist in bacterial cells, cho... | Plant neurobiology | 0.845856 |
902 | One can check that the set of those strings with this operation forms a group with the empty string ε := "" being the identity element (Usually the quotation marks are left off; this is why the symbol ε is required). This is another infinite non-abelian group. Free groups are important in algebraic topology; the free g... | Dihedral group of order eight | 0.845853 |
903 | Mathematically, 1 is: in arithmetic (algebra) and calculus, the natural number that follows 0 and the multiplicative identity element of the integers, real numbers and complex numbers; more generally, in algebra, the multiplicative identity (also called unity), usually of a group or a ring.Formalizations of the natural... | 1 | 0.845852 |
904 | Usually, the structure has an addition, multiplication, and scalar multiplication (see Algebra over a field). When some authors use the term "algebra", they make a subset of the following additional assumptions: associative, commutative, unital, and/or finite-dimensional. In universal algebra, the word "algebra" refers... | Algebra | 0.845848 |
905 | It does not say how to choose the source resistance for a given load resistance. In fact, the source resistance that maximizes power transfer from a voltage source is always zero (the hypothetical ideal voltage source), regardless of the value of the load resistance. The theorem can be extended to alternating current c... | Maximum power transfer theorem | 0.845847 |
906 | In 2013, pgEd created a mobile educational quiz called Map-Ed. Map-Ed invites players to work their way through five questions that address key concepts in genetics and then pin themselves on a world map. Within weeks of its launch, Map-Ed gained over 1,000 pins around the world, spanning across all 7 continents. Trans... | Personal Genetics Education Project | 0.845817 |
907 | The most common type of equation is a polynomial equation (commonly called also an algebraic equation) in which the two sides are polynomials. The sides of a polynomial equation contain one or more terms. | Mathematical equations | 0.845813 |
908 | For example, students are typically taught to "solve" the hydrogen atom by a laborious process which begins by inserting the Coulomb potential into the Schrödinger equation. After a considerable amount of work using many differential equations, the analysis produces a recursion relation for the Laguerre polynomials. Th... | Supersymmetric Quantum Mechanics | 0.845805 |
909 | Machine Learning. 5 (2): 197–227. doi:10.1007/BF00116037. | Machine Learning (journal) | 0.845796 |
910 | If the sum of the degrees of x and y in each term is always even or always odd, then the curve is symmetric about the origin and the origin is called a center of the curve. Determine any bounds on the values of x and y. If the curve passes through the origin then determine the tangent lines there. For algebraic curves,... | Curve sketching | 0.845792 |
911 | This technology was pioneered by the NIXT and MSSTA sounding rockets in the 1990s, and it has been used to make telescopes for solar imaging. See also the Extreme Ultraviolet Explorer satellite. Some sources use the distinction of "hard UV" and "soft UV". For instance, in the case of astrophysics, the boundary may be a... | UV lamp | 0.845788 |
912 | The theoretical calculation of a material's constitutive equations is a common, important, and sometimes difficult task in theoretical condensed-matter physics and materials science. In general, the constitutive equations are theoretically determined by calculating how a molecule responds to the local fields through th... | Constitutive relations | 0.845779 |
913 | In two-dimensional geometry, it is known that if a point lies on two circles, then the circle centers and the two radii provide sufficient information to narrow the possible locations down to two – one of which is the desired solution and the other is an ambiguous solution. Additional information often narrow the possi... | True-range trilateration | 0.845774 |
914 | The Division 2 contest contains more difficult questions and is made for students with advanced conceptual understanding of physics. Students participating in the Division 2 contest usually take more than a year of physics while students who participate in the Division 1 contest usually take a year or less of physics. ... | Physics Bowl | 0.845772 |
915 | The empty product on numbers and most algebraic structures has the value of 1 (the identity element of multiplication), just like the empty sum has the value of 0 (the identity element of addition). However, the concept of the empty product is more general, and requires special treatment in logic, set theory, computer ... | Product (mathematics) | 0.845767 |
916 | Elimination of x {\displaystyle x} , y {\displaystyle y} , z {\displaystyle z} respectively yields: The orthogonal projection of the intersection curve onto the x {\displaystyle x} - y {\displaystyle y} -plane is the circle with equation ( x − r 2 ) 2 + y 2 = ( r 2 ) 2 . {\displaystyle \;\left(x-{\tfrac {r}{2}}\right)^... | Viviani's curve | 0.845765 |
917 | If the known sample sequence and questioned sequence originated from the same matriline, one would expect to see identical sequences and identical differences from the rCRS. Cases arise where there are no known samples to collect and the unknown sequence can be searched in a database such as EMPOP. The Scientific Worki... | Mitochondrial genome | 0.845762 |
918 | Type IV: The algebra generated by = 0, = y, = y + z. It is solvable and not unimodular. The simply connected group has trivial center and outer automorphism group the product of the reals and a group of order 2. The matrix M has two equal non-zero eigenvalues, but is not diagonalizable. | Bianchi classification | 0.845753 |
919 | The system is divided into two regions - one of which is treated with quantum mechanics (QM) allowing breaking and formation of bonds and the rest of the protein is modeled using molecular mechanics (MM). MM alone does not allow the study of mechanisms of enzymes, which QM allows. QM also produces more exact energy cal... | Molecular mechanics | 0.845732 |
920 | Fitness functions and selection environments (called training datasets in machine learning) are the two facets of fitness and are therefore intricately connected. Indeed, the fitness of a program depends not only on the cost function used to measure its performance but also on the training data chosen to evaluate fitne... | Gene expression programming | 0.845729 |
921 | Within the first part, the topics are grouped into statements related to the well-ordering principle, the axiom of choice itself, trichotomy (the ability to compare cardinal numbers), and Zorn's lemma and related maximality principles. This section also includes three more chapters, on statements in abstract algebra, s... | Equivalents of the Axiom of Choice | 0.845723 |
922 | Work on symbolic/knowledge-based learning did continue within AI, leading to inductive logic programming, but the more statistical line of research was now outside the field of AI proper, in pattern recognition and information retrieval. : 708–710, 755 Neural networks research had been abandoned by AI and computer scie... | Learning algorithms | 0.845712 |
923 | 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 | 0.845698 |
924 | Both the wet-lab and the bioinformatics parts of genome skimming have certain challenges with scalability. Although the cost of sequencing in genome skimming is affordable at $80 for 1 Gb in 2016, the library preparation for sequencing is still very expensive, at least ~$200 per sample (as of 2016). Additionally, most ... | Genome skimming | 0.845684 |
925 | {\displaystyle \mathrm {maj} =\mathrm {th} _{2}^{3}=(x\land y)\lor (x\land z)\lor (y\land z).} We denote elements of 2n (i.e., truth-assignments) as vectors: a = (a1, ..., an). The set 2n carries a natural product Boolean algebra structure. That is, ordering, meets, joins, and other operations on n-ary truth assignment... | Post's lattice | 0.845663 |
926 | A statement that is neither provable nor disprovable from a set of axioms is called undecidable (from those axioms). One example is the parallel postulate, which is neither provable nor refutable from the remaining axioms of Euclidean geometry. Mathematicians have shown there are many statements that are neither provab... | Proof method | 0.84565 |
927 | Problems 1–7, 7B and 8–40 are concerned with arithmetic and elementary algebra. Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions. | Rhind Mathematical Papyrus | 0.845645 |
928 | The wavelength of the station is λ = c/ν = 3 m, so that λ/(2π) = 48 cm and the volume is 0.109 m3. The energy content of this volume element is 2.1 × 10−10 × 0.109 = 2.3 × 10−11 J, which amounts to 3.4 × 1014 photons per λ 3 ( 2 π ) 3 . {\displaystyle {\tfrac {\lambda ^{3}}{(2\pi )^{3}}}.} Obviously, 3.4 × 1014 > 1 and... | Quantization of the electromagnetic field | 0.845628 |
929 | The usual rules of elementary arithmetic form an abstract rewriting system. For example, the expression (11 + 9) × (2 + 4) can be evaluated starting either at the left or at the right parentheses; however, in both cases the same result is eventually obtained. If every arithmetic expression evaluates to the same result ... | Confluence (abstract rewriting) | 0.845623 |
930 | Pentarane A, also known as D'6-pentarane or pregna-D'6-pentarane, as well as 16α,17α-cyclohexanoprogesterone, 16α,17α-tetramethylenepregn-4-ene-3,20-dione, or 17α-acetyl-16β,24-cyclo-21-norchol-4-en-3-one, is a steroidal progestin that was developed by the Zelinskii Institute of Organic Chemistry of the Russian Academy... | Pentarane A | 0.845622 |
931 | The age of the Sun cannot be measured directly; one way to estimate it is from the age of the oldest meteorites, and models of the evolution of the Solar System. The composition in the photosphere of the modern-day Sun, by mass, is 74.9% hydrogen and 23.8% helium. All heavier elements, called metals in astronomy, accou... | Standard Solar Model | 0.845616 |
932 | Sets are ubiquitous in modern mathematics. For example, structures in abstract algebra, such as groups, fields and rings, are sets closed under one or more operations. One of the main applications of naive set theory is in the construction of relations. A relation from a domain A to a codomain B is a subset of the Cart... | Finite subset | 0.845611 |
933 | Critics argue that the technique is inaccurate for comparison of closely related species, as any attempt to measure differences between orthologous sequences between organisms is overwhelmed by the hybridization of paralogous sequences within an organism's genome. DNA sequencing and computational comparisons of sequenc... | DNA–DNA hybridization | 0.845598 |
934 | A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xis which belong to some algebraically closed... | Polynomial system | 0.845592 |
935 | In chemistry and atomic physics, an electron shell, or principal energy level, may be thought of as the orbit of one or more electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), ... | Energy levels | 0.84559 |
936 | In mathematics, in the area of algebra known as group theory, a more than fifty-year effort was made to answer a conjecture of (Burnside 1911): are all groups of odd order solvable? Progress was made by showing that CA-groups, groups in which the centralizer of a non-identity element is abelian, of odd order are solvab... | CN-group | 0.845585 |
937 | Principle: If {X, R} is a partially ordered set, then {X, R(inverse)} is also a partially ordered set. There is nothing magical about the choice of symbols for the values of Boolean algebra. We could rename 0 and 1 to say α and β, and as long as we did so consistently throughout it would still be Boolean algebra, albei... | Boolean problem | 0.845583 |
938 | Both subgroups and normal subgroups of a given group form a complete lattice under inclusion of subsets; this property and some related results are described by the lattice theorem. Group homomorphism. These are functions f: ( G , ∗ ) → ( H , × ) {\displaystyle f\colon (G,*)\to (H,\times )} that have the special proper... | Glossary of group theory | 0.845579 |
939 | Terminal velocity depends on atmospheric drag, the coefficient of drag for the object, the (instantaneous) velocity of the object, and the area presented to the airflow. Apart from the last formula, these formulas also assume that g negligibly varies with height during the fall (that is, they assume constant accelerati... | Equations for a falling body | 0.845578 |
940 | The transfer homomorphism is a homomorphism that can be defined from any group G to the abelian group H/ defined by a subgroup H ≤ G of finite index, that is < ∞. The transfer map from a finite group G into its Sylow p-subgroup has a kernel that is easy to describe: The kernel of the transfer homomorphism from a finit... | Focal subgroup theorem | 0.845576 |
941 | Methods of importance to cellular biology, such as fluorescence probes (e.g., FRAP, FRET and GFP) and imaging, will be covered as appropriate within the context of the content below. A. Cellular Compartments of Prokaryotes and Eukaryotes: Organization, Dynamics and Functions Cellular membrane systems (e.g., structure a... | GRE Biochemistry, Cell and Molecular Biology Test | 0.845569 |
942 | Legend: NCBI SRA – National center for biotechnology information sequence read archive. Currently RNA-Seq relies on copying RNA molecules into cDNA molecules prior to sequencing; therefore, the subsequent platforms are the same for transcriptomic and genomic data. Consequently, the development of DNA sequencing technol... | Transcriptomics technique | 0.845566 |
943 | A set of five particular nitrogenous bases – adenine (A), guanine (G), cytosine (C), thymine (T), and uracil (U) – are especially relevant to biology because they are components of nucleotides, which in turn are the primary monomers that make up nucleic acids. non-canonical amino acid (ncAA) Also non-standard amino aci... | Glossary of genetics (M–Z) | 0.845563 |
944 | Ring-like structures with two binary operations and no other restrictions are a broad class, one which is too general to study. For this reason, the best-known kinds of non-associative algebras satisfy identities, or properties, which simplify multiplication somewhat. These include the following ones. | Nonassociative algebra | 0.845561 |
945 | In astronomy, the term albedo can be defined in several different ways, depending upon the application and the wavelength of electromagnetic radiation involved. | Albedo effects | 0.845542 |
946 | The first class of groups to undergo a systematic study was permutation groups. Given any set X and a collection G of bijections of X into itself (known as permutations) that is closed under compositions and inverses, G is a group acting on X. If X consists of n elements and G consists of all permutations, G is the sym... | Group Theory | 0.845542 |
947 | Because of the small RAM capacity of most systems originally used to run BASIC interpreters, clever memory management techniques had to be employed. Altair BASIC let users reclaim the space for trigonometry functions if those weren't being used during a session. PATB placed the start of the most common subroutines at t... | BASIC interpreter | 0.845541 |
948 | There is no net flow of water through the membrane. Osmosis can be demonstrated when potato slices are added to a high salt solution. The water from inside the potato moves out to the solution, causing the potato to shrink and to lose its 'turgor pressure'. The more concentrated the salt solution, the bigger the loss i... | Osmotic gradient | 0.845537 |
949 | The outer membrane, plasma membrane, and thylakoid membranes each have specialized roles in the cyanobacterial cell. Understanding the organization, functionality, protein composition, and dynamics of the membrane systems remains a great challenge in cyanobacterial cell biology.In contrast to the thylakoid network of h... | Thylakoid lumen | 0.845524 |
950 | Bisulfite sequencing DNA sequencing Expression cloning Fluorescence in situ hybridization Lab-on-a-chip Comparison of nucleic acid simulation software Northern blot Nuclear run-on assay Radioactivity in the life sciences Southern blot Differential centrifugation (sucrose gradient) Toeprinting assay Several bioinformati... | DNA purification | 0.845522 |
951 | The correct answer is then found by proportional adjustment, x = b/ b′ x′. Double false position is aimed at solving more difficult problems that can be written algebraically in the form: determine x such that f ( x ) = a x + c = 0 , {\displaystyle f(x)=ax+c=0,} if it is known that f ( x 1 ) = b 1 , f ( x 2 ) = b 2 . {... | False position | 0.845514 |
952 | He imagined an observer performing experiments on a rotating turntable. He noted that such an observer would find a different value for the mathematical constant π than the one predicted by Euclidean geometry. | History of general relativity | 0.845496 |
953 | Per EU directive 80/181/EEC (the "metric directive"), the correct symbol is lower-case "var", although the spellings "Var" and "VAr" are commonly seen, and "VAR" is widely used throughout the power industry. Volta potentialThe Volta potential (also called Volta potential difference, contact potential difference, outer ... | Virtual leak | 0.845489 |
954 | Multiplication is often defined for natural numbers, then extended to whole numbers, fractions, and irrational numbers. However, abstract algebra has a more general definition of multiplication as a binary operation on some objects that may or may not be numbers. Notably, one can multiply complex numbers, vectors, matr... | Multiplication and repeated addition | 0.845486 |
955 | In analytic geometry: The equation of a line: Ax + By = C, with A2 + B2 = 1 and C ≥ 0 The equation of a circle: ( x − h ) 2 + ( y − k ) 2 = r 2 {\displaystyle (x-h)^{2}+(y-k)^{2}=r^{2}} By contrast, there are alternative forms for writing equations. For example, the equation of a line may be written as a linear equatio... | Data normalization | 0.845469 |
956 | In computer science, tradeoffs are viewed as a tool of the trade. A program can often run faster if it uses more memory (a space–time tradeoff). Consider the following examples: By compressing an image, you can reduce transmission time/costs at the expense of CPU time to perform the compression and decompression. Depen... | Tradeoff analysis | 0.845465 |
957 | If the elements in the problem are real numbers, the decision-tree lower bound extends to the real random-access machine model with an instruction set that includes addition, subtraction and multiplication of real numbers, as well as comparison and either division or remaindering ("floor"). It follows that the problem'... | Element uniqueness problem | 0.84544 |
958 | A5 is the evident result of applying A2, A3 and A4 to the equation a ∗ = 1 ∪ a ; a ∗ {\displaystyle a{*}=1\cup a{\mathbin {;}}a{*}\,\!} of Kleene algebra. A6 asserts that if p {\displaystyle p\,\!} | Propositional dynamic logic | 0.845439 |
959 | Additionally, the model provides the spectrally-integrated (or "broadband") irradiance values, which can then be compared to measurements from a pyrheliometer (for direct radiation) or pyranometer (for diffuse or global radiation) at any instant. Besides the atmospheric conditions, another important input is the solar ... | Simple Model of the Atmospheric Radiative Transfer of Sunshine | 0.845437 |
960 | As the next result shows, these algebraic lattices are difficult to represent. Theorem (Freese, Lampe, and Taylor 1979). | Huhn's theorem | 0.84542 |
961 | The SAT Subject Test in Biology was the name of a one-hour multiple choice test given on biology by the College Board. A student chose whether to take the test depending upon college entrance requirements for the schools in which the student is planning to apply. Until 1994, the SAT Subject Tests were known as Achievem... | SAT Subject Test in Biology E/M | 0.845417 |
962 | This electromagnetic radiation is at the precise frequency of 1420.40575177 MHz, which is equivalent to the vacuum wavelength of 21.10611405413 cm in free space. This wavelength or frequency falls within the microwave radio region of the electromagnetic spectrum, and it is observed frequently in radio astronomy, since ... | Primeval Structure Telescope | 0.845409 |
963 | Solvability is closed under a number of operations. If G is solvable, and H is a subgroup of G, then H is solvable. If G is solvable, and there is a homomorphism from G onto H, then H is solvable; equivalently (by the first isomorphism theorem), if G is solvable, and N is a normal subgroup of G, then G/N is solvable. T... | Solvable subgroup | 0.845405 |
964 | The algebraic solutions do not distinguish between internal and external tangencies among the circles and the given triangle; if the problem is generalized to allow tangencies of either kind, then a given triangle will have 32 different solutions and conversely a triple of mutually tangent circles will be a solution fo... | Malfatti circles | 0.845401 |
965 | This casts fresh light on the ancient conundrum of the divisibility of matter. The multiplicity of a material object—the number of its parts—depends on the existence, not of delimiting surfaces, but of internal spatial relations (relative positions between parts), and these lack determinate values. According to the Sta... | Infinite divisibility | 0.845396 |
966 | Arthur Cayley's solution would be later found to be isomorphic to Solution II. Both solutions could be embedded in PG(3,2) though that geometry was not known at the time. However, in publishing his solutions to the schoolgirl problem, Kirkman neglected to refer readers to his own 1847 paper, and this omission would hav... | Kirkman's schoolgirl problem | 0.845382 |
967 | However, specialized cases (such as bounded/integer weights, directed acyclic graphs etc.) can indeed be improved further as detailed in Specialized variants. Additionally, if preprocessing is allowed algorithms such as contraction hierarchies can be up to seven orders of magnitude faster. In some fields, artificial in... | Dijkstra’s Algorithm | 0.845376 |
968 | Molecular biology techniques:Cloning and sequencing of genes such as that of ribosomal RNA, which allows researchers to determine total diversity within a sample DGGE (Denaturing Gel Electrophoresis), that is faster than the previous approach allows researchers to have an idea of the global diversity within a sample In... | Photosynthetic picoplankton | 0.845371 |
969 | A memory model allows a compiler to perform many important optimizations. Compiler optimizations like loop fusion move statements in the program, which can influence the order of read and write operations of potentially shared variables. Changes in the ordering of reads and writes can cause race conditions. Without a m... | Memory model (programming) | 0.845361 |
970 | Efficient solutions to these problems would have enormous implications for logistics. Many other important problems, such as some problems in protein structure prediction, are also NP-complete; if these problems were efficiently solvable, it could spur considerable advances in life sciences and biotechnology. But such ... | P vs. NP | 0.845357 |
971 | There may be several meanings of "solving an equation". One may want to express the solutions as explicit numbers; for example, the unique solution of 2x − 1 = 0 is 1/2. Unfortunately, this is, in general, impossible for equations of degree greater than one, and, since the ancient times, mathematicians have searched to... | Integer polynomial | 0.845344 |
972 | O1 Mathematics O2 Applied mathematics O3 Mechanics O4 Physics O6 Chemistry O7 Crystallography | Chinese Library Classification | 0.845331 |
973 | Around 1945, Alfred Tarski asked whether the free groups on two or more generators have the same first-order theory, and whether this theory is decidable. Sela (2006) answered the first question by showing that any two nonabelian free groups have the same first-order theory, and Kharlampovich & Myasnikov (2006) answere... | Free subgroup | 0.84533 |
974 | In convex geometry, two disjoint convex sets in n-dimensional Euclidean space are separated by a hyperplane, a result called the hyperplane separation theorem. In machine learning, hyperplanes are a key tool to create support vector machines for such tasks as computer vision and natural language processing. The datapoi... | Hyperplane | 0.845317 |
975 | Advanced Placement (AP) Physics C: Electricity and Magnetism (also known as AP Physics C: E&M or AP E&M) is an introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a second-semester calculus-based university course in electricity and magnetism.... | AP Physics C: Electricity and Magnetism | 0.845305 |
976 | With non-black surfaces, the deviations from ideal blackbody behavior are determined by both the surface structure, such as roughness or granularity, and the chemical composition. On a "per wavelength" basis, real objects in states of local thermodynamic equilibrium still follow Kirchhoff's Law: emissivity equals absor... | Thermal cavity | 0.845297 |
977 | For polynomials with more than one indeterminate, the combinations of values for the variables for which the polynomial function takes the value zero are generally called zeros instead of "roots". The study of the sets of zeros of polynomials is the object of algebraic geometry. For a set of polynomial equations with s... | Integer polynomial | 0.845293 |
978 | Trees possess the features to act like living pumps as it pulls water out of the ground for its physiological process. This feature attracted environmentalists and led them to think about the possibility of biological hydraulic containment. Plants such as willow, sunflower, okra, most of the poplars (such as aspen and ... | Hydraulic containment | 0.845287 |
979 | For any A, B, and C subgroups of a group with A ≤ C (A subgroup of C) then AB ∩ C = A(B ∩ C); the multiplication here is the product of subgroups. This property has been called the modular property of groups (Aschbacher 2000) or (Dedekind's) modular law (Robinson 1996, Cohn 2000). Since for two normal subgroups the pro... | Lattice of subgroups | 0.845266 |
980 | Whereas the above reciprocity theorems were for oscillating fields, Green's reciprocity is an analogous theorem for electrostatics with a fixed distribution of electric charge (Panofsky and Phillips, 1962). In particular, let ϕ 1 {\displaystyle \phi _{1}} denote the electric potential resulting from a total charge dens... | Lorentz reciprocity theorem | 0.845245 |
981 | Malhotra–Kumar–Maheshwari blocking flow (ru.) Manhattan distance many-one reduction Markov chain marriage problem (see assignment problem) Master theorem (analysis of algorithms) matched edge matched vertex matching (graph theory) matrix matrix-chain multiplication problem max-heap property maximal independent set maxi... | List of terms relating to algorithms and data structures | 0.845236 |
982 | NLP researchers were evenly split when asked, in a 2022 survey, whether (untuned) LLMs "could (ever) understand natural language in some nontrivial sense". Proponents of "LLM understanding" believe that some LLM abilities, such as mathematical reasoning, imply an ability to "understand" certain concepts. A Microsoft te... | Large Language Model | 0.845233 |
983 | A general system of m linear equations with n unknowns and coefficients can be written as { a 11 x 1 + a 12 x 2 + ⋯ + a 1 n x n + b 1 = 0 a 21 x 1 + a 22 x 2 + ⋯ + a 2 n x n + b 2 = 0 ⋮ a m 1 x 1 + a m 2 x 2 + ⋯ + a m n x n + b m = 0 , {\displaystyle {\begin{cases}a_{11}x_{1}+a_{12}x_{2}+\dots +a_{1n}x_{n}+b_{1}=0\\a_{... | Homogeneous system of linear equations | 0.845224 |
984 | Suppose now that in this classical system one of the N {\displaystyle N} charges, which we can label as number “1”, is pinned at some arbitrary position r 1 = r {\displaystyle \mathbf {r} _{1}=\mathbf {r} } inside the container. Clearly, the equilibrium position of the other N − 1 {\displaystyle N-1} charges will now n... | Strictly-Correlated-Electrons density functional theory | 0.845214 |
985 | In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mat... | Abstract group | 0.845199 |
986 | On-line Questions are uploaded again after the Summer School. The leftovers of the Summer School and other people who didn't join the Summer School have to take this test to join the Winter School 1. First grade students in the high school take this test. In this test, Organic Chemistry questions will appear more often... | Korean Chemistry Olympiad | 0.845197 |
987 | The front cover has a picture of the handwritten Poisson's equations for electricity and magnetism on a chalkboard. The first inner cover contains vector identities, vector derivatives in Cartesian, spherical, and cylindrical coordinates, and the fundamental theorems of vector calculus. The second inner cover contains ... | Introduction to Electrodynamics | 0.845173 |
988 | A specialized icosahedron die provides the answers of the Magic 8 Ball, conventionally used to provide answers to yes-or-no questions. Dice can be used to generate random numbers for use in passwords and cryptography applications. The Electronic Frontier Foundation describes a method by which dice can be used to genera... | Normal dice | 0.845164 |
989 | In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity el... | Multiplicative identity | 0.845159 |
990 | In it, he was asked by a professional gambler why if he bet on rolling at least one six in four throws of a die he won in the long term, whereas betting on throwing at least one double-six in 24 throws of two dice resulted in his losing. Fermat showed mathematically why this was the case.The first variational principle... | Pierre de Fermat | 0.845158 |
991 | As a whole, the phase diagram represents all that the system can be, and its shape can easily elucidate qualities of the system that might not be obvious otherwise. A phase space may contain a great number of dimensions. For instance, a gas containing many molecules may require a separate dimension for each particle's ... | Thermodynamic phase space | 0.845157 |
992 | In that programming paradigm, a given search problem is represented by a logic program so that the stable models of the program correspond to solutions. Then programs with many stable models correspond to problems with many solutions, and programs without stable models correspond to unsolvable problems. For instance, t... | Stable model | 0.845151 |
993 | Other metrics have also been applied to vectors of n-grams with varying, sometimes better, results. For example, z-scores have been used to compare documents by examining how many standard deviations each n-gram differs from its mean occurrence in a large collection, or text corpus, of documents (which form the "backgr... | Word n-gram language model | 0.845147 |
994 | Bioinformatics involves the development of techniques to store, data mine, search and manipulate biological data, including DNA nucleic acid sequence data. These have led to widely applied advances in computer science, especially string searching algorithms, machine learning, and database theory. String searching or ma... | Naked DNA | 0.84513 |
995 | In the Geometry paper, set on the second morning of the papers for candidates for the Gold Medal in the General Examination of the University of Dublin in October 1820, the following three problems appear. Question 10. Three equilateral triangles are thus constructed on the sides of a given triangle, A, B, D, the lines... | Napoleon's triangle | 0.845127 |
996 | Level 4. Rigor: At this level, geometry is understood at the level of a mathematician. Students understand that definitions are arbitrary and need not actually refer to any concrete realization. | Van Hiele model | 0.845125 |
997 | In computer science, shared memory is memory that may be simultaneously accessed by multiple programs with an intent to provide communication among them or avoid redundant copies. Shared memory is an efficient means of passing data between programs. Depending on context, programs may run on a single processor or on mul... | Shared memory (interprocess communication) | 0.845117 |
998 | The calculators includes program capacity of 26 kilobytes. This is divided among storage blocks for programs, statistics, matrices, lists, static and dynamic graphs and their associated settings, functions, recursions, equations, financial data, and variables (all of which are global). These can be cleared individually... | Casio 9850 series | 0.845099 |
999 | The Bohr model was able to explain the emission and absorption spectra of hydrogen. The energies of electrons in the n = 1, 2, 3, etc. states in the Bohr model match those of current physics. However, this did not explain similarities between different atoms, as expressed by the periodic table, such as the fact that he... | Sp orbital | 0.845098 |
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