id int32 0 100k | text stringlengths 20 3.54k | source stringlengths 1 104 | similarity float32 0.8 0.91 |
|---|---|---|---|
4,000 | (p. 11)With regard to the second theorem that "A 3CM can compute any partial recursive function" the author challenges the reader with a "Hard Problem: Multiply two numbers using only three counters" (p. 2). | Counter machine | 0.83337 |
4,001 | In both the and elements, coordinate-dependent formulas can be used instead of constants. These formulas can use various standard algebraic and mathematical operators and expressions. | Additive Manufacturing File Format | 0.833368 |
4,002 | In developing the Participatory Anthropic Principle (PAP), an interpretation of quantum mechanics, Wheeler used a variant on Twenty Questions, called Negative Twenty Questions, to show how the questions we choose to ask about the universe may dictate the answers we get. In this variant, the respondent does not choose o... | John Archibald Wheeler | 0.833365 |
4,003 | Although the operators ∧ {\displaystyle \wedge } (conjunction) and ∨ {\displaystyle \lor } (disjunction) are very useful in logic systems, they fail a more generalizable structure in the following way: The systems ( { T , F } , ∧ ) {\displaystyle (\{T,F\},\wedge )} and ( { T , F } , ∨ ) {\displaystyle (\{T,F\},\lor )} ... | Exclusive or | 0.833363 |
4,004 | In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short). In simple terms, problems in this class... | Constant ratio approximation | 0.83336 |
4,005 | As with much steroid chemistry, the Marker degradation relies heavily on kinetic control to degrade the sapogenin side chain while leaving similar functional groups on the steroid nucleus (relatively) unaffected. The first step is the reaction that led Marker to discover that the sapogenins had a ketone spiro acetal st... | Marker degradation | 0.833359 |
4,006 | Unit conversion is a notorious source of errors. Many people apply individual rules, e.g. "to obtain length in centimeters multiply the length in inches by 2.54", but combining several such conversions is laborious and prone to mistakes. A better way is to use the factor-label method, which is closely related to dimens... | Quantities, Units and Symbols in Physical Chemistry | 0.833348 |
4,007 | Fat Chance: Probability from 0 to 1 is an introductory undergraduate-level textbook on probability theory, centered on the metaphor of games of chance. It was written by Benedict Gross, Joe Harris, and Emily Riehl, based on a course for non-mathematicians taught to Harvard University undergraduates, and published by th... | Fat Chance: Probability from 0 to 1 | 0.833345 |
4,008 | There have been attempts to scour the literature for the papers in which ENCODE plays a significant part and since 2012 there have been 300 papers, 110 of which come from labs without ENCODE funding. An additional problem is that ENCODE is not a unique name dedicated to the ENCODE project exclusively, so the word 'enco... | ENCODE | 0.833343 |
4,009 | A Decision Procedure for a Class of Set Constraints (Technical report). School of Computer Science, Carnegie Mellon University. {{cite tech report}}: CS1 maint: multiple names: authors list (link) Kozen, D. | Set constraint | 0.83334 |
4,010 | Magnetohydrodynamics (MHD): Magnetic fields and turbulence in stars, accretion disks and galaxies; computer simulations ao dynamos, magnetic instabilities and magnetic convection Solar physics: Observation of sunspots and of solar magnetic field with spectro-polarimetry; Helioseismology and hydrodynamic numerical model... | Leibniz Institute for Astrophysics Potsdam | 0.833336 |
4,011 | Their existence would prove that the complexity classes P and NP are not equal, thus resolving the foremost unsolved question of theoretical computer science. : ex. 2.2, page 70 The converse is not known to be true, i.e. the existence of a proof that P≠NP would not directly imply the existence of one-way functions.In a... | One-way functions | 0.833335 |
4,012 | 1- Case-control study (Retrospective study) 2- Prospective study (Cohort study). 3- Population statistics. and 4- Intensive event report. 5- The spontaneous report in the case is the population of the single case report. | Pharmacovigilance | 0.833333 |
4,013 | Any group that is virtually abelian. Any nilpotent group. Any semidirect product N ⋊ H {\displaystyle N\rtimes H} where N is nilpotent and H is finite. Any semidirect product N ⋊ H {\displaystyle N\rtimes H} where N is finite and H is nilpotent.Gromov's theorem says that a finitely generated group is virtually nilpoten... | Virtually nilpotent | 0.833331 |
4,014 | However, there are other number systems that are not accurately described by these axioms; in particular, the theory defined in the same way for integers instead of real numbers is undecidable, even for existential sentences (Diophantine equations) by Matiyasevich's theorem.The existential theory of the reals is the fr... | Existential theory of the reals | 0.83333 |
4,015 | Finding the integer solutions of an equation or of a system of equations. These problems are now called Diophantine equations, which are considered a part of number theory (see also integer programming). Systems of polynomial equations: Because of their difficulty, these systems, with few exceptions, have been studied ... | Theory of equations | 0.83333 |
4,016 | Because the flat spring is anchored and strong in tension the curved spring cannot move it to the right. The curved spring presses, or pulls, the flat spring upward, that is away, from the anchor point. Owing to the geometry, the upward force is proportional to the displacement which decreases as the flat spring moves ... | Micro switch | 0.833327 |
4,017 | Using traditional pulse timing methods the range of the shell could be determined at the same instant. Simple trigonometry using the range and the known fixed vertical angle of the beam revealed the shell's vertical location. The time it took to cross one beam and then the other revealed the shell's speed. | Foster scanner | 0.833327 |
4,018 | If the compiler saves registers on the stack before calling a subroutine and restores them when returning, consecutive calls to subroutines may have redundant stack instructions. Suppose the compiler generates the following Z80 instructions for each procedure call: If there were two consecutive subroutine calls, they w... | Peephole optimizer | 0.833326 |
4,019 | List of combinatorial computational geometry topics enumerates the topics of computational geometry that states problems in terms of geometric objects as discrete entities and hence the methods of their solution are mostly theories and algorithms of combinatorial character. See List of numerical computational geometry ... | List of combinatorial computational geometry topics | 0.833323 |
4,020 | In biochemistry, phosphorylation is the attachment of a phosphate group to a molecule or an ion. This process and its inverse, dephosphorylation, are common in biology. Protein phosphorylation often activates (or deactivates) many enzymes. | Phosphorylation | 0.833322 |
4,021 | Subsequent work also used GPUs, initially for other types of neural networks (different from CNNs), especially unsupervised neural networks.In 2010, Dan Ciresan et al. at IDSIA showed that even deep standard neural networks with many layers can be quickly trained on GPU by supervised learning through the old method kno... | Max pooling | 0.833322 |
4,022 | The Rosseland Centre for Solar Physics combines theory, numerics and observations to provide insights into the solar atmosphere. It is regarded as one of the world's foremost solar physics research institutions. With an allocated amount of 115 million CPU hours in 2018, it also is the most data intensive research group... | Institute of Theoretical Astrophysics | 0.833321 |
4,023 | Strassen's algorithm can be parallelized to further improve the performance. As of December 2020, the best matrix multiplication algorithm is by Josh Alman and Virginia Vassilevska Williams and has complexity O(n2.3728596). It is not known whether matrix multiplication can be performed in n2 + o(1) time. This would be ... | Matrix–vector product | 0.833321 |
4,024 | Protein interactions: To screen for protein–protein interactions and protein interactions with other molecules such as metabolites, lipids, DNA and small molecules. ; enzyme inhibition assay: for high throughput drug candidate screening and to discover novel enzymes for use in biotechnology; screening antibody specific... | Cell-free protein array | 0.833321 |
4,025 | Nucleic acid analogues are used in molecular biology for several purposes: Investigation of possible scenarios of the origin of life: By testing different analogs, researchers try to answer the question of whether life's use of DNA and RNA was selected over time due to its advantages, or if they were chosen by arbitrar... | Base analog | 0.833318 |
4,026 | In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drud... | Free electron model | 0.833318 |
4,027 | Numbers, Powers, and Logarithms 1.2.3. Sums and Products 1.2.4. Integer Functions and Elementary Number Theory 1.2.5. | The Art of Computer Programming | 0.833318 |
4,028 | From June 23 to August 29, 1941, electrical engineering student J. Presper Eckert assisted in teaching a 10-week ESMDT course in electronics at the University of Pennsylvania's Moore School of Electrical Engineering. The course had 30 students, 16 of whom held Ph.D. degrees. | Engineering, Science, and Management War Training | 0.833315 |
4,029 | The "mean" operation x ⊕ y = ( x + y ) / 2 {\displaystyle x\oplus y=(x+y)/2} on the rational numbers (or any commutative number system closed under division) is also commutative but not in general associative, e.g. − 4 ⊕ ( 0 ⊕ + 4 ) = − 4 ⊕ + 2 = − 1 {\displaystyle -4\oplus (0\oplus +4)=-4\oplus +2=-1} but ( − 4 ⊕ 0 ) ... | Commutative non-associative magmas | 0.833313 |
4,030 | To release the DNA from the cells, the PCR is either started with an extended time at 95 °C (when standard polymerase is used), or with a shortened denaturation step at 100 °C and special chimeric DNA polymerase.The digital polymerase chain reaction simultaneously amplifies thousands of samples, each in a separate drop... | Variants of PCR | 0.833306 |
4,031 | Solutions to polynomial systems computed using numerical algebraic geometric methods can be certified, meaning that the approximate solution is "correct". This can be achieved in several ways, either a priori using a certified tracker, or a posteriori by showing that the point is, say, in the basin of convergence for N... | Homotopy continuation | 0.833305 |
4,032 | The relative simplicity of the algorithm makes it a popular first choice amongst optimizing algorithms. It is used widely in artificial intelligence, for reaching a goal state from a starting node. Different choices for next nodes and starting nodes are used in related algorithms. | Random-restart hill climbing | 0.833302 |
4,033 | AC, DC and transient electromagnetics Electrostatics, DC, AC and transient electric analysis Steady-state and transient heat transfer Stress analysis Coupled multiphysics | Quickfield | 0.833301 |
4,034 | In biochemistry, protein carbonylation refers to oxidation of the side chains of proteins to introduce ketone (>C=O) and aldehyde (−CH=O) groups in a protein. The following amino acid residues are affected: prolyl to pyrrolidone glutamyl to glutamic semialdehyde lysyl to aminoadipic acid semialdehyde threonyl to amino ... | Protein carbonylation | 0.833299 |
4,035 | BioEssays is a monthly peer-reviewed review journal covering molecular and cellular biology. Areas covered include genetics, genomics, epigenetics, evolution, developmental biology, neuroscience, human biology, physiology, systems biology, and plant biology. The journal also publishes commentaries on aspects of science... | BioEssays | 0.833297 |
4,036 | : 214–15 (Both the numerical factor and the power of the dependence on r would change if space were higher-dimensional; the correct expressions can be deduced from the geometry of higher-dimensional spheres. : 51 ) Likewise for Newton's law of universal gravitation: a factor of 4π naturally appears in Poisson's equatio... | Reduced Planck mass | 0.833295 |
4,037 | Possible catastrophic risks from nature include super-volcanism, impact events, and energetic astronomical events such as gamma-ray bursts, cosmic rays, solar flares, and supernovae. These dangers are characterized as relatively small and relatively well understood, though pandemics may be exceptions as a result of bei... | Future of Humanity Institute | 0.833293 |
4,038 | When developing a new test method, trial and error is often necessary in order to determine the proper spindle and speeds. Successful test methods will deliver a % torque reading between 10 and 100. The rheological behavior of the test fluid can be observed using the same spindle at different speeds, but because the ge... | Brookfield Engineering | 0.83329 |
4,039 | In computer science, counting sort is an algorithm for sorting a collection of objects according to keys that are small positive integers; that is, it is an integer sorting algorithm. It operates by counting the number of objects that possess distinct key values, and applying prefix sum on those counts to determine the... | Counting sort | 0.833288 |
4,040 | How much storage space will the master file consume? How many lines of program code will it take to perform this function? How can we cut down on CPU time when we run the system? What are the most efficient ways of storing this data? What database management system should we use? | Deployment management | 0.833287 |
4,041 | Source: Mathematical Optimization Society 1979: Richard M. Karp for classifying many important NP-complete problems. Kenneth Appel and Wolfgang Haken for the four color theorem. Paul Seymour for generalizing the max-flow min-cut theorem to matroids. 1982: D.B. | Fulkerson Prize | 0.833286 |
4,042 | The airfoil is generating lift, and the magnitude of the lift is given by the Kutta–Joukowski theorem. : § 4.5 One of the consequences of the Kutta condition is that the airflow over the topside of the airfoil travels much faster than the airflow under the underside. A parcel of air which approaches the airfoil along t... | Kutta condition | 0.833285 |
4,043 | For simple objects with geometric symmetry, one can often determine the moment of inertia in an exact closed-form expression. Typically this occurs when the mass density is constant, but in some cases the density can vary throughout the object as well. In general, it may not be straightforward to symbolically express t... | List of moments of inertia | 0.833284 |
4,044 | A first condition may be: necessary but not sufficient sufficient but not necessary both necessary and sufficient neither necessary nor sufficientfor a second condition to be true.Laypersons or novice scientists may prefer to think of these concepts of necessity and sufficiency in certain ways. In a study of undergradu... | Biological tests of necessity and sufficiency | 0.833282 |
4,045 | In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems are decidable if membership in their set of logically valid formulas (or th... | Decidability (logic) | 0.833282 |
4,046 | In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be.Leo Breiman distinguished two statistical modeling paradigms: data model and algorithm... | Machine learning algorithm | 0.833282 |
4,047 | Toolkits provide the following functionality: Read and save structures in various chemistry file formats. Determine if one structure is a substructure of another (substructure matching). Determine if two structures are equal (exact matching). Identification of substructures common to structures in a set (maximal common... | Cheminformatics toolkits | 0.833269 |
4,048 | A scientist may ask "why?" and proceed to research the answer to the question. By contrast, engineers want to know how to solve a problem, and how to implement that solution. Exploratory engineering often posits that a highly detailed solution exists, and explores the putative characteristics of such a solution, while ... | Exploratory engineering | 0.833268 |
4,049 | However, MICE can suffer from performance problems when the number of observation is large and the data have complex features, such as nonlinearities and high dimensionality. More recent approaches to multiple imputation use machine learning techniques to improve its performance. | Imputation (statistics) | 0.833265 |
4,050 | Otherwise, the letters x and y will be used for the variables. Explicit differential plots are differential equations whereby the highest derivative is given in terms of the lower derivatives. Differentiation is denoted by a prime (’). | KmPlot | 0.833262 |
4,051 | With the College of Engineering, the College of Chemistry offers two joint majors: chemical engineering/materials science & engineering and chemical engineering/nuclear engineering. Its graduate programs confer M.S. and Ph.D. degrees in chemical engineering, a Ph.D. in chemistry, and three professional master's degrees... | UC Berkeley College of Chemistry | 0.833254 |
4,052 | The multiple sequence alignment problem is generally based on pairwise sequence alignment and currently, for a pairwise sequence alignment problem, biologists can use a dynamic programming approach to obtain its optimal solution. However, the multiple sequence alignment problem is still one of the more challenging prob... | Tree alignment | 0.833251 |
4,053 | In fact, this approach can be considered as one of the implementations of the Artificial Intelligence thesis, which states that a computer can act as powerful advisor to humans. The development of GMDH consists of a synthesis of ideas from different areas of science: the cybernetic concept of "black box" and the princi... | Group method of data handling | 0.83325 |
4,054 | However, there is no exact definition of the term "discrete mathematics".The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business... | Discrete math | 0.833246 |
4,055 | Given a class of algebraic structures of the same signature, we can define the notions of homomorphism, subalgebra, and product. Garrett Birkhoff proved that a class of algebraic structures of the same signature is a variety if and only if it is closed under the taking of homomorphic images, subalgebras and arbitrary p... | Finitary algebraic category | 0.833241 |
4,056 | This type of sequencing is useful to capture isoforms and splice variants.SMRT sequencing has several applications in reproductive medical genetics research when investigating families with suspected parental gonadal mosaicism. Long reads enable haplotype phasing in patients to investigate parent-of-origin of mutations... | Single Molecule Real Time Sequencing | 0.83324 |
4,057 | A stable learning algorithm would produce a similar classifier with both the 1000-element and 999-element training sets. Stability can be studied for many types of learning problems, from language learning to inverse problems in physics and engineering, as it is a property of the learning process rather than the type o... | Stability (learning theory) | 0.833235 |
4,058 | The original paper Glauberman (1966) gave several criteria for an element to lie outside Z*(G). Its theorem 4 states: For an element t in T, it is necessary and sufficient for t to lie outside Z*(G) that there is some g in G and abelian subgroup U of T satisfying the following properties: g normalizes both U and the ce... | Z* theorem | 0.833235 |
4,059 | For example, the problem of trisecting an angle with a compass and straightedge is one that naturally occurs within the theory, since the axioms refer to constructive operations that can be carried out with those tools. However, centuries of efforts failed to find a solution to this problem, until Pierre Wantzel publis... | Euclid's postulates | 0.833233 |
4,060 | To become an electromechanical engineer, typical college courses involve mathematics, engineering, computer science, designing of machines, and other automotive classes that help gain skill in troubleshooting and analyzing issues with machines. To be an electromechanical engineer a bachelor's degree is required, usuall... | Electromechanics | 0.833232 |
4,061 | In reality, these long-range effects are suppressed by the flow of particles in response to electric fields. This flow reduces the effective interaction between particles to a short-range "screened" Coulomb interaction. This system corresponds to the simplest example of a renormalized interaction.In solid-state physics... | Electric-field screening | 0.833225 |
4,062 | There are numerous special classes of semigroups, semigroups with additional properties, which appear in particular applications. Some of these classes are even closer to groups by exhibiting some additional but not all properties of a group. Of these we mention: regular semigroups, orthodox semigroups, semigroups with... | Semigroup | 0.833225 |
4,063 | Function generators and wave-shaping circuits. Power supplies. Digital circuits: Boolean algebra, minimization of Boolean functions; logic gates digital IC families (DTL, TTL, ECL, MOS, CMOS). | Education and training of electrical and electronics engineers | 0.833223 |
4,064 | There are several formal analogies that can be made between electricity, which is invisible to the eye, and more familiar physical behaviors, such as the flowing of water or the motion of mechanical devices. In the case of capacitance, one analogy to a capacitor in mechanical rectilineal terms is a spring where the com... | Capacitor-spring analogy | 0.833219 |
4,065 | Prior to yield, material response can be assumed to be of a nonlinear elastic, viscoelastic, or linear elastic behavior. In materials science and engineering the von Mises yield criterion can also be formulated in terms of the von Mises stress or equivalent tensile stress, σ v {\displaystyle \sigma _{v}} . This is a sc... | Virtual leak | 0.833215 |
4,066 | Fractional cascading is a technique that speeds up binary searches for the same element in multiple sorted arrays. Searching each array separately requires O ( k log n ) {\textstyle O(k\log n)} time, where k {\textstyle k} is the number of arrays. Fractional cascading reduces this to O ( k + log n ) {\textstyle O(k... | Binary search algorithm | 0.833213 |
4,067 | They must study epidemiology, virology, parasitology, and statistics, as well as the training required of an ordinary MD. Research on tropical diseases and how to treat them comes from both field research and research centers, including those of the military.Sir Patrick Manson is recognized as the father of tropical me... | Tropical medicine | 0.833209 |
4,068 | Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins. The study of the former is historically older in, for example, the law of evidence, while the mathematical treatment ... | History of probability | 0.833208 |
4,069 | Conserved sequences are typically identified by bioinformatics approaches based on sequence alignment. Advances in high-throughput DNA sequencing and protein mass spectrometry has substantially increased the availability of protein sequences and whole genomes for comparison since the early 2000s. | Sequence conservation | 0.833204 |
4,070 | The process has been automated since the late 1970s and can be used to form desired genetic sequences as well as for other uses in medicine and molecular biology. However, creating sequences chemically is impractical beyond 200-300 bases, and is an environmentally hazardous process. These oligos, of around 200 bases, c... | DNA synthesis | 0.833204 |
4,071 | In Europe, the subject of probability was first formally developed in the 16th century with the work of Gerolamo Cardano, whose interest in the branch of mathematics was largely due to his habit of gambling. He formalized what is now called the classical definition of probability: if an event has a possible outcomes an... | Ars Conjectandi | 0.8332 |
4,072 | Therefore, if the compression variant is solvable in fixed-parameter tractable time, i.e., f(k) · nc for some constant c, then the iterative compression procedure solving the entire problem runs in f(k) · nc+1 time. The same technique can be applied to finding sets of edges for graph properties closed under subgraphs (... | Iterative compression | 0.8332 |
4,073 | Precisely: 2E6,sc(q) is a covering of 2E6(q), and 2E6,ad(q) lies in its automorphism group; when q+1 is not divisible by 3, all three coincide, and otherwise (when q is congruent to 2 mod 3), the degree of 2E6,sc(q) over 2E6(q) is 3 and 2E6(q) is of index 3 in 2E6,ad(q), which explains why 2E6,sc(q) and 2E6,ad(q) are o... | E6 (mathematics) | 0.833199 |
4,074 | The complete classification of Boolean clones given by Post helps to resolve various questions about classes of Boolean functions. For example: An inspection of the lattice shows that the maximal clones different from ⊤ (often called Post's classes) are M, D, A, P0, P1, and every proper subclone of ⊤ is contained in on... | Post's lattice | 0.833198 |
4,075 | The name, "Learning Classifier System (LCS)", is a bit misleading since there are many machine learning algorithms that 'learn to classify' (e.g. decision trees, artificial neural networks), but are not LCSs. The term 'rule-based machine learning (RBML)' is useful, as it more clearly captures the essential 'rule-based'... | Classifier system | 0.833194 |
4,076 | Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuit... | Magnetic field strength | 0.833192 |
4,077 | A subsequent report focused on biosecurity, especially the so-called dual-use challenge. For example, while synthetic biology may lead to more efficient production of medical treatments, it may also lead to synthesis or modification of harmful pathogens (e.g., smallpox). The biohacking community remains a source of spe... | Artificial life form | 0.833192 |
4,078 | {\displaystyle {\begin{aligned}\mathbb {Q} ({\sqrt {2}},{\sqrt {3}})&=\mathbb {Q} ({\sqrt {2}}+{\sqrt {3}})\\&=\left\{a+b({\sqrt {2}}+{\sqrt {3}})+c({\sqrt {2}}+{\sqrt {3}})^{2}+d({\sqrt {2}}+{\sqrt {3}})^{3}\mid a,b,c,d\in \mathbb {Q} \right\}.\end{aligned}}} Finite extensions of Q {\displaystyle \mathbb {Q} } are als... | Extension field | 0.833191 |
4,079 | Linear algebra is one of the central tools to modern engineering. Central to linear algebra is the notion of an orbit of vectors, with the matrices forming groups (matrices with inverses and identity) which act on the vectors. In linear algebra the equations describing the orbit elements the vectors are linear in the v... | Bayesian Estimation of Templates in Computational Anatomy | 0.833191 |
4,080 | Bioinformatics is not only taught as in-person masters degree at many universities. The computational nature of bioinformatics lends it to computer-aided and online learning. Software platforms designed to teach bioinformatics concepts and methods include Rosalind and online courses offered through the Swiss Institute ... | Bio informatics | 0.83319 |
4,081 | "In studying coin flipping, to observe the rotation speed of coin flips, Diaconis first used a strobe light and a coin with one side painted black, the other white, so that when the speed of the strobe flash equaled the rotation rate of the coin, it would appear to always show the same side. This proved difficult to us... | Coin flip | 0.833187 |
4,082 | A consequence arises from basic algebra in problems where people or systems work together. As an example, if a gas-powered pump can drain a pool in 4 hours and a battery-powered pump can drain the same pool in 6 hours, then it will take both pumps 6·4/6 + 4, which is equal to 2.4 hours, to drain the pool together. | Weighted harmonic mean | 0.833186 |
4,083 | f-block Faraday constant (F) A unit of electric charge widely used in electrochemistry equal to the negative of the molar charge (electric charge per mole) of electrons. It is equal to approximately 96,500 coulombs per mole (F = 96485.33212... C/mol). Faraday's laws of electrolysis A set of two laws pertaining to elect... | Glossary of chemistry terms | 0.833184 |
4,084 | But if the qij satisfy the Plücker relation q 23 + q 02 q 31 + q 03 q 12 = 0 , {\displaystyle q_{23}+q_{02}q_{31}+q_{03}q_{12}=0,} then p23 = q23, completing the set of identities. Consequently, α is a surjection onto the algebraic variety consisting of the set of zeros of the quadratic polynomial p 01 p 23 + p 02 p 31... | Plücker coordinates | 0.833181 |
4,085 | In chemistry the polyhedral skeletal electron pair theory (PSEPT) provides electron counting rules useful for predicting the structures of clusters such as borane and carborane clusters. The electron counting rules were originally formulated by Kenneth Wade, and were further developed by others including Michael Mingos... | Polyhedral skeletal electron pair theory | 0.833179 |
4,086 | The third part of the Rhind papyrus consists of the remainder of the 91 problems, being 61, 61B, 62–82, 82B, 83–84, and "numbers" 85–87, which are items that are not mathematical in nature. This final section contains more complicated tables of data (which frequently involve Horus eye fractions), several pefsu problems... | Rhind papyrus | 0.833177 |
4,087 | One of the better such formulae is that by Cromer, namely: T ≈ 2 π T 0 ln ( 4 / a ) {\textstyle T\approx {\frac {2}{\pi }}\,T_{0}\,\ln {(4/a)}} .Of course, the increase of T {\displaystyle T} with amplitude is more apparent when π / 2 < θ 0 < π {\displaystyle \pi /2<\theta _{0}<\pi } , as has been observed in many ex... | Physical pendulum | 0.833175 |
4,088 | The third decision was simple but crucial and added the 'R' to 'NURBS'. Circles were to be represented exactly: no cubic approximations would be allowed. By late 1979 there were 5 or 6 well-educated mathematicians (PhD's from Stanford, Harvard, Washington and Minnesota) and some had many years of software experience, b... | Solid Modeling Solutions | 0.833175 |
4,089 | ".Modern-day machine learning has two objectives, one is to classify data based on models which have been developed, the other purpose is to make predictions for future outcomes based on these models. A hypothetical algorithm specific to classifying data may use computer vision of moles coupled with supervised learning... | Applications of machine learning | 0.833174 |
4,090 | In mathematics, a group is said to have the infinite conjugacy class property, or to be an ICC group, if the conjugacy class of every group element but the identity is infinite.The von Neumann group algebra of a group is a factor if and only if the group has the infinite conjugacy class property. It will then be, provi... | Infinite conjugacy class property | 0.833174 |
4,091 | These systems can be compared by physical characteristics to which they respond, for example, trapped ions respond to electrical fields while spin systems will respond to magnetic fields. Trapped Ions are useful in their quantized motional levels which are strongly coupled to the electric field. They have been proposed... | Quantum sensor | 0.833173 |
4,092 | Source: NAS Mark E. Hay (2018) For developing algae as the major model for marine chemical ecology, and for elucidating how chemical cues and signals from algae structure marine and aquatic populations, communities, and ecosystems. Takao Kondo (2015) For demonstrating the occurrence of circadian clocks in prokaryotes, ... | Gilbert Morgan Smith Medal | 0.833168 |
4,093 | Common questions include: design of experiments and research studies plotting data measurement instruments (choosing, constructing and analysing) determination of adequate sample size to detect a hypothesised effect determination of an adequate sampling procedure for a study, survey or experiment supervision of data co... | Statistical consultant | 0.833167 |
4,094 | Acad. Arts Sciences 39 (17) (1904), 377–386. "Some elementary theorems concerning the steady flow of electricity in solid conductors", Ann. | Benjamin Osgood Peirce | 0.833165 |
4,095 | Assume that n > 2. Let u = e1e2en. It is easy to see that u2 = 1 (this only works if n > 2). If D were a division algebra, 0 = u2 − 1 = (u − 1)(u + 1) implies u = ±1, which in turn means: en = ∓e1e2 and so e1, ..., en−1 generate D. This contradicts the minimality of W. | Frobenius theorem (real division algebras) | 0.833162 |
4,096 | The classic applications of bispherical coordinates are in solving partial differential equations, e.g., Laplace's equation, for which bispherical coordinates allow a separation of variables. However, the Helmholtz equation is not separable in bispherical coordinates. A typical example would be the electric field surro... | Bispherical coordinates | 0.833161 |
4,097 | In electrochemistry, the electrochemical potential (ECP), μ, is a thermodynamic measure of chemical potential that does not omit the energy contribution of electrostatics. Electrochemical potential is expressed in the unit of J/mol. | Electrochemical potential | 0.833161 |
4,098 | A soft-switching three-level inverter (S3L inverter) is a high-efficiency power electronic inverter intended, in particular, for use with three-phase drives, as a grid-tie inverter for photovoltaic installations or wind turbines and in power supplies. The topology was developed in 2009 at HTWG Konstanz (Constance Unive... | Soft-switching three-level inverter | 0.833159 |
4,099 | Given the wide range of bacterial, viral, fungal, protozoal, and helminthic pathogens that cause debilitating and life-threatening illnesses, the ability to quickly identify the cause of infection is important yet often challenging. For example, more than half of cases of encephalitis, a severe illness affecting the br... | Infectious disease | 0.833155 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.