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2,400 | In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity. I... | Consistent and inconsistent equations | 0.837569 |
2,401 | Plant physiology is a subdiscipline of botany concerned with the functioning, or physiology, of plants. Closely related fields include plant morphology (structure of plants), plant ecology (interactions with the environment), phytochemistry (biochemistry of plants), cell biology, genetics, biophysics and molecular biol... | Plant Physiology | 0.837568 |
2,402 | Theorem. Every group has a presentation. To see this, given a group G, consider the free group FG on G. By the universal property of free groups, there exists a unique group homomorphism φ: FG → G whose restriction to G is the identity map. Let K be the kernel of this homomorphism. | Finitely presented group | 0.837566 |
2,403 | A homogeneous binary relation is found in the power set of X × X for some set X, while a heterogeneous relation is found in the power set of X × Y, where X ≠ Y. Whether a given relation holds for two individuals is one bit of information, so relations are studied with Boolean arithmetic. Elements of the power set are p... | Calculus of relations | 0.837563 |
2,404 | Red–black trees offer worst-case guarantees for insertion time, deletion time, and search time. Not only does this make them valuable in time-sensitive applications such as real-time applications, but it makes them valuable building blocks in other data structures that provide worst-case guarantees; for example, many d... | Red–black tree | 0.837562 |
2,405 | Consequently, the group induced by the symmetric difference is in fact a vector space over the field with 2 elements Z2. If X is finite, then the singletons form a basis of this vector space, and its dimension is therefore equal to the number of elements of X. This construction is used in graph theory, to define the cy... | Disjunctive union | 0.837561 |
2,406 | electrodynamics The branch of physics that studies electrical charges and electrical currents. electrolyte A liquid or solid medium that carries electric current in the form of ions. electromagnet A magnet that generates a magnetic field from an electric current. | Glossary of electrical and electronics engineering | 0.837561 |
2,407 | n-grams find use in several areas of computer science, computational linguistics, and applied mathematics. They have been used to: design kernels that allow machine learning algorithms such as support vector machines to learn from string data find likely candidates for the correct spelling of a misspelled word improve ... | Word n-gram language model | 0.837556 |
2,408 | However, while its value is not known to great precision, the possibility of observing type Ia supernovae which happened in the universe's remote past, paired with the assumption that the physics involved in these events is universal, allows for an upper bound of less than 10−10 per year for the gravitational constant ... | Physical constant | 0.837552 |
2,409 | One flaw specific to LCGs is that, if used to choose points in an n-dimensional space, the points will lie on, at most, n√n!⋅m hyperplanes (Marsaglia's theorem, developed by George Marsaglia). This is due to serial correlation between successive values of the sequence Xn. Carelessly chosen multipliers will usually have... | Linear congruential generator | 0.83755 |
2,410 | The elastic deformation of bone is measured in μStrain. 1000μStrain = 0.1% change of length of the bone. Strain E at length l and change of length Δl: E = Δ l l {\displaystyle E={\frac {\Delta l}{l}}} It has to be considered that bone strength is highly dependent on geometry and direction of the acting forces in relati... | Mechanostat | 0.83755 |
2,411 | Directly related problems in computer science include: Pattern matching with don't cares or gaps, an unanchored string search with only the equivalent of ? defined. Pattern matching with wildcards, an unanchored string search with the equivalent of both wildcards defined. Has an exponential runtime unless a length-boun... | Matching wildcards | 0.837543 |
2,412 | Fixation is usually the first stage in a multistep process to prepare a sample of biological material for microscopy or other analysis. Therefore, the choice of fixative and fixation protocol may depend on the additional processing steps and final analyses that are planned. For example, immunohistochemistry uses antibo... | Fixation (histology) | 0.837542 |
2,413 | The NP-hardness of the Knapsack problem relates to computational models in which the size of integers matters (such as the Turing machine). In contrast, decision trees count each decision as a single step. Dobkin and Lipton show an 1 2 n 2 {\displaystyle {1 \over 2}n^{2}} lower bound on linear decision trees for the kn... | Knapsack constraints | 0.83754 |
2,414 | In computer science, one approach to the dynamic optimality problem on online algorithms for binary search trees involves reformulating the problem geometrically, in terms of augmenting a set of points in the plane with as few additional points as possible in order to avoid rectangles with only two points on their boun... | Geometry of binary search trees | 0.837539 |
2,415 | In mathematics, a group G is called the direct sum of two normal subgroups with trivial intersection if it is generated by the subgroups. In abstract algebra, this method of construction of groups can be generalized to direct sums of vector spaces, modules, and other structures; see the article direct sum of modules fo... | Direct sum of groups | 0.837528 |
2,416 | The positions are usually chosen such that the points ( t , x 1 , x 2 , … , x n ) {\displaystyle (t,x_{1},x_{2},\ldots ,x_{n})} make a uniform grid. The standard case, described above, represents n = 1 {\displaystyle n=1} . The general case of the slope field for systems of differential equations is not easy to visuali... | Slope field | 0.837527 |
2,417 | Available computational models provide molecular, thermodynamic, QSAR, atomic, graphical, and spectral properties. A calculation dialogue provides access to the following computational tasks: Energy – For a given geometry, provides energy and associated properties of a molecule or system. If quantum chemical models are... | Spartan (chemistry software) | 0.837521 |
2,418 | They do their computations using nine figures and symbol zero".In the Middle Ages, arithmetic was one of the seven liberal arts taught in universities. The flourishing of algebra in the medieval Islamic world, and also in Renaissance Europe, was an outgrowth of the enormous simplification of computation through decimal... | Arithmetic operations | 0.83752 |
2,419 | "In Physics II.3 and Metaphysics V.2, Aristotle holds that there are four kinds of answers to "why" questions: Matter The material cause of a change or movement. This is the aspect of the change or movement that is determined by the material that composes the moving or changing things. For a table, this might be wood; ... | Final causation | 0.837514 |
2,420 | The definition of the metre per second above satisfies this requirement since it, together with the definition of velocity, implies that v/mps = (d/m)/(t/s); thus if the ratios of distance and time to their units are determined, then so is the ratio of velocity to its unit. The definition, by itself, is inadequate sinc... | Coherent unit | 0.837513 |
2,421 | The ability to do algebra is a skill cultivated in mathematics education. As explained by Andrew Warwick, Cambridge University students in the early 19th century practiced "mixed mathematics", doing exercises based on physical variables such as space, time, and weight. Over time the association of variables with physic... | Syncopated algebra | 0.837512 |
2,422 | J. Algebra. 17 (2): 212–237. doi:10.1016/0021-8693(71)90030-5. | Algebraic K-group | 0.837511 |
2,423 | cDNA is also generated to analyze transcriptomic profiles in bulk tissue, single cells, or single nuclei in assays such as microarrays, qPCR, and RNA-seq. cDNA is also produced naturally by retroviruses (such as HIV-1, HIV-2, simian immunodeficiency virus, etc.) and then integrated into the host's genome, where it crea... | Complementary DNA | 0.83751 |
2,424 | Of the topics approached with the tools of theoretical physics, particular consideration is often given to stellar photospheres, stellar atmospheres, the solar atmosphere, planetary atmospheres, gaseous nebulae, nonstationary stars, and the interstellar medium. Special attention is given to the internal structure of st... | Theoretical astronomy | 0.8375 |
2,425 | Genomics in clinical careGenomic data are used to identify the genes involvement in unknown or rare conditions/syndromes. Currently, the most vigorous area of using genomics is oncology. The identification of genomic sequencing of cancer may define reasons of drug(s) sensitivity and resistance during oncological treatm... | Pharmacy informatics | 0.837499 |
2,426 | Near set theory provides a formal basis for the observation, comparison, and classification of elements in sets based on their closeness, either spatially or descriptively. Near sets offer a framework for solving problems based on human perception that arise in areas such as image processing, computer vision as well as... | Near sets | 0.837495 |
2,427 | For example, in the word sense induction and disambiguation task, there are three separate phases: In the training phase, evaluation task participants were asked to use a training dataset to induce the sense inventories for a set of polysemous words. The training dataset consisting of a set of polysemous nouns/verbs an... | SemEval | 0.837495 |
2,428 | Arguments against Dewdney's position are that neural nets have been successfully used to solve many complex and diverse tasks, such as autonomously flying aircraft.Technology writer Roger Bridgman commented on Dewdney's statements about neural nets: Neural networks, for instance, are in the dock not only because they h... | Neural networks | 0.837494 |
2,429 | Games of chance are not merely pure applications of probability calculus and gaming situations are not just isolated events whose numerical probability is well established through mathematical methods; they are also games whose progress is influenced by human action. In gambling, the human element has a striking charac... | Gambling mathematics | 0.837493 |
2,430 | In mathematics, there exist magmas that are commutative but not associative. A simple example of such a magma may be derived from the children's game of rock, paper, scissors. Such magmas give rise to non-associative algebras. A magma which is both commutative and associative is a commutative semigroup. | Commutative magma | 0.837491 |
2,431 | TOPOFIT-DB: Protein structural alignments based on the TOPOFIT method. Electron Density Server (EDS): Electron-density maps and statistics about the fit of crystal structures and their maps. CASP: Prediction Center Community-wide, worldwide experiment for protein structure prediction CASP. | Structural bioinformatics | 0.83749 |
2,432 | Testosterone was identified as 17β-hydroxyandrost-4-en-3-one (C19H28O2), a solid polycyclic alcohol with a hydroxyl group at the 17th carbon atom. This also made it obvious that additional modifications on the synthesized testosterone could be made, i.e., esterification and alkylation. The partial synthesis in the 1930... | Testosterone | 0.83749 |
2,433 | A four-point probe is used to avoid contact resistance, which can often have the same magnitude as the sheet resistance. Typically a constant current is applied to two probes, and the potential on the other two probes is measured with a high-impedance voltmeter. A geometry factor needs to be applied according to the sh... | Sheet resistance | 0.837488 |
2,434 | A motivating example that is neither a ring nor a lattice is the set of natural numbers N {\displaystyle \mathbb {N} } under ordinary addition and multiplication, when including the number zero. Semirings are abundant, because a suitable multiplication operation arises as the function composition of endomorphism over a... | Star semiring | 0.837487 |
2,435 | A Lie group is abelian exactly when all structure constants are 0. A Lie group is real exactly when its structure constants are real. The structure constants are completely anti-symmetric in all indices if and only if the Lie algebra is a direct sum of simple compact Lie algebras. A nilpotent Lie group admits a lattice... | Structure constant | 0.837486 |
2,436 | The additional factor of c in the metric is needed in physics if space and time are measured in different units; a similar factor would be required if, for example, the x direction were measured in meters while the y direction were measured in centimeters. Indeed, theoretical physicists usually work in units such that ... | Laplacian operator | 0.837485 |
2,437 | Mathematics Advanced: An advanced level calculus-based course with detailed study in probability and statistics, trigonometry, curve sketching, and applications of calculus. It is the highest level non-extension mathematics course. The calculus is only a single variable in all of year 12 mathematics in NSW. | Mathematics education in Australia | 0.83748 |
2,438 | In Proposition 43, he showed that the added force must be a central force, one whose magnitude depends only upon the distance r between the particle and a point fixed in space (the center). In Proposition 44, he derived a formula for the force, showing that it was an inverse-cube force, one that varies as the inverse c... | Newton's theorem of revolving orbits | 0.837479 |
2,439 | In principle, some of the sites can intersect and even coincide (an application is described below for sites representing shops), but usually they are assumed to be disjoint. In addition, infinitely many sites are allowed in the definition (this setting has applications in geometry of numbers and crystallography), but ... | Voronoi cell | 0.837473 |
2,440 | Specific applications of search algorithms include: Problems in combinatorial optimization, such as: The vehicle routing problem, a form of shortest path problem The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total wei... | Search algorithms | 0.837472 |
2,441 | In practice, it is often necessary to keep performance goals in mind when first designing software, but the programmer balances the goals of design and optimization. Modern compilers and operating systems are so efficient that the intended performance increases often fail to materialize. As an example, caching data at ... | Software optimization | 0.837471 |
2,442 | Arora, Sanjeev; Barak, Boaz (2009), Computational Complexity: A Modern Approach, Cambridge University Press, ISBN 978-0-521-42426-4, Zbl 1193.68112 Downey, Rod; Fellows, Michael (1999), Parameterized complexity, Monographs in Computer Science, Berlin, New York: Springer-Verlag, ISBN 9780387948836 Du, Ding-Zhu; Ko, Ker-... | Complexity of algorithms | 0.837461 |
2,443 | To: Paul Seeburger, Monroe Community College For: Dynamic Visualization for Multivariable Calculus | ICTCM Award | 0.837459 |
2,444 | Proof: Apply Statement 2 to M / N {\displaystyle M/N} .The following result manifests Nakayama's lemma in terms of generators.Statement 5: If M {\displaystyle M} is a finitely generated module over R {\displaystyle R} and the images of elements m {\displaystyle m} 1,..., m {\displaystyle m} n {\displaystyle n} of M {\d... | Nakayama lemma | 0.837457 |
2,445 | In this section, a ring can be viewed as merely an abstract set in which one can perform the operations of addition and multiplication; analogous to the integers. The ring of integers (that is, the set of integers with the natural operations of addition and multiplication) satisfy many important properties. One such pr... | Atomic domain | 0.837455 |
2,446 | :56The zero-degree relations represent true and false in relational algebra. :57 Under the closed-world assumption, an n-ary relation is interpreted as the extension of some n-adic predicate: all and only those n-tuples whose values, substituted for corresponding free variables in the predicate, yield propositions that... | Relation of degree zero | 0.837454 |
2,447 | Strip Algebra is a set of elements and operators for the description of carbon nanotube structures, considered as a subgroup of polyhedra, and more precisely, of polyhedra with vertices formed by three edges. This restriction is imposed on the polyhedra because carbon nanotubes are formed of sp2 carbon atoms. Strip Alg... | Strip algebra | 0.837451 |
2,448 | Using the rock-paper-scissors example, one can construct a commutative non-associative algebra over a field K {\displaystyle K}: take A {\displaystyle A} to be the three-dimensional vector space over K {\displaystyle K} whose elements are written in the form ( x , y , z ) = x r + y p + z s , {\displaystyle (x,y,z)=xr+y... | Commutative non-associative magmas | 0.837444 |
2,449 | Numerical or analytic solutions in quantum mechanics can be expressed as pure states. These solution states, called eigenstates, are labeled with quantized values, typically quantum numbers. For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant pure states are identified by... | Pure state | 0.837443 |
2,450 | In permutation groups, it has been proven, in Kantor and Kantor and Taylor, that a Sylow p-subgroup and its normalizer can be found in polynomial time of the input (the degree of the group times the number of generators). These algorithms are described in textbook form in Seress, and are now becoming practical as the c... | Sylow subgroup | 0.837442 |
2,451 | Preference is given to outstanding achievers at competitions and recipients of national prizes during the previous years of their education. The ranking process for candidates enrolling in the elementary school classes is similar, with mathematics entrance exam (max. 120 points), performance from the previous grades in... | Mathematical Grammar School | 0.837442 |
2,452 | They can be solved in time O ( n log n ) {\displaystyle O(n\log n)} for two or three dimensional point sets, and in time matching the worst-case output complexity given by the upper bound theorem in higher dimensions. As well as for finite point sets, convex hulls have also been studied for simple polygons, Brownian ... | Minimum convex polygon | 0.837441 |
2,453 | Whatever name is applied, it deals with the ways in which plants respond to their environment and so overlaps with the field of ecology. Environmental physiologists examine plant response to physical factors such as radiation (including light and ultraviolet radiation), temperature, fire, and wind. | Plant Physiology | 0.83744 |
2,454 | In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined in the early 20th century to distinguish it from older... | Abstract Algebra | 0.83744 |
2,455 | It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{*}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to ... | Learnable function class | 0.837438 |
2,456 | The general cubic equation a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} with integer coefficients has three solutions in the complex plane. If the rational root test finds no rational solutions, then the only way to express the solutions algebraically uses cube roots. But if the test finds a rationa... | Rational root test | 0.837437 |
2,457 | GF(2) (also denoted F 2 {\displaystyle \mathbb {F} _{2}} , Z/2Z or Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } ) is the finite field of two elements (GF is the initialism of Galois field, another name for finite fields). Notations Z2 and Z 2 {\displaystyle \mathbb {Z} _{2}} may be encountered although they can b... | Binary field | 0.837436 |
2,458 | The most careful example is taken from geometry, from where we shall give some definitions. He introduces the Class I concepts, which are primitive. Class I 1 point, 2 space, 3 included, 9 parts, 10 total, 14 number, 15 various Class II contains simple combinations. | De Arte Combinatoria | 0.837433 |
2,459 | In basic thermodynamics problems, when using the canonical ensemble, the use of just one parameter β {\displaystyle \beta } reflects the fact that there is only one expectation value that must be held constant: the free energy (due to conservation of energy). For chemistry problems involving chemical reactions, the gra... | Partition function (mathematics) | 0.837432 |
2,460 | When backgammon is played for money, the most common arrangement is to assign a monetary value to each point, and to play to a certain score, or until either player chooses to stop. The stakes are raised by gammons, backgammons, and use of the doubling cube. Backgammon is sometimes available in casinos. Before the comm... | Backgammon software | 0.837423 |
2,461 | This depends on the number of cards among the remaining 42 that will give him the best hand, and the current size of the pot. (Here, as in arguments involving the fundamental theorem, we assume that each player has complete information of their opponents' cards.) E = 0 {\displaystyle \operatorname {E} \left=0} E ... | Morton's theorem | 0.837423 |
2,462 | In computer science, merge-insertion sort or the Ford–Johnson algorithm is a comparison sorting algorithm published in 1959 by L. R. Ford Jr. and Selmer M. Johnson. It uses fewer comparisons in the worst case than the best previously known algorithms, binary insertion sort and merge sort, and for 20 years it was the so... | Ford–Johnson algorithm | 0.837419 |
2,463 | The strong equivalence principle can be tested by searching for a variation of Newton's gravitational constant G over the life of the universe, or equivalently, variation in the masses of the fundamental particles. A number of independent constraints, from orbits in the Solar System and studies of Big Bang nucleosynthe... | Principle of Equivalence | 0.837411 |
2,464 | By step 2, we have a complete and precise description of the character table of the CA group G. From this, and using the fact that G has odd order, sufficient information is available to obtain estimates for |G| and arrive at a contradiction to the assumption that G is simple. This part of the argument works similarly ... | Odd order theorem | 0.837408 |
2,465 | It is assessed in the categories: Knowledge & Procedures (KAPS); Modelling & Problem Solving (MAPS); Communication & Justification (CAJ). Although Maths A is not a pre-requisite subject, but it is sufficient for entrance to many tertiary courses.The course is divided into four semesters. The skills learned in each seme... | Mathematics education in Australia | 0.837407 |
2,466 | A modular complemented lattice is relatively complemented.17. A boolean algebra is relatively complemented. (1,15,16) 18. | Map of lattices | 0.837407 |
2,467 | In the experiment of rolling a die: Event {3, 5} (whose literal definition is the occurrence of 3 or 5) is compound because {3, 5}= {3} U {5}; Events {1}, {2}, {3}, {4}, {5}, {6} are elementary; Events {3, 5} and {4} are incompatible or exclusive because their intersection is empty; that is, they cannot occur simultane... | Gambling mathematics | 0.837404 |
2,468 | Distributed systems like Google Map Reduce, Microsoft Dryad, Apache Hadoop (an open-source project) and Google Pregel provide such platforms for businesses and users. However, even with these systems, big data analytics can take several hours, days or weeks to run, simply due to the data volumes involved. For example, ... | Data provenance | 0.837404 |
2,469 | Algorithms for computing the Pareto frontier of a finite set of alternatives have been studied in computer science and power engineering. They include: "The maxima of a point set". "The maximum vector problem" or the skyline query. "The scalarization algorithm" or the method of weighted sums. "The ϵ {\displaystyle \eps... | Pareto frontier | 0.837401 |
2,470 | In this basic urn model in probability theory, the urn contains x white and y black balls, well-mixed together. One ball is drawn randomly from the urn and its color observed; it is then placed back in the urn (or not), and the selection process is repeated.Possible questions that can be answered in this model are: Can... | Urn problem | 0.8374 |
2,471 | Pythagorean quadruples are sets of four integers such that the sum of the squares of the first three equals the square of the fourth. The Basel problem, solved by Euler in terms of π {\displaystyle \pi } , asked for an exact expression for the sum of the squares of the reciprocals of all positive integers. Rational tri... | Sum of squares | 0.837395 |
2,472 | Making decisions in many domains (such as natural language processing and computer vision problems) often involves assigning values to sets of interdependent variables where the expressive dependency structure can influence, or even dictate, what assignments are possible. These settings are applicable not only to Struc... | Constrained conditional model | 0.837395 |
2,473 | Lecture Notes in Computer Science. Vol. 4780. | Paraconsistent logics | 0.83739 |
2,474 | Helicopter dynamics is a field within aerospace engineering concerned with theoretical and practical aspects of helicopter flight. Its comprises helicopter aerodynamics, stability, control, structural dynamics, vibration, and aeroelastic and aeromechanical stability.By studying the forces in helicopter flight, improved... | Helicopter dynamics | 0.837386 |
2,475 | Mechatronics students take courses in various fields: Engineering Mathematics Mechanical engineering Electronics engineering Electrical engineering Materials science and engineering Computer engineering Computer aided and integrated manufacturing systems Computer-aided design Electronic design automation Computer Scien... | Mechatronic engineering | 0.837381 |
2,476 | The Genetic Analysis area includes capillary-based genotyping (Applied Biosystems TaqMan and SNaPshot, microsatellites), custom genotyping (e.g. heteroduplex analysis), mouse genotyping (for cross progeny and genetic linkage analysis), and methylation analysis (for epigenetics research). | Centre for Applied Genomics | 0.83738 |
2,477 | One useful application of calculating the rank of a matrix is the computation of the number of solutions of a system of linear equations. According to the Rouché–Capelli theorem, the system is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If on the other hand, the ... | Rank of a linear transformation | 0.837378 |
2,478 | Analyzing and quantifying the observation that the simplex algorithm is efficient in practice despite its exponential worst-case complexity has led to the development of other measures of complexity. The simplex algorithm has polynomial-time average-case complexity under various probability distributions, with the prec... | Simplex method | 0.837378 |
2,479 | Boolean algebra treats the equational theory of the maximal two-element finitary algebra, called the Boolean prototype, and the models of that theory, called Boolean algebras. These terms are defined as follows. An algebra is a family of operations on a set, called the underlying set of the algebra. We take the underly... | Boolean algebras canonically defined | 0.83737 |
2,480 | If the coloring fails one variable is "spilled" to memory and the coloring is retried.Instruction selection Most architectures, particularly CISC architectures and those with many addressing modes, offer several different ways of performing a particular operation, using entirely different sequences of instructions. The... | Compiler optimization | 0.83737 |
2,481 | E&M is equivalent to an introductory college course in electricity and magnetism for physics or engineering majors. The course modules are: Electrostatics Conductors, capacitors, and dielectrics Electric circuits Magnetic fields Electromagnetism.Methods of calculus are used wherever appropriate in formulating physical ... | AP Physics C: Electricity and Magnetism | 0.837365 |
2,482 | Because each H1 has the canonical order structure, G1 is a direct sum of Z 's (with the number of copies possible less than that in H1). So this gives a finite-dimensional algebra A1 whose dimension group is (G1 G1+, ). Next move u1 forward by defining u2 = φ12(u1). | AF C*-algebra | 0.837361 |
2,483 | Axioms (4) and (5) are the standard recursive definition of addition; (6) and (7) do the same for multiplication. Robinson arithmetic can be thought of as Peano arithmetic without induction. Q is a weak theory for which Gödel's incompleteness theorem holds. | List of first-order theories | 0.837357 |
2,484 | It also yields two other quantum numbers and the shape of the electron's wave function ("orbital") for the various possible quantum-mechanical states, thus explaining the anisotropic character of atomic bonds. The Schrödinger equation also applies to more complicated atoms and molecules. When there is more than one ele... | Hydrogen atom | 0.837357 |
2,485 | In image processing, a binary picture is a discrete square grid of 0 and 1, or equivalently, a compact subset of Z 2 {\displaystyle \mathbb {Z} ^{2}} . Topological invariants on R 2 {\displaystyle \mathbb {R} ^{2}} , such as number of components, might fail to be well-defined for Z 2 {\displaystyle \mathbb {Z} ^{2}} if... | Simple closed curve | 0.837357 |
2,486 | Board puzzles with algebra of binary variables ask players to locate the hidden objects based on a set of clue cells and their neighbors marked as variables (unknowns). A variable with value of 1 corresponds to a cell with an object. Contrary, a variable with value of 0 corresponds to an empty cell—no hidden object. | Board puzzles with algebra of binary variables | 0.837353 |
2,487 | For instance, the electric field is another rank-1 tensor field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime, or as a single-rank 2-tensor field.In the modern framework of the quantum theory of fields, even without referring to a test particle, a field oc... | Relativistic field theory | 0.837345 |
2,488 | Computational approaches will remain critical for research and teaching, especially when information science and genome biology is taught in conjunction. Comparative genomics starts with basic comparisons of genome size and gene density. For instance, genome size is important for coding capacity and possibly for regula... | Comparative Genomics | 0.837345 |
2,489 | Multicellularity has evolved independently at least 25 times in eukaryotes, and also in some prokaryotes, like cyanobacteria, myxobacteria, actinomycetes, Magnetoglobus multicellularis or Methanosarcina. However, complex multicellular organisms evolved only in six eukaryotic groups: animals, symbiomycotan fungi, brown ... | Multicellular organism | 0.837342 |
2,490 | Most courses involve algebra and calculus. Oftentimes, a MET graduate could get hired as an engineer; job titles may include Mechanical Engineer and Manufacturing Engineer. In the U.S. | Mechanical engineering technology | 0.837341 |
2,491 | At the fourth year students are taught the basics in all the special areas of Medical Laboratory Science. At the end of 400 level programme, successful students are presented for the First professional examination, to be moderated by the Medical Laboratory Science Council of Nigeria At the fifth year, students break in... | Medical technician | 0.837341 |
2,492 | Subjects taught in a prealgebra course may include: Review of natural number arithmetic Types of numbers such as integers, fractions, decimals and negative numbers Ratios and percents Factorization of natural numbers Properties of operations such as associativity and distributivity Simple (integer) roots and powers Rul... | Pre-algebra | 0.837338 |
2,493 | The basis evaluations for g may be performed by recursive calls to Chan's algorithm, and the violation tests may be performed by calls to the decision algorithm.With the assumption that the decision algorithm takes an amount of time O(T(n)) that grows at least polynomially as a function of the input size n, Chan shows ... | LP-type problem | 0.837337 |
2,494 | The culmination of all of those discoveries was a new field called genomics that links the molecular structure of a gene to the protein or RNA encoded by that segment of DNA and the functional expression of that protein within an organism. Today, through the application of molecular genetic techniques, genomics is bein... | Molecular Genetics | 0.837325 |
2,495 | : 31: 41 In 1922, Pauling graduated with a degree in chemical engineering. He went on to graduate school at the California Institute of Technology (Caltech) in Pasadena, California, under the guidance of Roscoe Dickinson and Richard Tolman. His graduate research involved the use of X-ray diffraction to determine the st... | Linus Pauling | 0.837324 |
2,496 | Hilbert's Entscheidungsproblem. Type inference and type checking for the second-order lambda calculus (or equivalent). Determining whether a first-order sentence in the logic of graphs can be realized by a finite undirected graph. Trakhtenbrot's theorem - Finite satisfiability is undecidable. Satisfiability of first or... | List of undecidable problems | 0.837321 |
2,497 | These graduate degree programs may include classroom and fieldwork, research at a laboratory, and a dissertation. Although a degree in a medicine or biology (biochemistry, microbiology, zoology, biophysics) is common, recent research projects also need graduates in statistics, bioinformatics, physics and chemistry. Abi... | Biomedical scientist | 0.837312 |
2,498 | Unsolved problems in astronomy Unsolved problems in biology Unsolved problems in chemistry Unsolved problems in geoscience Unsolved problems in medicine Unsolved problems in neuroscience Unsolved problems in physics | Lists of unsolved problems | 0.837312 |
2,499 | power electronicsThe class of electronic devices handling power greater than a watt. power engineeringThat part of electrical engineering that deals with the generation, distribution and consumption of electrical power. power-factor correctionApparatus intended to bring the power factor of some load closer to 1. power ... | Glossary of electrical and electronics engineering | 0.837312 |
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