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In algebraic geometry, a branch of mathematics, the Lefschetz theorem on (1,1)-classes, named after Solomon Lefschetz, is a classical statement relating holomorphic line bundles on a compact Kähler manifold to classes in its integral cohomology. It is the only case of the Hodge conjecture which has been proved for all ... | https://en.wikipedia.org/wiki/Lefschetz_theorem_on_%281%2C1%29-classes |
Engineering ethics is the field concerned with the system of moral principles that apply to the practice of engineering. The field examines and sets the obligations by engineers to society, to their clients, and to the profession. As a scholarly discipline, it is closely related to subjects such as the philosophy of sc... | https://en.wikipedia.org/wiki/Engineering_ethics |
The porous medium equation, also called the nonlinear heat equation, is a nonlinear partial differential equation taking the form:where
$$
\Delta
$$
is the Laplace operator. It may also be put into its equivalent divergence form:
$$
{\partial u\over{\partial t}} = \nabla \cdot \left[ D(u)\nabla u \right]
$$
where
$$... | https://en.wikipedia.org/wiki/Porous_medium_equation |
A van Emde Boas tree (), also known as a vEB tree or van Emde Boas priority queue, is a tree data structure which implements an associative array with -bit integer keys. It was invented by a team led by Dutch computer scientist Peter van Emde Boas in 1975. It performs all operations in time (assuming that an
$$
m
$$
... | https://en.wikipedia.org/wiki/Van_Emde_Boas_tree |
In discrete geometry, Tverberg's theorem, first stated by Helge Tverberg in 1966, is the result that sufficiently many points in Euclidean space can be partitioned into subsets with intersecting convex hulls. Specifically, for any positive integers
$$
d, r
$$
and any set of
$$
(d + 1)(r - 1) + 1\
$$
points in
$$
d
$... | https://en.wikipedia.org/wiki/Tverberg%27s_theorem |
Johnson's algorithm is a way to find the shortest paths between all pairs of vertices in an edge-weighted directed graph. It allows some of the edge weights to be negative numbers, but no negative-weight cycles may exist. It works by using the Bellman–Ford algorithm to compute a transformation of the input graph that r... | https://en.wikipedia.org/wiki/Johnson%27s_algorithm |
The random walker algorithm is an algorithm for image segmentation. In the first description of the algorithm, a user interactively labels a small number of pixels with known labels (called seeds), e.g., "object" and "background". The unlabeled pixels are each imagined to release a random walker, and the probability i... | https://en.wikipedia.org/wiki/Random_walker_algorithm |
A polyphase merge sort is a variation of a bottom-up merge sort that sorts a list using an initial uneven distribution of sub-lists (runs), primarily used for external sorting, and is more efficient than an ordinary merge sort when there are fewer than eight external working files (such as a tape drive or a file on a h... | https://en.wikipedia.org/wiki/Polyphase_merge_sort |
In graph theory, an orientation of an undirected graph is an assignment of a direction to each edge, turning the initial graph into a directed graph.
## Oriented graphs
A directed graph is called an oriented graph if none of its pairs of vertices is linked by two mutually symmetric edges. Among directed graphs, the ori... | https://en.wikipedia.org/wiki/Orientation_%28graph_theory%29 |
In physics, the cluster decomposition property states that experiments carried out far from each other cannot influence each other. Usually applied to quantum field theory, it requires that vacuum expectation values of operators localized in bounded regions factorize whenever these regions becomes sufficiently distant ... | https://en.wikipedia.org/wiki/Cluster_decomposition |
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance. Given that a system obeys detailed balance, the theorem is a proof that thermodynamic fluctuations in a physical variable pred... | https://en.wikipedia.org/wiki/Fluctuation%E2%80%93dissipation_theorem |
In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, sum type, or coproduct, is a data structure used to hold a value that could take on several different, but fixed, types. Only one of the types can be in use at any one time, and a tag field expl... | https://en.wikipedia.org/wiki/Tagged_union |
A Fenwick tree or binary indexed tree (BIT) is a data structure that stores an array of values and can efficiently compute prefix sums of the values and update the values. It also supports an efficient rank-search operation for finding the longest prefix whose sum is no more than a specified value. Its primary use is... | https://en.wikipedia.org/wiki/Fenwick_tree |
In computer science and operations research, randomized rounding
is a widely used approach for designing and analyzing approximation algorithms.
Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). For such problems, randomized rounding can be used to design fast ... | https://en.wikipedia.org/wiki/Randomized_rounding |
In statistics, the Wishart distribution is a generalization of the gamma distribution to multiple dimensions. It is named in honor of John Wishart, who first formulated the distribution in 1928. Other names include Wishart ensemble (in random matrix theory, probability distributions over matrices are usually called "en... | https://en.wikipedia.org/wiki/Wishart_distribution |
In mathematics, the Ornstein isomorphism theorem is a deep result in ergodic theory. It states that if two Bernoulli schemes have the same Kolmogorov entropy, then they are isomorphic.Donald Ornstein, "Ergodic Theory, Randomness and Dynamical Systems" (1974) Yale University Press, The result, given by Donald Ornstein... | https://en.wikipedia.org/wiki/Ornstein_isomorphism_theorem |
A rocket (from , and so named for its shape) is a vehicle that uses jet propulsion to accelerate without using any surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely from propellant carried within the vehicle; therefore a rocket can fly in the va... | https://en.wikipedia.org/wiki/Rocket |
In the mathematical subject of group theory, the Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality of a generating set) of a free product of two groups is equal to the sum of the ranks of the two free factors. The theorem was first obtained in a 1940 ar... | https://en.wikipedia.org/wiki/Grushko_theorem |
A kernel is a computer program at the core of a computer's operating system that always has complete control over everything in the system. The kernel is also responsible for preventing and mitigating conflicts between different processes. It is the portion of the operating system code that is always resident in memory... | https://en.wikipedia.org/wiki/Kernel_%28operating_system%29 |
In engineering, deformation (the change in size or shape of an object) may be elastic or plastic.
If the deformation is negligible, the object is said to be rigid.
## Main concepts
Occurrence of deformation in engineering applications is based on the following background concepts:
- Displacements are any change in posi... | https://en.wikipedia.org/wiki/Deformation_%28engineering%29 |
The Lomax distribution, conditionally also called the Pareto Type II distribution, is a heavy-tail probability distribution used in business, economics, actuarial science, queueing theory and Internet traffic modeling. It is named after K. S. Lomax. It is essentially a Pareto distribution that has been shifted so that... | https://en.wikipedia.org/wiki/Lomax_distribution |
A database transaction symbolizes a unit of work, performed within a database management system (or similar system) against a database, that is treated in a coherent and reliable way independent of other transactions. A transaction generally represents any change in a database. Transactions in a database environment ha... | https://en.wikipedia.org/wiki/Database_transaction |
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.
As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function ... | https://en.wikipedia.org/wiki/Asymptotic_analysis |
Fracture is the appearance of a crack or complete separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface... | https://en.wikipedia.org/wiki/Fracture |
Subjectivism is the doctrine that "our own mental activity is the only unquestionable fact of our experience", instead of shared or communal, and that there is no external or objective truth.
While Thomas Hobbes was an early proponent of subjectivism, the success of this position is historically attributed to Descartes... | https://en.wikipedia.org/wiki/Subjectivism |
In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set called the codomain. Precisely, a binary relation over sets
$$
X
$$
and
$$
Y
$$
is a set of ordered pairs
$$
(x, y)
$$
, where
$$
x
$$
is an element of
$$
X
$$
and
$$
y
$$
is an element... | https://en.wikipedia.org/wiki/Binary_relation |
John Scott Russell (9 May 1808, Parkhead, Glasgow – 8 June 1882, Ventnor, Isle of Wight) was a Scottish civil engineer, naval architect and shipbuilder who built Great Eastern in collaboration with Isambard Kingdom Brunel. He made the discovery of the wave of translation that gave birth to the modern study of solitons,... | https://en.wikipedia.org/wiki/John_Scott_Russell |
In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time) is a specific type of "random time": a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behav... | https://en.wikipedia.org/wiki/Stopping_time |
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function:
$$
\psi(z) = \frac{\mathrm{d}}{\mathrm{d}z}\ln\Gamma(z) = \frac{\Gamma'(z)}{\Gamma(z)}.
$$
It is the first of the polygamma functions. This function is strictly increasing and strictly concave on
$$
(0,\infty)
$$
, and... | https://en.wikipedia.org/wiki/Digamma_function |
The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.
In ... | https://en.wikipedia.org/wiki/Exterior_angle_theorem |
In the mathematical field of order theory, a partially ordered set is bounded complete if all of its subsets that have some upper bound also have a least upper bound. Such a partial order can also be called consistently or coherently complete (Visser 2004, p. 182), since any upper bound of a set can be interpreted as s... | https://en.wikipedia.org/wiki/Bounded_complete_poset |
In game theory, a sequential game is defined as a game where one player selects their action before others, and subsequent players are informed of that choice before making their own decisions. This turn-based structure, governed by a time axis, distinguishes sequential games from simultaneous games, where players act ... | https://en.wikipedia.org/wiki/Sequential_game |
In economics, Kondratiev waves (also called supercycles, great surges, long waves, K-waves or the long economic cycle) are hypothesized cycle-like phenomena in the modern world economy. The phenomenon is closely connected with the technology life cycle.
It is stated that the period of a wave ranges from forty to sixty ... | https://en.wikipedia.org/wiki/Kondratiev_wave |
Filtering in the context of large eddy simulation (LES) is a mathematical operation intended to remove a range of small scales from the solution to the Navier-Stokes equations. Because the principal difficulty in simulating turbulent flows comes from the wide range of length and time scales, this operation makes turbu... | https://en.wikipedia.org/wiki/Filter_%28large_eddy_simulation%29 |
In business, engineering, and manufacturing, quality – or high quality – has a pragmatic interpretation as the non-inferiority or superiority of something (goods or services); it is also defined as being suitable for the intended purpose (fitness for purpose) while satisfying customer expectations. Quality is a percept... | https://en.wikipedia.org/wiki/Quality_%28business%29 |
In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma.
Different states are distinguished by the ways the component particles (atoms, molecules, ions and electrons) are arranged, and how they behave col... | https://en.wikipedia.org/wiki/State_of_matter |
In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as
$$
ax^2 + bx + c = 0\,,
$$
where the variable represents an unknown number, and , , and represent known numbers, where . (If and then the equation is linear, not quadratic.) The numbers , , and are the coefficients of... | https://en.wikipedia.org/wiki/Quadratic_equation |
The El Farol bar problem is a problem in game theory. Every Thursday night, a fixed population want to go have fun at the El Farol Bar, unless it's too crowded.
- If less than 60% of the population go to the bar, they'll all have more fun than if they stayed home.
- If more than 60% of the population go to the bar, the... | https://en.wikipedia.org/wiki/El_Farol_Bar_problem |
For parsing algorithms in computer science, the inside–outside algorithm is a way of re-estimating production probabilities in a probabilistic context-free grammar. It was introduced by James K. Baker in 1979 as a generalization of the forward–backward algorithm for parameter estimation on hidden Markov models to stoch... | https://en.wikipedia.org/wiki/Inside%E2%80%93outside_algorithm |
A nomogram (), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne (1862–1938) and... | https://en.wikipedia.org/wiki/Nomogram |
Rock, Paper, Scissors (also known by several other names and word orders) is an intransitive hand game, usually played between two people, in which each player simultaneously forms one of three shapes with an outstretched hand. These shapes are "rock" (a closed fist: ✊), "paper" (a flat hand: 🖐), and "scissors" (a fis... | https://en.wikipedia.org/wiki/Rock_paper_scissors |
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occur... | https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance |
In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers.
The study of hypercomplex numbers in the late 19th century forms the basis of modern group representation theory.
## History
In the nineteenth century, number systems called q... | https://en.wikipedia.org/wiki/Hypercomplex_number |
In particle physics, bremsstrahlung (; ; ) is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., photons), thus satisfying ... | https://en.wikipedia.org/wiki/Bremsstrahlung |
In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle , and a transversal line that crosses at points respectively, with distinct from . A weak version of the theorem states that
$$
\left|\frac{\overline{AF}}{\overl... | https://en.wikipedia.org/wiki/Menelaus%27s_theorem |
In computer graphics, the winged edge data structure is a way to represent polygon meshes in computer memory. It is a type of boundary representation and describes both the geometry and topology of a model. Three types of records are used: vertex records, edge records, and face records. Given a reference to an edge rec... | https://en.wikipedia.org/wiki/Winged_edge |
In formal language theory, an alphabet, sometimes called a vocabulary, is a non-empty set of indivisible symbols/characters/glyphs, typically thought of as representing letters, characters, digits, phonemes, or even words. The definition is used in a diverse range of fields including logic, mathematics, computer scienc... | https://en.wikipedia.org/wiki/Alphabet_%28formal_languages%29 |
Politics () is the set of activities that are associated with making decisions in groups, or other forms of power relations among individuals, such as the distribution of status or resources.
The branch of social science that studies politics and government is referred to as political science.
Politics may be used posi... | https://en.wikipedia.org/wiki/Politics |
Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections of decreasing nested sequences of non-empty compact sets.
## Topological statement
Theorem. Let be a topological space. A decreasing nested sequence of non-empty com... | https://en.wikipedia.org/wiki/Cantor%27s_intersection_theorem |
In differential calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem, named after Osborne Reynolds (1842–1912), is a three-dimensional generalization of the Leibniz integral rule. It is used to recast time derivatives of integrated quantities an... | https://en.wikipedia.org/wiki/Reynolds_transport_theorem |
Control tables are tables that control the control flow or play a major part in program control. There are no rigid rules about the structure or content of a control table—its qualifying attribute is its ability to direct control flow in some way through "execution" by a processor or interpreter. The design of such tab... | https://en.wikipedia.org/wiki/Control_table |
A pairing heap is a type of heap data structure with relatively simple implementation and excellent practical amortized performance, introduced by Michael Fredman, Robert Sedgewick, Daniel Sleator, and Robert Tarjan in 1986.
Pairing heaps are heap-ordered multiway tree structures, and can be considered simplified Fibon... | https://en.wikipedia.org/wiki/Pairing_heap |
The Caverphone within linguistics and computing, is a phonetic matching algorithm invented to identify English names with their sounds, originally built to process a custom dataset compound between 1893 and 1938 in southern Dunedin, New Zealand. Started from a similar concept as metaphone, it has been developed to acco... | https://en.wikipedia.org/wiki/Caverphone |
In theoretical physics a nonrenormalization theorem is a limitation on how a certain quantity in the classical description of a quantum field theory may be modified by renormalization in the full quantum theory. Renormalization theorems are common in theories with a sufficient amount of supersymmetry, usually at least... | https://en.wikipedia.org/wiki/Supersymmetry_nonrenormalization_theorems |
In computer science, introselect (short for "introspective selection") is a selection algorithm that is a hybrid of quickselect and median of medians which has fast average performance and optimal worst-case performance. Introselect is related to the introsort sorting algorithm: these are analogous refinements of the b... | https://en.wikipedia.org/wiki/Introselect |
A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the thousands separator used in digit grouping.... | https://en.wikipedia.org/wiki/Decimal_separator |
In mathematics, a percentage () is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign (%), although the abbreviations pct., pct, and sometimes pc are also used. A percentage is a dimensionless number (pure number), primarily used for expressing proportions, but percent is nonet... | https://en.wikipedia.org/wiki/Percentage |
In mathematics, Grunsky's theorem, due to the German mathematician Helmut Grunsky, is a result in complex analysis concerning holomorphic univalent functions defined on the unit disk in the complex numbers. The theorem states that a univalent function defined on the unit disc, fixing the point 0, maps every disk |z| <... | https://en.wikipedia.org/wiki/Grunsky%27s_theorem |
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation between the group means to the amount of variation within each group. If the between-group variation is substantially larger than th... | https://en.wikipedia.org/wiki/Analysis_of_variance |
In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) of a partially ordered set
$$
(X, \leq)
$$
is a subset
$$
S \subseteq X
$$
with the following property: if s is in S and if x in X is larger than s (that is, if
$$
s < x
$$
), then x is in S. In other words, this mean... | https://en.wikipedia.org/wiki/Upper_set |
In computer science, the maximum sum subarray problem, also known as the maximum segment sum problem, is the task of finding a contiguous subarray with the largest sum, within a given one-dimensional array A[1...n] of numbers. It can be solved in
$$
O(n)
$$
time and
$$
O(1)
$$
space.
Formally, the task is to find i... | https://en.wikipedia.org/wiki/Maximum_subarray_problem |
A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds, or some combination of these effects. Chemical bonds are des... | https://en.wikipedia.org/wiki/Chemical_bond |
Millimeter-wave cloud radars, also denominated cloud radars, are radar systems designed to monitor clouds with operating frequencies between 24 and 110 GHz (Table 1). Accordingly, their wavelengths range from 1 mm to 1.11 cm, about ten times shorter than those used in conventional S band radars such as NEXRAD.
## Purpo... | https://en.wikipedia.org/wiki/Millimeter_cloud_radar |
The basic study of system design is the understanding of component parts and their subsequent interaction with one another.
Systems design has appeared in a variety of fields, including sustainability, computer/software architecture, and sociology.
## Product Development
If the broader topic of product development "ble... | https://en.wikipedia.org/wiki/Systems_design |
Slow-wave sleep (SWS), often referred to as deep sleep, is the third stage of non-rapid eye movement sleep (NREM), where electroencephalography activity is characterised by slow delta waves.
Slow-wave sleep usually lasts between 70 and 90 minutes, taking place during the first hours of the night. Slow-wave sleep is cha... | https://en.wikipedia.org/wiki/Slow-wave_sleep |
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solution... | https://en.wikipedia.org/wiki/Quantum_chemistry |
In mathematics, the Riemann series theorem, also called the Riemann rearrangement theorem, named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an a... | https://en.wikipedia.org/wiki/Riemann_series_theorem |
In statistics and machine learning, when one wants to infer a random variable with a set of variables, usually a subset is enough, and other variables are useless. Such a subset that contains all the useful information is called a
## Markov blanket
. If a Markov blanket is minimal, meaning that it cannot drop any vari... | https://en.wikipedia.org/wiki/Markov_blanket |
In mathematics, particularly in the field of topology, the K-topology, also called Smirnov's deleted sequence topology, is a topology on the set R of real numbers which has some interesting properties. Relative to the standard topology on R, the set
$$
K = \{1/n:n=1,2,\dots\}
$$
is not closed since it doesn't contain... | https://en.wikipedia.org/wiki/K-topology |
Rayleigh waves are a type of surface acoustic wave that travel along the surface of solids. They can be produced in materials in many ways, such as by a localized impact or by piezo-electric transduction, and are frequently used in non-destructive testing for detecting defects. Rayleigh waves are part of the seismic wa... | https://en.wikipedia.org/wiki/Rayleigh_wave |
The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets ... | https://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle |
Alpha waves, or the alpha rhythm, are neural oscillations in the frequency range of 8–12 Hz likely originating from the synchronous and coherent (in phase or constructive) neocortical neuronal electrical activity possibly involving thalamic pacemaker cells. Historically, they are also called "Berger's waves" after Hans... | https://en.wikipedia.org/wiki/Alpha_wave |
Cuckoo hashing is a scheme in computer programming for resolving hash collisions of values of hash functions in a table, with worst-case constant lookup time. The name derives from the behavior of some species of cuckoo, where the cuckoo chick pushes the other eggs or young out of the nest when it hatches in a variatio... | https://en.wikipedia.org/wiki/Cuckoo_hashing |
An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosphere is the outer region of a star, which includes the layers above the opaque phot... | https://en.wikipedia.org/wiki/Atmosphere |
Tetris () is a series of puzzle video games created in 1985 by Alexey Pajitnov, a Soviet software engineer. In Tetris games, falling tetromino shapes must be neatly sorted into a pile; once a horizontal line of the game board is filled in, it disappears, granting points and preventing the pile from overflowing. Differe... | https://en.wikipedia.org/wiki/Tetris |
In computer programming and software design, code refactoring is the process of restructuring existing source code—changing the factoring—without changing its external behavior. Refactoring is intended to improve the design, structure, and/or implementation of the software (its non-functional attributes), while preserv... | https://en.wikipedia.org/wiki/Code_refactoring |
In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short-rate model as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives, and has also been adapte... | https://en.wikipedia.org/wiki/Vasicek_model |
In physics, a surface wave is a mechanical wave that propagates along the interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at the interface between two fluids with different densities. Elastic surface ... | https://en.wikipedia.org/wiki/Surface_wave |
Zero to the power of zero, denoted as , is a mathematical expression with different interpretations depending on the context. In certain areas of mathematics, such as combinatorics and algebra, is conventionally defined as 1 because this assignment simplifies many formulas and ensures consistency in operations involvi... | https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero |
In mathematics, a binary relation
$$
R
$$
on a set
$$
X
$$
is antisymmetric if there is no pair of distinct elements of
$$
X
$$
each of which is related by
$$
R
$$
to the other. More formally,
$$
R
$$
is antisymmetric precisely if for all
$$
a, b \in X,
$$
$$
\text{if } \,aRb\, \text{ with } \,a \neq b\, \te... | https://en.wikipedia.org/wiki/Antisymmetric_relation |
In quantum field theory, the Casimir effect (or Casimir force) is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of a field. The term Casimir pressure is sometimes used when it is described in units of force per unit area. It is named after the Dutch... | https://en.wikipedia.org/wiki/Casimir_effect |
In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
The distribution is... | https://en.wikipedia.org/wiki/Weibull_distribution |
In computer programming, a software framework is a software abstraction that provides generic functionality which developers can extend with custom code to create applications. It establishes a standard foundation for building and deploying software, offering reusable components and design patterns that handle common p... | https://en.wikipedia.org/wiki/Software_framework |
The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows:
Let be the midpoint of a chord of a circle, through which two other chords and are drawn; and intersect chord at and correspondingly. Then is the midpoint of .
## Proof
A formal proof of the theorem is as follow... | https://en.wikipedia.org/wiki/Butterfly_theorem |
In computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program consists of commands for the computer to perform. Imperative programming focu... | https://en.wikipedia.org/wiki/Imperative_programming |
In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example,
is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and ... | https://en.wikipedia.org/wiki/Finite_set |
In the mathematical field of topology, a regular homotopy refers to a special kind of homotopy between immersions of one manifold in another. The homotopy must be a 1-parameter family of immersions.
Similar to homotopy classes, one defines two immersions to be in the same regular homotopy class if there exists a regula... | https://en.wikipedia.org/wiki/Regular_homotopy |
In mathematical folklore, the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and William Macready, alludes to the saying "no such thing as a free lunch", that is, there are no easy shortcuts to success. It appeared in the 1997 "No Free Lunch Theorems for Optimization". Wolpert had previously deri... | https://en.wikipedia.org/wiki/No_free_lunch_theorem |
The generalized normal distribution (GND) or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "symmetric"... | https://en.wikipedia.org/wiki/Generalized_normal_distribution |
In the mathematical field of differential geometry, a smooth map between Riemannian manifolds is called harmonic if its coordinate representatives satisfy a certain nonlinear partial differential equation. This partial differential equation for a mapping also arises as the Euler-Lagrange equation of a functional called... | https://en.wikipedia.org/wiki/Harmonic_map |
Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes ... | https://en.wikipedia.org/wiki/Conversion_of_units |
Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together is called the "physical sciences".
## Definition
Physical science can be described as all of the following:
- A branch of science... | https://en.wikipedia.org/wiki/Outline_of_physical_science |
Configuration management (CM) is a management process for establishing and maintaining consistency of a product's performance, functional, and physical attributes with its requirements, design, and operational information throughout its life. The CM process is widely used by military engineering organizations to manage... | https://en.wikipedia.org/wiki/Configuration_management |
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855.
While studying at the... | https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss |
In computer science, an implicit data structure or space-efficient data structure is a data structure that stores very little information other than the main or required data: a data structure that requires low overhead. They are called "implicit" because the position of the elements carries meaning and relationship be... | https://en.wikipedia.org/wiki/Implicit_data_structure |
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer condition) from the object (in the far-field region), and also when it i... | https://en.wikipedia.org/wiki/Fraunhofer_diffraction |
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equatio... | https://en.wikipedia.org/wiki/Equation_of_state |
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus)... | https://en.wikipedia.org/wiki/Ricci_calculus |
The concept of a linewidth is borrowed from laser spectroscopy. The linewidth of a laser is a measure of its phase noise. The spectrogram of a laser is produced by passing its light through a prism. The spectrogram of the output of a pure noise-free laser will consist of a single infinitely thin line. If the laser exh... | https://en.wikipedia.org/wiki/Oscillator_linewidth |
Inertial waves, also known as inertial oscillations, are a type of mechanical wave possible in rotating fluids. Unlike surface gravity waves commonly seen at the beach or in the bathtub, inertial waves flow through the interior of the fluid, not at the surface. Like any other kind of wave, an inertial wave is caused by... | https://en.wikipedia.org/wiki/Inertial_wave |
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