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A g-factor (also called g value) is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus. It is the ratio of the magnetic moment (or, equivalently, the gyromagnetic ratio) of a particle to that expected of a classical particle of the same charge and ... | Wikipedia/G-factor_(physics) |
The United States Department of Energy (DOE) is an executive department of the U.S. federal government that oversees U.S. national energy policy and energy production, the research and development of nuclear power, the military's nuclear weapons program, nuclear reactor production for the United States Navy, energy-rel... | Wikipedia/U.S._Department_of_Energy |
In quantum field theory, a branch of theoretical physics, crossing is the property of scattering amplitudes that allows antiparticles to be interpreted as particles going backwards in time.
Crossing states that the same formula that determines the S-matrix elements and scattering amplitudes for particle
... | Wikipedia/Crossing_(physics) |
In physics, the Schwinger model, named after Julian Schwinger, is the model describing 1+1D (1 spatial dimension + time) Lorentzian quantum electrodynamics which includes electrons, coupled to photons.
The model defines the usual QED Lagrangian
L
... | Wikipedia/Schwinger_model |
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. As the study of the statistical mechanics of black-body radiation led to the development of the theory of quantum mechanics, the effort to understand the statis... | Wikipedia/Black_hole_thermodynamics |
In quantum field theory, the Nambu–Jona-Lasinio model (or more precisely: the Nambu and Jona-Lasinio model) is a complicated effective theory of nucleons and mesons constructed from interacting Dirac fermions with chiral symmetry, paralleling the construction of Cooper pairs from electrons in the BCS theory of supercon... | Wikipedia/Nambu–Jona-Lasinio_model |
In mathematical physics, two-dimensional Yang–Mills theory is the special case of Yang–Mills theory in which the dimension of spacetime is taken to be two. This special case allows for a rigorously defined Yang–Mills measure, meaning that the (Euclidean) path integral can be interpreted as a measure on the set of conne... | Wikipedia/Two-dimensional_Yang–Mills_theory |
In theoretical physics, the six-dimensional (2,0)-superconformal field theory is a quantum field theory whose existence is predicted by arguments in string theory. It is still poorly understood because there is no known description of the theory in terms of an action functional. Despite the inherent difficulty in study... | Wikipedia/6D_(2,0)_superconformal_field_theory |
In mathematical physics, constructive quantum field theory is the field devoted to showing that quantum field theory can be defined in terms of precise mathematical structures. This demonstration requires new mathematics, in a sense analogous to classical real analysis, putting calculus on a mathematically rigorous fo... | Wikipedia/Constructive_quantum_field_theory |
In scientific modeling, a toy model is a deliberately simplistic model with many details removed so that it can be used to explain a mechanism concisely. It is also useful in a description of the fuller model.
In "toy" mathematical models, this is usually done by reducing or extending the number of dimensions or reduc... | Wikipedia/Toy_model |
In quantum field theory, scalar chromodynamics, also known as scalar quantum chromodynamics or scalar QCD, is a gauge theory consisting of a gauge field coupled to a scalar field. This theory is used experimentally to model the Higgs sector of the Standard Model.
It arises from a coupling of a scalar field to gauge fie... | Wikipedia/Scalar_chromodynamics |
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word crystallography is derived from the Ancient Greek word κρύσταλλος (krústallos; "clear ice, rock-crystal"), and γράφειν (gráphein; "to write"). In July 2012, the United Nations recognised the imp... | Wikipedia/Crystallographic |
Glass fiber reinforced concrete (GFRC) is a type of fiber-reinforced concrete. The product is also known as glassfibre reinforced concrete or GRC in British English. Glass fiber concretes are mainly used in exterior building façade panels and as architectural precast concrete. Somewhat similar materials are fiber cemen... | Wikipedia/Glass_fiber_reinforced_concrete |
Carbon fibre reinforced carbon (CFRC),
carbon–carbon (C/C),
or reinforced carbon–carbon (RCC)
is a composite material consisting of carbon fiber reinforcement in a matrix of graphite. It was developed for the reentry vehicles of intercontinental ballistic missiles, and is most widely known as the material for the no... | Wikipedia/Reinforced_Carbon-Carbon |
Industrial engineering (IE) is concerned with the design, improvement and installation of integrated systems of people, materials, information, equipment and energy. It draws upon specialized knowledge and skill in the mathematical, physical, and social sciences together with the principles and methods of engineering a... | Wikipedia/Industrial_engineering |
Heat treating (or heat treatment) is a group of industrial, thermal and metalworking processes used to alter the physical, and sometimes chemical, properties of a material. The most common application is metallurgical. Heat treatments are also used in the manufacture of many other materials, such as glass. Heat treatme... | Wikipedia/Heat_treatment |
A doctorate (from Latin doctor, meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism licentia docendi ("licence to teach").
In most countries, a research degree qualifies the holder to teach at univers... | Wikipedia/Doctorate |
A Bachelor of Science (BS, BSc, B.S., B.Sc., SB, or ScB; from the Latin scientiae baccalaureus) is a bachelor's degree that is awarded for programs that generally last three to five years.
The first university to admit a student to the degree of Bachelor of Science was the University of London in 1860. In the United St... | Wikipedia/Bachelor_of_Science |
The Faber–Evans model for crack deflection, is a fracture mechanics-based approach to predict the increase in toughness in two-phase ceramic materials due to crack deflection. The effect is named after Katherine Faber and her mentor, Anthony G. Evans, who introduced the model in 1983. The Faber–Evans model is a princip... | Wikipedia/Faber-Evans_model |
Forensic materials engineering, a branch of forensic engineering, focuses on the material evidence from crime or accident scenes, seeking defects in those materials which might explain why an accident occurred, or the source of a specific material to identify a criminal. Many analytical methods used for material ident... | Wikipedia/Forensic_materials_engineering |
Substrate is a term used in materials science and engineering to describe the base material on which processing is conducted. Surfaces have different uses, including producing new film or layers of material and being a base to which another substance is bonded.
== Description ==
In materials science and engineering, ... | Wikipedia/Substrate_(materials_science) |
A multi-function material is a composite material. The traditional approach to the development of structures is to address the load-carrying function and other functional requirements separately. Recently, however, there has been increased interest in the development of load-bearing materials and structures which have ... | Wikipedia/Multi-function_structure |
Carbon nanotubes (CNTs) are cylinders of one or more layers of graphene (lattice). Diameters of single-walled carbon nanotubes (SWNTs) and multi-walled carbon nanotubes (MWNTs) are typically 0.8 to 2 nm and 5 to 20 nm, respectively, although MWNT diameters can exceed 100 nm. CNT lengths range from less than 100 nm to 0... | Wikipedia/Potential_applications_of_carbon_nanotubes |
Energy-dispersive X-ray spectroscopy (EDS, EDX, EDXS or XEDS), sometimes called energy dispersive X-ray analysis (EDXA or EDAX) or energy dispersive X-ray microanalysis (EDXMA), is an analytical technique used for the elemental analysis or chemical characterization of a sample. It relies on an interaction of some sourc... | Wikipedia/Energy-dispersive_X-ray_spectroscopy |
Instrumentation and control engineering (ICE) is a branch of engineering that studies the measurement and control of process variables, and the design and implementation of systems that incorporate them. Process variables include pressure, temperature, humidity, flow, pH, force and speed.
ICE combines two branches of ... | Wikipedia/Instrumentation_and_control_engineering |
A DNA microarray (also commonly known as DNA chip or biochip) is a collection of microscopic DNA spots attached to a solid surface. Scientists use DNA microarrays to measure the expression levels of large numbers of genes simultaneously or to genotype multiple regions of a genome. Each DNA spot contains picomoles (10−1... | Wikipedia/DNA_microarray |
A phase-field model is a mathematical model for solving interfacial problems. It has mainly been applied to solidification dynamics, but it has also been applied to other situations such as viscous fingering, fracture mechanics, hydrogen embrittlement, and vesicle dynamics.
The method substitutes boundary conditions at... | Wikipedia/Phase_field_models |
Quantum mechanics is the fundamental physical theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms.: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum... | Wikipedia/Quantum_physics |
Potential graphene applications include lightweight, thin, and flexible electric/photonics circuits, solar cells, and various medical, chemical and industrial processes enhanced or enabled by the use of new graphene materials, and favoured by massive cost decreases in graphene production.
== Medicine ==
Researchers i... | Wikipedia/Potential_applications_of_graphene |
Clinical engineering is a specialty within biomedical engineering responsible for using medical technology to optimize healthcare delivery.
Clinical engineers train and supervise biomedical equipment technicians (BMETs), working with governmental regulators on hospital inspections and audits, and serve as technological... | Wikipedia/Clinical_engineering |
Optical lens design is the process of designing a lens to meet a set of performance requirements and constraints, including cost and manufacturing limitations. Parameters include surface profile types (spherical, aspheric, holographic, diffractive, etc.), as well as radius of curvature, distance to the next surface, ma... | Wikipedia/Optical_lens_design |
Integrated Computational Materials Engineering (ICME) is an approach to design products, the materials that comprise them, and their associated materials processing methods by linking materials models at multiple length scales. Key words are "Integrated", involving integrating models at multiple length scales, and "En... | Wikipedia/Integrated_computational_materials_engineering |
Graphite () is a crystalline allotrope (form) of the element carbon. It consists of many stacked layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on a large scale (1.3 mi... | Wikipedia/Graphite |
Materials science in science fiction is the study of how materials science is portrayed in works of science fiction. The accuracy of the materials science portrayed spans a wide range – sometimes it is an extrapolation of existing technology, sometimes it is a physically realistic portrayal of a far-out technology, and... | Wikipedia/Materials_science_in_science_fiction |
Computer network engineering is a technology discipline within engineering that deals with the design, implementation, and management of computer networks. These systems contain both physical components, such as routers, switches, cables, and some logical elements, such as protocols and network services. Computer netwo... | Wikipedia/Computer_network_engineering |
Electromechanics combine processes and procedures drawn from electrical engineering and mechanical engineering. Electromechanics focus on the interaction of electrical and mechanical systems as a whole and how the two systems interact with each other. This process is especially prominent in systems such as those of DC ... | Wikipedia/Electromechanics |
The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of ... | Wikipedia/Strength_of_materials |
An accumulator is an energy storage device: a device which accepts energy, stores energy, and releases energy as needed. Some accumulators accept energy at a low rate (low power) over a long time interval and deliver the energy at a high rate (high power) over a short time interval. Some accumulators accept energy at a... | Wikipedia/Accumulator_(energy) |
A design engineer is an engineer focused on the engineering design process in any of the various engineering disciplines (including civil, mechanical, electrical, chemical, textiles, aerospace, nuclear, manufacturing, systems, and structural /building/architectural) and design disciplines like Human-Computer Interacti... | Wikipedia/Design_engineer |
Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result fro... | Wikipedia/Solid_state_physics |
Graphene () is a carbon allotrope consisting of a single layer of atoms arranged in a honeycomb planar nanostructure. The name "graphene" is derived from "graphite" and the suffix -ene, indicating the presence of double bonds within the carbon structure.
Graphene is known for its exceptionally high tensile strength, e... | Wikipedia/Graphene |
Nanomaterials describe, in principle, chemical substances or materials of which a single unit is sized (in at least one dimension) between 1 and 100 nm (the usual definition of nanoscale).
Nanomaterials research takes a materials science-based approach to nanotechnology, leveraging advances in materials metrology and s... | Wikipedia/Nanomaterials |
The foot-pound force (symbol: ft⋅lbf, ft⋅lbf, or ft⋅lb ) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a force of one pound-force (lbf) through a linear displacement of one foot. The corres... | Wikipedia/Foot-pound_force |
In mathematical knot theory, a link is a collection of knots that do not intersect, but which may be linked (or knotted) together. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory. Implicit in this definition is that there is a trivial refer... | Wikipedia/Link_(knot_theory) |
Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology.
Dirac notation provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associated with topological spaces and the related embedding of one space within an... | Wikipedia/Quantum_topology |
Physical knot theory is the study of mathematical models of knotting phenomena, often motivated by considerations from biology, chemistry, and physics (Kauffman 1991). Physical knot theory is used to study how geometric and topological characteristics of filamentary structures, such as magnetic flux tubes, vortex filam... | Wikipedia/Physical_knot_theory |
The vortex theory of the atom was a 19th-century attempt by William Thomson (later Lord Kelvin) to explain why the atoms recently discovered by chemists came in only relatively few varieties but in very great numbers of each kind. Based on the idea of stable, knotted vortices in the ether or aether, it contributed an i... | Wikipedia/Vortex_theory_of_the_atom |
The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture.
== ... | Wikipedia/Tait_conjectures |
In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear. It composes a knot using certain operations on tangles to construct it.
== Basic concepts ==
=== Tangles ===
In Conway notation, the tangles are generally algebraic 2-tangles. Th... | Wikipedia/Conway_notation_(knot_theory) |
In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant.
== Examples ==
By way of example, the unknot has crossing number zero, the trefoil knot three and the figure-eight knot four. There are no other knots with a c... | Wikipedia/Crossing_number_(knot_theory) |
In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial mappings).
Semialgebraic geometry is the study of semialgebraic sets, i.... | Wikipedia/Real_algebraic_set |
In mathematics, a tangle is generally one of two related concepts:
In John Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n marked points on the ball's boundary.
In link theory, a tangle is an embedding of n ar... | Wikipedia/Algebraic_tangle |
In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram. Consider a disc D in the projection plane of the diagram whose boundary circle intersects K exactly four times. We may suppose that (after planar isot... | Wikipedia/Mutation_(knot_theory) |
In differential geometry, a ribbon (or strip) is the combination of a smooth space curve and its corresponding normal vector. More formally, a ribbon denoted by
(
X
,
U
)
{\displaystyle (X,U)}
includes a curve
X
... | Wikipedia/Ribbon_theory |
When Topology Meets Chemistry: A Topological Look At Molecular Chirality is a book in chemical graph theory on the graph-theoretic analysis of chirality in molecular structures. It was written by Erica Flapan, based on a series of lectures she gave in 1996 at the Institut Henri Poincaré, and was published in 2000 by th... | Wikipedia/When_Topology_Meets_Chemistry |
In geometric topology, the spherical space form conjecture (now a theorem) states that a finite group acting on the 3-sphere is conjugate to a group of isometries of the 3-sphere.
== History ==
The conjecture was posed by Heinz Hopf in 1926 after determining the fundamental groups of three-dimensional spherical space... | Wikipedia/Spherical_space_form_conjecture |
In the mathematical field of geometric topology, the Poincaré conjecture (UK: , US: , French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
Originally conjectured by Henri Poincaré in 1904, the theorem concerns spaces t... | Wikipedia/Ricci_flow_with_surgery |
William Thurston's elliptization conjecture states that a closed 3-manifold with finite fundamental group is spherical, i.e. has a Riemannian metric of constant positive sectional curvature.
== Relation to other conjectures ==
A 3-manifold with a Riemannian metric of constant positive sectional curvature is covered b... | Wikipedia/Thurston_elliptization_conjecture |
Clay Mathematics Monographs is a series of expositions in mathematics co-published by AMS and Clay Mathematics Institute. Each volume in the series offers an exposition of an active area of current research, provided by a group of mathematicians.
== List of books ==
Morgan, John; Tian, Gang (2014). The Geometrization... | Wikipedia/Clay_Mathematics_Monographs |
In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct Boolean-valued models of set theory in the theory of forcing. Every Boolean algebra A has an essentially unique completion, which is a complete Bool... | Wikipedia/Complete_Boolean_algebra |
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces. As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two... | Wikipedia/Point_(topology) |
In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra that is complete as a lattice. Complete Heyting algebras are the objects of three different categories; the category CHey, the category Loc of locales, and its opposite, the category Frm of frames. Although these three categorie... | Wikipedia/Complete_Heyting_algebra |
In mathematics, an algebraic structure or algebraic system consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that these operations must satis... | Wikipedia/Algebraic_system |
In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by
∨
{\displaystyle \lor }
, and a single unary operation usually denoted by
¬
{\displaystyle \neg }
satisfying the following ... | Wikipedia/Robbins_conjecture |
In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique and algorithmic paradigm that consists of systematically checking all possible candidates for whether or not each candidate satisfies the problem's statement.
A brute-force algorith... | Wikipedia/Brute_force_search |
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function
f
:
A
→
A
{\displaystyle f:A\rightarrow A}
, where A is ... | Wikipedia/Unary_functional_symbol |
In probability theory, a conditional event algebra (CEA) is an alternative to a standard, Boolean algebra of possible events (a set of possible events related to one another by the familiar operations and, or, and not) that contains not just ordinary events but also conditional events that have the form "if A, then B".... | Wikipedia/Conditional_event_algebra |
In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure A = (A, ∨, ∧, 0, 1, ¬) such that:
(A, ∨, ∧, 0, 1) is a bounded distributive lattice, and
¬ is a De Morgan involution: ¬(x ∧ y) = ¬x ∨ ¬y and ¬¬x = x. (i.e. an involution that additionally satisfi... | Wikipedia/Kleene_algebra_(with_involution) |
In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure A = (A, ∨, ∧, 0, 1, ¬) such that:
(A, ∨, ∧, 0, 1) is a bounded distributive lattice, and
¬ is a De Morgan involution: ¬(x ∧ y) = ¬x ∨ ¬y and ¬¬x = x. (i.e. an involution that additionally satisfi... | Wikipedia/De_Morgan_algebra |
In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube.
Qn has 2n vertices, 2n − 1n edges, and is a regular graph with n edges touching each ver... | Wikipedia/Hypercube_graph |
In mathematics, a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that:
Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean operations, and
The generators are as independent as possible, in the sense that ... | Wikipedia/Free_Boolean_algebra |
Journal of Algebra (ISSN 0021-8693) is an international mathematical research journal in algebra. An imprint of Academic Press, it is published by Elsevier. Journal of Algebra was founded by Graham Higman, who was its editor from 1964 to 1984. From 1985 until 2000, Walter Feit served as its editor-in-chief.
In 2004, Jo... | Wikipedia/Journal_of_Algebra |
The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward J. McCluskey in 1956. As a general principle this approach had already been demonstrated by the logician Hugh Mc... | Wikipedia/Quine–McCluskey_algorithm |
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF), minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form (CCNF), maxterm canonical form, or Product of Sums (PoS or POS... | Wikipedia/Canonical_form_(Boolean_algebra) |
In propositional logic and Boolean algebra, there is a duality between conjunction and disjunction, also called the duality principle. It is the most widely known example of duality in logic. The duality consists in these metalogical theorems:
In classical propositional logic, the connectives for conjunction and disju... | Wikipedia/Duality_principle_(Boolean_algebra) |
In mathematics, a cofinite subset of a set
X
{\displaystyle X}
is a subset
A
{\displaystyle A}
whose complement in
X
{\displaystyle X}
is a finite set. In other words,
... | Wikipedia/Finite–cofinite_algebra |
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.
A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving problems t... | Wikipedia/Computational_topology |
In mathematical logic, the Lindenbaum–Tarski algebra (or Lindenbaum algebra) of a logical theory T consists of the equivalence classes of sentences of the theory (i.e., the quotient, under the equivalence relation ~ defined such that p ~ q exactly when p and q are provably equivalent in T). That is, two sentences are e... | Wikipedia/Lindenbaum_algebra |
In the branch of mathematics known as universal algebra (and in its applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect product of "simpler" algebras. Subdirectly irreducible algebras play a somewhat analogous role in algebra to primes in number theory.
== Definition ... | Wikipedia/Subdirectly_irreducible_algebra |
In abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are to topology and the modal logic S4 what Boolean algebras are to set theory and ordinary propositional logic. Interior algebras form a variety of modal alge... | Wikipedia/Generalized_topology |
In mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form that gives it useful properties for use in logic programming, formal specification, universal algebra and model theory. Horn clauses are named for the logician Alfred Horn, who first pointed out their signific... | Wikipedia/Universal_Horn_theory |
Łukasiewicz–Moisil algebras (LMn algebras) were introduced in the 1940s by Grigore Moisil (initially under the name of Łukasiewicz algebras) in the hope of giving algebraic semantics for the n-valued Łukasiewicz logic. However, in 1956 Alan Rose discovered that for n ≥ 5, the Łukasiewicz–Moisil algebra does not model t... | Wikipedia/Łukasiewicz–Moisil_algebra |
In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation
⊕
{\displaystyle \oplus }
, a unary operation
¬
{\displaystyle \neg }
, and the constant
0
... | Wikipedia/MV-algebras |
In mathematics, an Ockham algebra is a bounded distributive lattice
L
{\displaystyle L}
with a dual endomorphism, that is, an operation
∼
:
L
→
L
{\displaystyle \sim \colon L\to L}
satisfying
... | Wikipedia/Ockham_algebra |
In the mathematical area of order theory, the compact elements or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any non-empty directed set that does not already contain members above the compact element. This notion of compactness simultaneously generalizes the ... | Wikipedia/Algebraic_poset |
In the mathematical area of order theory, the compact elements or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any non-empty directed set that does not already contain members above the compact element. This notion of compactness simultaneously generalizes the ... | Wikipedia/Algebraic_lattices |
In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective.
== Examples ==
The function
f
:
z
↦
2
z
+
z
2
... | Wikipedia/Univalent_function |
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Functions were originally the idealization of how a varying quantity depends on another quantity. For example, th... | Wikipedia/Empty_function |
In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. The method is closely related to the LCAO method (linear comb... | Wikipedia/Tight_binding_model |
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic tha... | Wikipedia/Mean-field_approximation |
In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state. The method is named after Douglas Hartree and Vladimir Fock.
The Hartree–Fock method often assumes that the exa... | Wikipedia/Hartree–Fock_method |
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... | Wikipedia/Free_electron_model |
A material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geological origin or biological function. Materials science is the study of materia... | Wikipedia/Materials |
In condensed matter physics, the Laughlin wavefunction is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas placed in a uniform background magnetic field in the presence of a uniform jellium background when the filling factor of the lowest Landau level is
... | Wikipedia/Laughlin_wavefunction |
Mesoscopic physics is a subdiscipline of condensed matter physics that deals with materials of an intermediate size. These materials range in size between the nanoscale for a quantity of atoms (such as a molecule) and of materials measuring micrometres. The lower limit can also be defined as being the size of individua... | Wikipedia/Mesoscopic_physics |
A composite or composite material (also composition material) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finishe... | Wikipedia/Composite_materials |
This is a list of computer programs that are predominantly used for molecular mechanics calculations.
== See also ==
Car–Parrinello molecular dynamics
Comparison of force-field implementations
Comparison of nucleic acid simulation software
List of molecular graphics systems
List of protein structure prediction softw... | Wikipedia/Comparison_of_software_for_molecular_mechanics_modeling |
In physics, critical phenomena is the collective name associated with the
physics of critical points. Most of them stem from the divergence of the
correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (suc... | Wikipedia/Critical_phenomena |
A raw material, also known as a feedstock, unprocessed material, or primary commodity, is a basic material that is used to produce goods, finished goods, energy, or intermediate materials/Intermediate goods that are feedstock for future finished products. As feedstock, the term connotes these materials are bottleneck a... | Wikipedia/Raw_materials |
In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lat... | Wikipedia/Lattice_model_(physics) |
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