id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
7,600 | The crystal structure of prophytepsin (from barley) was the first known structure to elucidate the molecular topology of any PSI. The crystal structure of prophytepsin derived PSI revealed that the overall length and position of the helices found in PSI is conserved with those of NK-lysin, another member of the SAPLIP ... | Plant-specific insert | 0.822531 |
7,601 | Even as DNA barcoding is more widely used and applied, there is no agreement concerning the methods for DNA preservation or extraction, the choices of DNA markers and primers set, or PCR protocols. The parameters of bioinformatics pipelines (for example OTU clustering, taxonomic assignment algorithms or thresholds etc.... | DNA barcode | 0.822524 |
7,602 | DNA barcoding also carries methodological bias, from sampling to bioinformatics data analysis. Beside the risk of contamination of the DNA sample by PCR inhibitors, primer bias is one of the major sources of errors in DNA barcoding. The isolation of an efficient DNA marker and the design of primers is a complex process... | DNA barcode | 0.822524 |
7,603 | Thus, there is a strong need for more robust bioinformatics algorithms that allow the differentiation between informative reads and artifacts. Complete reference libraries would also allow a better testing of bioinformatics algorithms, by permitting a better filtering of artifacts (i.e. the removal of sequences lacking... | DNA barcode | 0.822524 |
7,604 | Diat.barcode Diat.barcode database was first published under the name R-syst::diatom in 2016 starting with data from two sources: the Thonon culture collection (TCC) in the hydrobiological station of the French National Institute for Agricultural Research (INRA), and from the NCBI (National Center for Biotechnology Inf... | DNA barcode | 0.822524 |
7,605 | Research groups studying molecular physics are typically designated as one of these other fields. Molecular physics addresses phenomena due to both molecular structure and individual atomic processes within molecules. Like atomic physics, it relies on a combination of classical and quantum mechanics to describe interac... | Molecular physicist | 0.822524 |
7,606 | Molecular physics is the study of the physical properties of molecules and molecular dynamics. The field overlaps significantly with physical chemistry, chemical physics, and quantum chemistry. It is often considered as a sub-field of atomic, molecular, and optical physics. | Molecular physicist | 0.822524 |
7,607 | in which Eysenck and Prell concluded that, "The factor of neuroticism is not a statistical artifact, but constitutes a biological unit which is inherited as a whole....neurotic Genetic predisposition is to a large extent hereditarily determined."E. O. Wilson's book on sociobiology and his book Consilience discuss the i... | Genetic predisposition | 0.822518 |
7,608 | A matricial algebra over a field F is a finite product of rings of the form M n ( F ) {\displaystyle M_{n}(F)} , the ring of all square matrices with n rows and entries in F, for variable positive integers n. A direct limit of matricial algebras over F is a locally matricial algebra over F. Every locally matricial alge... | Refinement monoid | 0.822514 |
7,609 | The isomorphism type of a Boolean algebra B is the class of all Boolean algebras isomorphic to B. (If we want this to be a set, restrict to Boolean algebras of set-theoretical rank below the one of B.) The class of isomorphism types of Boolean algebras, endowed with the addition defined by + = {\displaystyle +=} (fo... | Refinement monoid | 0.822514 |
7,610 | He also proved that any element in an at most countable conical refinement monoid is measured by a unique (up to isomorphism) V-measure on a unique at most countable Boolean algebra. He raised there the problem whether any conical refinement monoid is measurable. This was answered in the negative by Friedrich Wehrung i... | Refinement monoid | 0.822514 |
7,611 | For a Boolean algebra A and a commutative monoid M, a map μ: A → M is a measure, if μ(a)=0 if and only if a=0, and μ(a ∨ b)=μ(a)+μ(b) whenever a and b are disjoint (that is, a ∧ b=0), for any a, b in A. We say in addition that μ is a Vaught measure (after Robert Lawson Vaught), or V-measure, if for all c in A and all x... | Refinement monoid | 0.822514 |
7,612 | In this case net energy may be transferred from the electron to the photon. The inverse Compton effect is seen in astrophysics when a low energy photon (e.g. of the cosmic microwave background) bounces off a high energy (relativistic) electron. Such electrons are produced in supernovae and active galactic nuclei. | Electron scattering | 0.822506 |
7,613 | Compton scattering, so named for Arthur Compton who first observed the effect in 1922 and which earned him the 1927 Nobel Prize in Physics; is the inelastic scattering of a high-energy photon by a free charged particle.This was demonstrated in 1923 by firing radiation of a given wavelength (X-rays in the given case) th... | Electron scattering | 0.822506 |
7,614 | RIKEN was founded in 1917 as a private research foundation in Tokyo, and is Japan's largest comprehensive research institution. Having grown rapidly in size and scope, it is today renowned for high-quality research in a diverse range of scientific disciplines, and encompasses a network of world-class research centers a... | Electron scattering | 0.822506 |
7,615 | Other scientific programs run at SLAC include: Advanced Accelerator Research ATLAS/Large Hadron Collider Elementary Particle Theory EXO - Enriched Xenon Observatory FACET - Facility for Advanced Accelerator Experimental Tests Fermi Gamma-ray Space Telescope Geant4 KIPAC - Kavli Institute for Particle Astrophysics and C... | Electron scattering | 0.822506 |
7,616 | The principle of the electron was first theorised in the period of 1838-1851 by a natural philosopher by the name of Richard Laming who speculated the existence of sub-atomic, unit charged particles; he also pictured the atom as being an 'electrosphere' of concentric shells of electrical particles surrounding a materia... | Electron scattering | 0.822506 |
7,617 | BII focuses on "computationally biology-driven life science research aimed at the discovery of biomolecular mechanisms." BII also develops computer based research tools and performs experimental verifications in its own experimental facilities or by collaborating with appropriate groups. BII is home to the journal Scie... | Bioinformatics Institute (Singapore) | 0.822506 |
7,618 | The Bioinformatics Institute (Abbreviation: BII) is one of the Biomedical Sciences Institutes of the Agency for Science, Technology and Research, (A*STAR). BII was originally founded in 2001 by Dr Rajagopal as a support unit for Bioinformatics and IT service management. However, since August 2007, it has been redefined... | Bioinformatics Institute (Singapore) | 0.822506 |
7,619 | Per Ampère's law, the excitation is the product of the current and the number of complete loops made and is measured in ampere-turns. Stated more generally: By Stokes's theorem, the closed line integral of H·dl around a contour is equal to the open surface integral of curl H·dA across the surface bounded by the closed ... | Magnetic circuit | 0.822506 |
7,620 | Researchers (Read 1991) have found within Gestalt psychology an integrated model of explaining attitude change that incorporates neuroscientific and social psychological concepts. Theories of cognitive dissonance as well as its alternatives are based on the assumption that the attitudes and beliefs one holds are fixed ... | Parallel constraint satisfaction processes | 0.822497 |
7,621 | Parallel constraint satisfaction processes (PCSP) is a model that integrates the fastest growing research areas in the study of the mind; Connectionism, neural networks, and parallel distributed processing models. | Parallel constraint satisfaction processes | 0.822497 |
7,622 | The least squares estimators are point estimates of the linear regression model parameters β. However, generally we also want to know how close those estimates might be to the true values of parameters. In other words, we want to construct the interval estimates. Since we haven't made any assumption about the distribut... | Normal equations | 0.822497 |
7,623 | Sometimes the variables and corresponding parameters in the regression can be logically split into two groups, so that the regression takes form y = X 1 β 1 + X 2 β 2 + ε , {\displaystyle y=X_{1}\beta _{1}+X_{2}\beta _{2}+\varepsilon ,} where X1 and X2 have dimensions n×p1, n×p2, and β1, β2 are p1×1 and p2×1 vectors, w... | Normal equations | 0.822497 |
7,624 | The forces between each pair of atoms may be characterized by a potential energy function V that depends on the distance of separation of the atoms. The potential energy of the entire lattice is the sum of all pairwise potential energies multiplied by a factor of 1/2 to compensate for double counting: 1 2 ∑ i ≠ j V ( r... | Atom vibrations | 0.822492 |
7,625 | In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical quantization of the modes of vibrations for elastic structures of interac... | Atom vibrations | 0.822492 |
7,626 | The equations in this section do not use axioms of quantum mechanics but instead use relations for which there exists a direct correspondence in classical mechanics. For example: a rigid regular, crystalline (not amorphous) lattice is composed of N particles. These particles may be atoms or molecules. N is a large numb... | Atom vibrations | 0.822492 |
7,627 | Hurwitz quaternions form a non-commutative *-ring with the quaternion conjugation. The matrix algebra of n × n matrices over R with * given by the transposition. The matrix algebra of n × n matrices over C with * given by the conjugate transpose. | *-algebra | 0.822489 |
7,628 | A quadratic integer ring (for some D) is a commutative *-ring with the * defined in the similar way; quadratic fields are *-algebras over appropriate quadratic integer rings. Quaternions, split-complex numbers, dual numbers, and possibly other hypercomplex number systems form *-rings (with their built-in conjugation op... | *-algebra | 0.822489 |
7,629 | The same about a commutative ring K and its polynomial ring K: the quotient by x = 0 restores K. In Hecke algebra, an involution is important to the Kazhdan–Lusztig polynomial. The endomorphism ring of an elliptic curve becomes a *-algebra over the integers, where the involution is given by taking the dual isogeny. A s... | *-algebra | 0.822489 |
7,630 | As a partial case, any *-ring is a *-algebra over integers. Any commutative *-ring is a *-algebra over itself and, more generally, over any its *-subring. For a commutative *-ring R, its quotient by any its *-ideal is a *-algebra over R. For example, any commutative trivially-*-ring is a *-algebra over its dual numbers... | *-algebra | 0.822489 |
7,631 | Its generalization, the Hermitian adjoint in the algebra of bounded linear operators on a Hilbert space also defines a *-algebra. The polynomial ring R over a commutative trivially-*-ring R is a *-algebra over R with P *(x) = P (−x). If (A, +, ×, *) is simultaneously a *-ring, an algebra over a ring R (commutative), an... | *-algebra | 0.822489 |
7,632 | Any commutative ring becomes a *-ring with the trivial (identical) involution. The most familiar example of a *-ring and a *-algebra over reals is the field of complex numbers C where * is just complex conjugation. More generally, a field extension made by adjunction of a square root (such as the imaginary unit √−1) is... | *-algebra | 0.822489 |
7,633 | A *-algebra A is a *-ring, with involution * that is an associative algebra over a commutative *-ring R with involution ′, such that (r x)* = r′ x* ∀r ∈ R, x ∈ A.The base *-ring R is often the complex numbers (with ′ acting as complex conjugation). It follows from the axioms that * on A is conjugate-linear in R, meanin... | *-algebra | 0.822489 |
7,634 | One can define a sesquilinear form over any *-ring. Also, one can define *-versions of algebraic objects, such as ideal and subring, with the requirement to be *-invariant: x ∈ I ⇒ x* ∈ I and so on. *-rings are unrelated to star semirings in the theory of computation. | *-algebra | 0.822489 |
7,635 | In mathematics, a *-ring is a ring with a map *: A → A that is an antiautomorphism and an involution. More precisely, * is required to satisfy the following properties: (x + y)* = x* + y* (x y)* = y* x* 1* = 1 (x*)* = xfor all x, y in A. This is also called an involutive ring, involutory ring, and ring with involution.... | *-algebra | 0.822489 |
7,636 | The Center for Applied Genomics is a research center at the Children's Hospital of Philadelphia that focuses on genomics research and the utilization of basic research findings in the development of new medical treatments. As one of the world's largest genetics research and analytical facilities, the Center for Applied... | Center for Applied Genomics | 0.822489 |
7,637 | Cylindrical fullerenes are also called carbon nanotubes or buckytubes. The bulk solid form of pure or mixed fullerenes is called fullerite.Fullerenes had been predicted for some time, but only after their accidental synthesis in 1985 were they detected in nature and outer space. The discovery of fullerenes greatly expa... | Higher fullerenes | 0.822485 |
7,638 | A fullerene is an allotrope of carbon whose molecule consists of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to seven atoms. The molecule may be a hollow sphere, ellipsoid, tube, or many other shapes and sizes. Fullerenes with a closed mesh... | Higher fullerenes | 0.822485 |
7,639 | In the projective model of elliptic geometry, the points of n-dimensional real projective space are used as points of the model. This models an abstract elliptic geometry that is also known as projective geometry. The points of n-dimensional projective space can be identified with lines through the origin in (n + 1)-di... | Elliptical geometry | 0.82247 |
7,640 | The distance formula is homogeneous in each variable, with d(λu, μv) = d(u, v) if λ and μ are non-zero scalars, so it does define a distance on the points of projective space. A notable property of the projective elliptic geometry is that for even dimensions, such as the plane, the geometry is non-orientable. It erases... | Elliptical geometry | 0.82247 |
7,641 | Recently the case of genus-1 fillings was settled affirmatively, as well (see reference by Bangert et al. below). Namely, it turns out that one can exploit a half-century old formula by J. Hersch from integral geometry. Namely, consider the family of figure-8 loops on a football, with the self-intersection point at the... | Systolic geometry | 0.822462 |
7,642 | The study of the asymptotic behavior for large genus g of the systole of hyperbolic surfaces reveals some interesting constants. Thus, Hurwitz surfaces Σg defined by a tower of principal congruence subgroups of the (2,3,7) hyperbolic triangle group satisfy the bound s y s π 1 ( Σ g ) ≥ 4 3 log g , {\displaystyle \mat... | Systolic geometry | 0.822462 |
7,643 | Namely, there is an upper bound for the entropy of a systolically extremal surface, in terms of its systole. By combining this upper bound with Katok's optimal lower bound in terms of the volume, one obtains a simpler alternative proof of Gromov's asymptotic estimate for the optimal systolic ratio of surfaces of large ... | Systolic geometry | 0.822462 |
7,644 | A bibliography at the Website for systolic geometry and topology currently contains over 160 articles. Systolic geometry is a rapidly developing field, featuring a number of recent publications in leading journals. Recently (see the 2006 paper by Katz and Rudyak below), the link with the Lusternik–Schnirelmann category... | Systolic geometry | 0.822462 |
7,645 | While the quaternionic projective plane with its symmetric metric has a middle-dimensional stable systolic ratio of 10/3, the analogous ratio for the symmetric metric of the complex projective 4-space gives the value 6, while the best available upper bound for such a ratio of an arbitrary metric on both of these spaces... | Systolic geometry | 0.822462 |
7,646 | A significant difference between 1-systolic invariants (defined in terms of lengths of loops) and the higher, k-systolic invariants (defined in terms of areas of cycles, etc.) should be kept in mind. While a number of optimal systolic inequalities, involving the 1-systoles, have by now been obtained, just about the onl... | Systolic geometry | 0.822462 |
7,647 | Such a strongly isometric imbedding is impossible if the ambient space is a Hilbert space, even when M is the Riemannian circle (the distance between opposite points must be π, not 2!). We then set E = L∞(M) in the formula above, and define F i l l R a d ( M ) = F i l l R a d ( M ⊂ L ∞ ( M ) ) . {\displaystyle \mathrm ... | Systolic geometry | 0.822462 |
7,648 | In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail Katz, Larry Guth, and others, in its arithmetical, ergodic, and topological manifestations. See also a slow... | Systolic geometry | 0.822462 |
7,649 | Music Tech Fest began as result of the Roadmap for Music Information Research (MIReS), a European FP7 project run by seven European research centers: Music Technology Group at the Universitat Pompeu Fabra in Barcelona; Stromatolite; OFAI, Austrian Research Institute for Artificial Intelligence, Vienna, Austria; INESCP,... | MTF Labs | 0.82246 |
7,650 | MTF Stockholm took place in Stockholm Sweden from the 7–9 September 2018. The showcase was held at KTH Royal Institute of Technology with performances from musicians and record producers Håkan Lidbo, Jan Bang, Graham Massey and more. MTF Stockholm had a 24hr Hack Camp led by technologist, TV presenter, sound designer, ... | MTF Labs | 0.82246 |
7,651 | MTF Labs is a series of innovation labs, festivals and events encouraging innovation through creative work, particularly music.Since the first Music Tech Fest in 2012, a community has formed around the festival with over 7,500 members from fields such as medicine, aviation, product design, AI, music composition, microc... | MTF Labs | 0.82246 |
7,652 | In relational algebra, if R ⊆ X × Y {\displaystyle R\subseteq X\times Y} and S ⊆ Y × Z {\displaystyle S\subseteq Y\times Z} are relations, then the composite relation S R ⊆ X × Z {\displaystyle SR\subseteq X\times Z} is defined so that x S R z {\displaystyle x\,SR\,z} if and only if there is a y ∈ Y {\displaystyle y\in... | Equivalence relation | 0.822447 |
7,653 | In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number a is equal to itself (reflexive). | Equivalence relation | 0.822447 |
7,654 | Other types include: Belleville washer A disc shaped spring commonly used to apply tension to a bolt (and also in the initiation mechanism of pressure-activated landmines) Constant-force spring A tightly rolled ribbon that exerts a nearly constant force as it is unrolled Gas spring A volume of compressed gas. Ideal spr... | Zero-length spring | 0.82244 |
7,655 | A hydrogen-like atom includes a positively charged core consisting of the atomic nucleus and any core electrons as well as a single valence electron. Because helium is common in the universe, the spectroscopy of singly ionized helium is important in EUV astronomy, for example, of DO white dwarf stars. The non-relativis... | Hydrogenic atom | 0.822438 |
7,656 | In a recent study, a powerful computer was shown to be unable to simulate a protein with more than 8 phosphorylation sites ( 2 8 = 256 {\displaystyle 2^{8}=256} phosphorylation states) using ordinary differential equations.Methods have been proposed to reduce the size of the state space. One is to consider only the sta... | Multi-state modeling of biomolecules | 0.822433 |
7,657 | This means that the space of all possible states can become very large. With some simulation methods implementing numerical integration of ordinary and partial differential equations or the Gillespie stochastic algorithm, all possible pools of molecules and the reactions they undergo are defined at the start of the sim... | Multi-state modeling of biomolecules | 0.822433 |
7,658 | Differential equations describe changes in molecular concentrations over time in a deterministic manner. Simulations based on differential equations usually do not attempt to solve those equations analytically, but employ a suitable numerical solver. The stochastic Gillespie algorithm changes the composition of pools o... | Multi-state modeling of biomolecules | 0.822433 |
7,659 | In Population-based rule evaluation, rules are applied to populations. All molecules of the same species in the same state are pooled together. Application of a specific rule reduces or increases the size of one of the pools, possibly at the expense of another. Some of the best-known classes of simulation approaches in... | Multi-state modeling of biomolecules | 0.822433 |
7,660 | Spatial particle-based methods differ from the methods described above by their explicit representation of space. One example of a particle-based simulator that allows for a representation of cellular compartments is SRSim. SRSim is integrated in the LAMMPS molecular dynamics simulator and allows the user to specify th... | Multi-state modeling of biomolecules | 0.822433 |
7,661 | To address the specification problem, modelers have in recent years moved away from explicit specification of all possible states, and towards rule-based modeling that allow for implicit model specification, including the κ-calculus, BioNetGen, the Allosteric Network Compiler and others. To tackle the computation probl... | Multi-state modeling of biomolecules | 0.822433 |
7,662 | A model (or part of a model) is represented as a Python programme. This allows users to store higher-order biochemical processes such as catalysis or polymerisation as macros and re-use them as needed. The models can be simulated and analysed using Python libraries, but PySB models can also be exported into BNGL, kappa... | Multi-state modeling of biomolecules | 0.822433 |
7,663 | A very useful feature of ANC is that it automatically computes dependent parameters, thereby imposing thermodynamic correctness.An extension of the κ-calculus is provided by React(C). The authors of React C show that it can express the stochastic π calculus. They also provide a stochastic simulation algorithm based on ... | Multi-state modeling of biomolecules | 0.822433 |
7,664 | BNGL provides a syntax for specifying these graphs and the associated rules as structured strings. BioNetGen can then use these rules to generate ordinary differential equations (ODEs) to describe each biochemical reaction. Alternatively, it can generate a list of all possible species and reactions in SBML, which can t... | Multi-state modeling of biomolecules | 0.822433 |
7,665 | The κ-calculus is merely concerned with providing a language to encode multi-state models, not with interpreting the models themselves. A simulator compatible with Kappa is KaSim.BioNetGen is a software suite that provides both specification and simulation capacities. | Multi-state modeling of biomolecules | 0.822433 |
7,666 | The problem of combinatorial explosion is also relevant to synthetic biology, with a recent model of a relatively simple synthetic eukaryotic gene circuit featuring 187 species and 1165 reactions.Of course, not all of the possible states of a multi-state molecule or complex will necessarily be populated. Indeed, in sys... | Multi-state modeling of biomolecules | 0.822433 |
7,667 | However, many solutions to the specification problem also contain a method of interpreting the specified model. This is done by providing a method to simulate the model or a method to convert it into a form that can be used for simulations in other programs. An early rule-based specification method is the κ-calculus, a... | Multi-state modeling of biomolecules | 0.822433 |
7,668 | The basic modes constructing a phase space crystal are not necessarily a many-body state, and need not break DTTS as for the single-particle phase space crystals. For many-body systems, phase space crystals study the interplay of the potential subharmonic modes that are arranged periodically in phase space. There is a ... | Phase space crystals | 0.82243 |
7,669 | In fact, the canonical equation of motion can also be rewritten in the Lorenz-force form reflecting the symplectic geometry of classical phase space In the phase space of dynamical systems, the stable points together with their neighbouring regions form the so called Poincaré-Birkhoff islands in the chaotic sea that ma... | Phase space crystals | 0.82243 |
7,670 | In his celebrated book Mathematical Foundations of Quantum Mechanics, John von Neumann constructed a phase space lattice by two commutative elementary displacement operators along position and momentum directions respectively, which is also called the von Neumann lattice nowadays. If the phase space is replaced a frequ... | Phase space crystals | 0.82243 |
7,671 | Combined with the phase space lattice potential from driving, there exist a stable regime where the particles arrange themselves periodically in phase space giving rise to many-body phase space crystals.In quantum mechanics, the point particle is replaced by a quantum wave packet and the divergence problem is naturally... | Phase space crystals | 0.82243 |
7,672 | Solid crystals are defined by a periodic arrangement of atoms in real space, atoms subject to a time-periodic drive can also form crystals in phase space. The interactions between these atoms give rise to collective vibrational modes similar to phonons in solid crystals. The honeycomb phase space crystal is particularl... | Phase space crystals | 0.82243 |
7,673 | Phase space is fundamentally different from real space as the two coordinates of phase space do not commute, i.e., = i λ {\displaystyle =i\lambda } where λ {\displaystyle \lambda } is the dimensionless Planck constant. The ladder operator is defined as a ^ = ( x ^ + i p ^ ) / 2 λ {\displaystyle {\hat {a}}=({\hat {x}}+... | Phase space crystals | 0.82243 |
7,674 | Phase space crystal is the state of a physical system that displays discrete symmetry in phase space instead of real space. For a single-particle system, the phase space crystal state refers to the eigenstate of the Hamiltonian for a closed quantum system or the eigenoperator of the Liouvillian for an open quantum syst... | Phase space crystals | 0.82243 |
7,675 | In structural geology and diagenesis, pressure solution or pressure dissolution is a deformation mechanism that involves the dissolution of minerals at grain-to-grain contacts into an aqueous pore fluid in areas of relatively high stress and either deposition in regions of relatively low stress within the same rock or ... | Pressure solution | 0.822429 |
7,676 | Apps must be compiled for 64-bit architecture in order to be supported on iOS 11. 32-bit apps are not supported or shown in the App Store in iOS 11, and users who attempt to open such apps receive an alert about the app's incompatibility.iOS 11 drops the native system integration with Twitter, Facebook, Flickr, and Vim... | Core ML | 0.822428 |
7,677 | A new "ARKit" application programming interface (API) lets third-party developers build augmented reality apps, taking advantage of a device's camera, CPU, GPU, and motion sensors. The ARKit functionality is only available to users of devices with Apple A9 and later processors. According to Apple, this is because "thes... | Core ML | 0.822428 |
7,678 | Leibniz's ideas have taken root in the philosophy of mathematics, where they have influenced the development of the predicate calculus as Leibniz's law. Mathematicians sometimes distinguish identity from equality. | Transitivity of identity | 0.822422 |
7,679 | We observe that Moreover, the sequence ( a 1 + a 2 + … a n ) {\displaystyle \left({\sqrt {a_{1}+{\sqrt {a_{2}+\dotsc {\sqrt {a_{n}}}}}}}\right)} is monotonically increasing. Therefore it converges, by the monotone convergence theorem. | Nested radicals | 0.822418 |
7,680 | In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include which arises in discussing the regular pentagon, and more complicated ones such as | Nested radicals | 0.822418 |
7,681 | Nested radicals appear in the algebraic solution of the cubic equation. Any cubic equation can be written in simplified form without a quadratic term, as whose general solution for one of the roots is In the case in which the cubic has only one real root, the real root is given by this expression with the radicands of ... | Nested radicals | 0.822418 |
7,682 | In solid state physics and physical chemistry, the fine electronic structure of a solid are the features of the electronic bands induced by intrinsic interactions between charge carriers. Valence and conduction bands split slightly compared to the difference between the various bands. Some mechanisms that allow it are ... | Fine electronic structure | 0.822417 |
7,683 | In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered. Thus, for examp... | Exchangeable random variables | 0.822415 |
7,684 | Tensile testing, also known as tension testing, is a fundamental materials science and engineering test in which a sample is subjected to a controlled tension until failure. Properties that are directly measured via a tensile test are ultimate tensile strength, breaking strength, maximum elongation and reduction in are... | Tensile testing | 0.822414 |
7,685 | The idea that naturalness will explain fine tuning was brought into question by Nima Arkani-Hamed, a theoretical physicist, in his talk "Why is there a Macroscopic Universe? ", a lecture from the mini-series "Multiverse & Fine Tuning" from the "Philosophy of Cosmology" project, a University of Oxford and Cambridge Coll... | Fine-tuning (physics) | 0.822413 |
7,686 | Although fine-tuning was traditionally measured by ad hoc fine-tuning measures, such as the Barbieri-Giudice-Ellis measure, over the past decade many scientists recognized that fine-tuning arguments were a specific application of Bayesian statistics. | Fine-tuning (physics) | 0.822413 |
7,687 | In theoretical physics, fine-tuning is the process in which parameters of a model must be adjusted very precisely in order to fit with certain observations. This had led to the discovery that the fundamental constants and quantities fall into such an extraordinarily precise range that if it did not, the origin and evol... | Fine-tuning (physics) | 0.822413 |
7,688 | In some cases, the Schrödinger equation can be solved analytically on a one-dimensional lattice of finite length using the theory of periodic differential equations. The length of the lattice is assumed to be L = N a {\displaystyle L=Na} , where a {\displaystyle a} is the potential period and the number of periods N {\... | Periodic potential | 0.822411 |
7,689 | The site was set up in former buildings of the University of Reading's Department of Microbiology. | National Centre for Biotechnology Education | 0.822404 |
7,690 | The National Centre for Biotechnology Education (NCBE) is a national resource centre at the University of Reading to teach pre-university biotechnology in schools in the UK. It was founded in 1990. | National Centre for Biotechnology Education | 0.822404 |
7,691 | It reaches out to schools to give up-to-date information on biotechnology. Biotechnology is a rapidly evolving subject, and schools cannot keep up-to-date with all that they would be required to know. It produces educational resources. It runs the Microbiology in Schools Advisory Committee (MISAC). | National Centre for Biotechnology Education | 0.822404 |
7,692 | The Dolan DNA Learning Center had been set up in the USA.It was set up as an education project by the Society for General Microbiology, now the Microbiology Society. Money from the Laboratory of the Government Chemist set up the National Centre for School Biotechnology (NCSB). Money also came from the Gatsby Charitable... | National Centre for Biotechnology Education | 0.822404 |
7,693 | It began as the National Centre for School Biotechnology (NCSB) in 1985 in the Department of Microbiology. It became the NCBE in 1990. For many years it was the only centre in Europe that was devoted to the teaching of biotechnology in schools. | National Centre for Biotechnology Education | 0.822404 |
7,694 | A careful distinction needs to be made between abstract quantities and measurable quantities. The multiplication and division rules of quantity calculus are applied to SI base units (which are measurable quantities) to define SI derived units, including dimensionless derived units, such as the radian (rad) and steradia... | Quantity calculus | 0.822403 |
7,695 | Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities.Its roots can be traced to Fourier's concept of dimensional analysis (1822). The basic axiom of quantity calculus is Maxwell's description of a physical quantity as the product of a "numerical value" an... | Quantity calculus | 0.822403 |
7,696 | Milne, a crater on the Moon The E.A. Milne Centre for Astrophysics at the University of Hull (opened 2015) | Kinematic Relativity | 0.822401 |
7,697 | Milne married Margaret Scott Campbell on 26 June 1928 at Withington, Manchester. Campbell, from Dornoch, Sutherland, Scotland, was the daughter of Hugh Fraser Campbell, an advocate in Aberdeen. Milne's brother, Geoffrey, then a lecturer in agricultural chemistry at the University of Leeds, was best man. | Kinematic Relativity | 0.822401 |
7,698 | Milne's earlier work was in mathematical astrophysics. Much of his research in the 1930s was concerned with the theory of relativity and cosmology. His later work, concerned with the interior structure of stars, aroused controversy. | Kinematic Relativity | 0.822401 |
7,699 | In 1917 he became a lieutenant in the Royal Navy Volunteer Reserve. He was a fellow of Trinity College, Cambridge, 1919–1925, being assistant director of the solar physics observatory, 1920–1924, mathematical lecturer at Trinity, 1924–1925, and university lecturer in astrophysics, 1922–1925. He was Beyer professor of a... | Kinematic Relativity | 0.822401 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.