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86,300 | In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A. Horn who proposed it in 1962. It provides a vast generalization of such conjectures as the Hardy and Littlewood conj... | Bateman-Horn conjecture | 0.782577 |
86,301 | Every smooth convex surface collapses to a point under the mean-curvature flow, without other singularities, and converges to the shape of a sphere as it does so. For surfaces of dimension two or more this is a theorem of Gerhard Huisken; for the one-dimensional curve-shortening flow it is the Gage–Hamilton–Grayson the... | Mean curvature flow | 0.782575 |
86,302 | In the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space). Intuitively, a family of surfaces evolves under mean curvature flow if the normal component of the veloci... | Mean curvature flow | 0.782575 |
86,303 | In statistics, an ecological correlation (also spatial correlation) is a correlation between two variables that are group means, in contrast to a correlation between two variables that describe individuals. For example, one might study the correlation between physical activity and weight among sixth-grade children. A s... | Ecological correlation | 0.782574 |
86,304 | Subsequently, due to the naming of the commercial product, PAG became the polymer gel dosimeter acronym of choice for most authors. Numerous authors subsequently published results of work investigating different compositions and formulations of polymer gel dosimeters which were summarised by Lepage et al.Although polym... | Gel dosimetry | 0.782572 |
86,305 | On any industrial site, there is a continuous stream of operational, maintenance and safety events occurring at all levels and areas within the process. An electronic shift logbook is used at power plants and in process industry where several shift teams cooperate in maintaining production. Typically the electronic shi... | Electronic logbook | 0.782572 |
86,306 | For good confinement there must be more particles moving perpendicular to the field than there are moving parallel to the field. Such a non-Maxwellian velocity distribution is, however, very difficult to maintain and energetically costly. The mirrors' advantage of simple machine geometry is maintained in machines which... | List of fusion experiments | 0.78257 |
86,307 | The alternative is to dispense with a solid core and rely on currents in the plasma to produce the toroidal field. Mirror machines have advantages in a simpler geometry and a better potential for direct conversion of particle energy to electricity. They generally require higher magnetic fields than toroidal machines, b... | List of fusion experiments | 0.78257 |
86,308 | Within the field of magnetic confinement experiments, there is a basic division between toroidal and open magnetic field topologies. Generally speaking, it is easier to contain a plasma in the direction perpendicular to the field than parallel to it. Parallel confinement can be solved either by bending the field lines ... | List of fusion experiments | 0.78257 |
86,309 | Trisops – 2 facing theta-pinch guns FF-2B, Lawrenceville Plasma Physics, United States | List of fusion experiments | 0.78257 |
86,310 | TMX, TMX-U Lawrence Livermore National Laboratory, Livermore CA. MFTF Lawrence Livermore National Laboratory, Livermore CA. Gas Dynamic Trap at Budker Institute of Nuclear Physics, Akademgorodok, Russia. | List of fusion experiments | 0.78257 |
86,311 | However, the majority of the population (i.e., the low-income population) follows a different distribution which is debated to be either Gibbs or log-normal. Basic tools used in this type of modelling are probabilistic and statistical methods mostly taken from the kinetic theory of statistical physics. Monte Carlo simu... | Kinetic exchange models of markets | 0.782568 |
86,312 | Kinetic exchange models are multi-agent dynamic models inspired by the statistical physics of energy distribution, which try to explain the robust and universal features of income/wealth distributions. Understanding the distributions of income and wealth in an economy has been a classic problem in economics for more th... | Kinetic exchange models of markets | 0.782568 |
86,313 | ß-hydrogen elimination does not explain the formation of metal tetranorbornyls complexes that are synthesized from lower valent metal center precursors, shortened bond lengths between the metal center and 1-norbornyl ligand carbons, or the resulting low-spin tetrahedral molecular geometry. Quantum mechanical calculatio... | Metal tetranorbornyl | 0.782567 |
86,314 | The resulting molecular geometry of the metal tetranorbornyls complexes is due to the unpaired and paired d electrons. Magnetic measurements have indicated that the d electrons of tetrakis(1-norbornyl)chromium (d2) and tetrakis(1-norbornyl)manganese (d3) are not spin paired. The four d electrons of tetrakis(1-norbornyl... | Metal tetranorbornyl | 0.782567 |
86,315 | Barton K. Bower and Howard G. Tennent were able to successfully synthesize and characterize the following metal tetranorbornyls derived from the first-, second-, and third-row transition metals: tetrakis(1-norbornyl)hafnium tetrakis(1-norbornyl)zirconium tetrakis(1-norbornyl)titanium tetrakis(1-norbornyl)vanadium tetra... | Metal tetranorbornyl | 0.782567 |
86,316 | Tetrakis(1-norbornyl)cobalt(IV) is a thermally stable homoleptic complex observed with σ-bonding ligands. The metal tetranorbornyl complex was the first isolated low-spin complex with tetrahedral molecular geometry. The tetrakis(1-norbornyl)cobalt(IV) complex was first synthesized by Barton K. Bower and Howard G. Tenne... | Metal tetranorbornyl | 0.782567 |
86,317 | In organometallic chemistry, metal tetranorbornyls are compounds with the formula M(nor)4 (M = a metal in a +4 oxidation state) (1-nor = 4bicyclohept-1-yl) and are one of the largest series of tetraalkyl complexes derived from identical ligands. Metal tetranorbornyls display uniform stoichiometry, low-spin configuratio... | Metal tetranorbornyl | 0.782567 |
86,318 | Pseudohalogens are polyatomic analogues of halogens, whose chemistry, resembling that of the true halogens, allows them to substitute for halogens in several classes of chemical compounds. Pseudohalogens occur in pseudohalogen molecules, inorganic molecules of the general forms Ps–Ps or Ps–X (where Ps is a pseudohaloge... | Pseudohalogen | 0.782566 |
86,319 | x k {\displaystyle x_{k}} is the state of the time k, it contains the past information and prepares it for future optimization. u k {\displaystyle u_{k}} is the control variable. w k {\displaystyle w_{k}} is the random parameter.For the cost function, it has the form: g N ( X N ) + ∑ k = 0 N − 1 g k ( x k , u k , W k )... | Simulation-based optimization | 0.782566 |
86,320 | See, for example, the following .2. When confronted with minimizing non-convex functions, it will show its limitation. 3. Derivative-free optimization methods are relatively simple and easy, but, like most optimization methods, some care is required in practical implementation (e.g., in choosing the algorithm parameter... | Simulation-based optimization | 0.782566 |
86,321 | Some methods cannot handle optimization problems with more than a few variables; the results are usually not so accurate. However, there are numerous practical cases where derivative-free methods have been successful in non-trivial simulation optimization problems that include randomness manifesting as "noise" in the o... | Simulation-based optimization | 0.782566 |
86,322 | Derivative-free optimization is a subject of mathematical optimization. This method is applied to a certain optimization problem when its derivatives are unavailable or unreliable. Derivative-free methods establish a model based on sample function values or directly draw a sample set of function values without exploiti... | Simulation-based optimization | 0.782566 |
86,323 | Simulation-based optimization has some limitations, such as the difficulty of creating a model that imitates the dynamic behavior of a system in a way that is considered good enough for its representation. Another problem is complexity in the determining uncontrollable parameters of both real-world system and simulatio... | Simulation-based optimization | 0.782566 |
86,324 | Optimization exists in two main branches of operations research: Optimization parametric (static) – The objective is to find the values of the parameters, which are “static” for all states, with the goal of maximizing or minimizing a function. In this case, one can use mathematical programming, such as linear programmi... | Simulation-based optimization | 0.782566 |
86,325 | For example, there might be too many possible values for input variables, or the simulation model might be too complicated and expensive to run for a large set of input variable values. In these cases, the goal is to iterative find optimal values for the input variables rather than trying all possible values. This proc... | Simulation-based optimization | 0.782566 |
86,326 | To obtain the optimal solution with minimum computation and time, the problem is solved iteratively where in each iteration the solution moves closer to the optimum solution. Such methods are known as ‘numerical optimization’, ‘simulation-based optimization’ or 'simulation-based multi-objective optimization' used when ... | Simulation-based optimization | 0.782566 |
86,327 | Simulation-based optimization (also known as simply simulation optimization) integrates optimization techniques into simulation modeling and analysis. Because of the complexity of the simulation, the objective function may become difficult and expensive to evaluate. Usually, the underlying simulation model is stochasti... | Simulation-based optimization | 0.782566 |
86,328 | Ranking and selection methods are designed for problems where the alternatives are fixed and known, and simulation is used to estimate the system performance. In the simulation optimization setting, applicable methods include indifference zone approaches, optimal computing budget allocation, and knowledge gradient algo... | Simulation-based optimization | 0.782566 |
86,329 | Neuro-dynamic programming is the same as dynamic programming except that the former has the concept of approximation architectures. It combines artificial intelligence, simulation-base algorithms, and functional approach techniques. “Neuro” in this term origins from artificial intelligence community. It means learning ... | Simulation-based optimization | 0.782566 |
86,330 | Heuristic methods change accuracy by speed. Their goal is to find a good solution faster than the traditional methods, when they are too slow or fail in solving the problem. Usually they find local optimal instead of the optimal value; however, the values are considered close enough of the final solution. Examples of t... | Simulation-based optimization | 0.782566 |
86,331 | Some important approaches in simulation optimization are discussed below. | Simulation-based optimization | 0.782566 |
86,332 | In response surface methodology, the objective is to find the relationship between the input variables and the response variables. The process starts from trying to fit a linear regression model. If the P-value turns out to be low, then a higher degree polynomial regression, which is usually quadratic, will be implemen... | Simulation-based optimization | 0.782566 |
86,333 | Other tests should be performed to get a baseline measurement of their current blood chemistry, such as an arterial blood gas or thromboelastography. In those with cardiac arrest due to trauma chest compressions are considered futile, but still recommended. Correcting the underlying cause such as a pneumothorax or peri... | Mechanical trauma | 0.782565 |
86,334 | This concept was introduced as a way of improving the ‘keyword approach' to ad placement were issues surrounding ambiguity in relation to a word's meaning in the prescribed context. The concept of analyzing the ‘entire' Webpage in order to promote relevant advertising material is to benefit both the viewer of advertisi... | Ad serving | 0.782565 |
86,335 | A Rydberg polaron is an exotic state of matter, created at low temperatures, in which a very large atom contains other ordinary atoms in the space between the nucleus and the electrons. For the formation of this atom, scientists had to combine two fields of atomic physics: Bose–Einstein condensates and Rydberg atoms. R... | Rydberg polaron | 0.782563 |
86,336 | The Hauptvermutung of geometric topology is a now refuted conjecture asking whether any two triangulations of a triangulable space have subdivisions that are combinatorially equivalent, i.e. the subdivided triangulations are built up in the same combinatorial pattern. It was originally formulated as a conjecture in 190... | Hauptvermutung | 0.782563 |
86,337 | The Cantor set itself is a Cantor space. But the canonical example of a Cantor space is the countably infinite topological product of the discrete 2-point space {0, 1}. This is usually written as 2 N {\displaystyle 2^{\mathbb {N} }} or 2ω (where 2 denotes the 2-element set {0,1} with the discrete topology). A point in ... | Cantor space | 0.782562 |
86,338 | The PadLock instruction set can be divided into four subsets: Random number generation (RNG) XSTORE: Store Available Random Bytes (aka XSTORERNG) REP XSTORE: Store ECX Random Bytes Advanced cryptography engine (ACE) - for AES crypto; two versions REP XCRYPTECB: Electronic code book REP XCRYPTCBC: Cipher Block Chaining ... | VIA PadLock | 0.782558 |
86,339 | The Ryzen 3000 series CPUs were released on July 7, 2019, while the Zen 2-based Epyc server CPUs (codename "Rome") were released on August 7, 2019. Zen 2 Matisse products were the first consumer CPUs to use TSMC's 7 nm process node. Zen 2 introduced the chiplet based architecture, where desktop, workstation, and server... | AMD Zen | 0.782558 |
86,340 | The Zermelo–Fraenkel axioms for set theory were formulated which provided a conceptual framework in which much mathematical discourse would be interpreted. In mathematics, as in physics, new and unexpected ideas had arisen and significant changes were coming. With Gödel numbering, propositions could be interpreted as r... | Set-theoretic Platonism | 0.782558 |
86,341 | Algebraic geometry of projective spaces Fano variety: a variety whose canonical bundle is anti-ample Matsusaka's big theorem Divisorial scheme: a scheme admitting an ample family of line bundles | Very ample line bundle | 0.782558 |
86,342 | Let X be a scheme over a field k (for example, an algebraic variety) with a line bundle L. (A line bundle may also be called an invertible sheaf.) Let a 0 , . . | Very ample line bundle | 0.782558 |
86,343 | The data bits that are sent through EI bus connections are aligned to the clock so that they latch to the data at the high speeds. EI bus connections require that the net topology and timing characteristics for each net on the bus are at least similar to each other in order to make lining up the edges of the data to th... | IBM Elastic Interface | 0.782552 |
86,344 | John Farey Jr. (20 March 1791 – 17 July 1851) was an English mechanical engineering, consulting engineer and patent agent, known for his pioneering contributions in the field of mechanical engineering.As consulting engineer Farey worked for many well-known inventors of the later Industrial Revolution, and was a witness... | A Treatise on the Steam Engine | 0.782549 |
86,345 | Nevertheless, the Hilbert transform is not bounded on L1(R) or L∞(R), and so we cannot use the Riesz–Thorin interpolation theorem directly. To see why we do not have these endpoint bounds, it suffices to compute the Hilbert transform of the simple functions 1(−1,1)(x) and 1(0,1)(x) − 1(0,1)(−x). We can show, however, t... | Riesz–Thorin theorem | 0.782548 |
86,346 | The Hilbert transform of f: R → C is given by where p.v. indicates the Cauchy principal value of the integral. The Hilbert transform is a Fourier multiplier operator with a particularly simple multiplier: It follows from the Plancherel theorem that the Hilbert transform maps L2(R) boundedly into itself. | Riesz–Thorin theorem | 0.782548 |
86,347 | Let f be a fixed integrable function and let T be the operator of convolution with f , i.e., for each function g we have Tg = f ∗ g. It is well known that T is bounded from L1 to L1 and it is trivial that it is bounded from L∞ to L∞ (both bounds are by || f ||1). Therefore the Riesz–Thorin theorem gives We take this in... | Riesz–Thorin theorem | 0.782548 |
86,348 | It has been shown in the first section that the Fourier transform F {\displaystyle {\mathcal {F}}} maps L1(Rd) boundedly into L∞(Rd) and L2(Rd) into itself. A similar argument shows that the Fourier series operator, which transforms periodic functions f: T → C into functions f ^: Z → C {\displaystyle {\hat {f}}:\mathbf... | Riesz–Thorin theorem | 0.782548 |
86,349 | Its usefulness stems from the fact that some of these spaces have rather simpler structure than others. Usually that refers to L2 which is a Hilbert space, or to L1 and L∞. Therefore one may prove theorems about the more complicated cases by proving them in two simple cases and then using the Riesz–Thorin theorem to pa... | Riesz–Thorin theorem | 0.782548 |
86,350 | In mathematics, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is a result about interpolation of operators. It is named after Marcel Riesz and his student G. Olof Thorin. This theorem bounds the norms of linear maps acting between Lp spaces. | Riesz–Thorin theorem | 0.782548 |
86,351 | If realistic models of particle physics such as the Standard Model suffer from triviality issues, the idea of an elementary scalar Higgs particle may have to be modified or abandoned. The situation becomes more complex in theories that involve other particles however. | Quantum triviality | 0.782548 |
86,352 | Strong evidence supports the idea that a field theory involving only a scalar Higgs boson is trivial in four spacetime dimensions, but the situation for realistic models including other particles in addition to the Higgs boson is not known in general. Nevertheless, because the Higgs boson plays a central role in the St... | Quantum triviality | 0.782548 |
86,353 | As a result, the question of whether the Standard Model of particle physics is nontrivial remains a serious unresolved question. Theoretical proofs of triviality of the pure scalar field theory exist, but the situation for the full standard model is unknown. The implied constraints on the standard model have been discu... | Quantum triviality | 0.782548 |
86,354 | Modern considerations of triviality are usually formulated in terms of the real-space renormalization group, largely developed by Kenneth Wilson and others. Investigations of triviality are usually performed in the context of lattice gauge theory. A deeper understanding of the physical meaning and generalization of the... | Quantum triviality | 0.782548 |
86,355 | Although they are not diffusive in nature, some quantum mechanics problems are also governed by a mathematical analog of the heat equation (see below). It also can be used to model some phenomena arising in finance, like the Black–Scholes or the Ornstein-Uhlenbeck processes. The equation, and various non-linear analogu... | Particle diffusion | 0.782546 |
86,356 | In the physics and engineering literature, it is common to use ∇2 to denote the Laplacian, rather than ∆. In mathematics as well as in physics and engineering, it is common to use Newton's notation for time derivatives, so that u ˙ {\displaystyle {\dot {u}}} is used to denote ∂u/∂t, so the equation can be written Note ... | Particle diffusion | 0.782546 |
86,357 | That is, the maximum temperature in a region R {\displaystyle R} can increase only if heat comes in from outside R {\displaystyle R} . This is a property of parabolic partial differential equations and is not difficult to prove mathematically (see below). Another interesting property is that even if u {\displaystyle u}... | Particle diffusion | 0.782546 |
86,358 | The split real forms for the complex semisimple Lie algebras are: A n , s l n + 1 ( C ): s l n + 1 ( R ) {\displaystyle A_{n},{\mathfrak {sl}}_{n+1}(\mathbf {C} ):{\mathfrak {sl}}_{n+1}(\mathbf {R} )} B n , s o 2 n + 1 ( C ): s o n , n + 1 ( R ) {\displaystyle B_{n},{\mathfrak {so}}_{2n+1}(\mathbf {C} ):{\mathfrak {so}... | Split Lie algebra | 0.782542 |
86,359 | Over a non-algebraically closed field, there exist non-splittable semisimple Lie algebras. In a splittable Lie algebra, there may exist Cartan subalgebras that are not splitting. Direct sums of splittable Lie algebras and ideals in splittable Lie algebras are splittable. | Split Lie algebra | 0.782542 |
86,360 | Over an algebraically closed field, all Cartan subalgebras are conjugate. Over a non-algebraically closed field, not all Cartan subalgebras are conjugate in general; however, in a splittable semisimple Lie algebra all splitting Cartan algebras are conjugate. Over an algebraically closed field, all semisimple Lie algebr... | Split Lie algebra | 0.782542 |
86,361 | With the advent of 3D printing – and especially the ability to use these to fabricate even better fabricators – and with machines that can search for and reprocess waste or discarded materials, the protagonists no longer have need of regular society for the basic essentials of life, such as food, clothing and shelter. ... | Post scarcity | 0.782542 |
86,362 | Advocates of technological abundance often argue for more extensive use of renewable energy and greater recycling in order to prevent future drops in availability of energy and raw materials, and reduce ecological damage. Solar energy in particular is often emphasized, as the cost of solar panels continues to drop (and... | Post scarcity | 0.782542 |
86,363 | Futurists who speak of "post-scarcity" suggest economies based on advances in automated manufacturing technologies, often including the idea of self-replicating machines, the adoption of division of labour which in theory could produce nearly all goods in abundance, given adequate raw materials and energy. More specula... | Post scarcity | 0.782542 |
86,364 | A World Future Society report looked at how historically capitalism takes advantage of scarcity. Increased resource scarcity leads to increase and fluctuation of prices, which drives advances in technology for more efficient use of resources such that costs will be considerably reduced, almost to zero. They thus claim ... | Post scarcity | 0.782542 |
86,365 | The Museum of Science and the Cosmos (Spanish: El Museo de las Ciencias y el Cosmos), is an astronomy, technology, and science museum located in the city of San Cristóbal de La Laguna on Tenerife island, in the Spanish Canary Islands of Macaronesia. It belongs to the Cabildo de Tenerife and the Tenerife Organization of... | Museum of Science and the Cosmos | 0.782539 |
86,366 | The museum was designed as modern science museum, focused on science communication through interactivity with the displays.It covers all sciences, with a bias towards astronomy. It has a permanent exhibition that covers such topics as the Earth's rotation, solar activity (including sunspots and flares), orbits around b... | Museum of Science and the Cosmos | 0.782539 |
86,367 | Unfortunately, Myc possesses several features that have rendered it difficult to drug to date, such that any anti-cancer drugs aimed at inhibiting Myc may continue to require perturbing the protein indirectly, such as by targeting the mRNA for the protein rather than via a small molecule that targets the protein itself... | Proto-oncogene proteins c-myc | 0.782537 |
86,368 | In phylogenetics, a single-access key (also called dichotomous key, sequential key, analytical key, or pathway key) is an identification key where the sequence and structure of identification steps is fixed by the author of the key. At each point in the decision process, multiple alternatives are offered, each leading ... | Single-access key | 0.782536 |
86,369 | If A is an involutive algebra over the complex numbers C, then a Fredholm module over A consists of an involutive representation of A on a Hilbert space H, together with a self-adjoint operator F, of square 1 and such that the commutator is a compact operator, for all a in A. | Fredholm module | 0.782534 |
86,370 | In noncommutative geometry, a Fredholm module is a mathematical structure used to quantize the differential calculus. Such a module is, up to trivial changes, the same as the abstract elliptic operator introduced by Atiyah (1970). | Fredholm module | 0.782534 |
86,371 | Current research into effective approaches to system of systems problems includes: Establishment of an effective frame of reference Crafting of a unifying lexicon Developing effective methodologies to visualize and communicate complex systems Distributed resource management Study of designing architecture Interoperabil... | System of systems | 0.782533 |
86,372 | System of systems is a collection of task-oriented or dedicated systems that pool their resources and capabilities together to create a new, more complex system which offers more functionality and performance than simply the sum of the constituent systems. Currently, systems of systems is a critical research discipline... | System of systems | 0.782533 |
86,373 | Mirrors and Reflections: The Geometry of Finite Reflection Groups is an undergraduate-level textbook on the geometry of reflection groups. It was written by Alexandre V. Borovik and Anna Borovik and published in 2009 by Springer in their Universitext book series. The Basic Library List Committee of the Mathematical Ass... | Mirrors and Reflections | 0.782532 |
86,374 | Mirrors and Reflections is aimed at undergraduate mathematics students, and uses an intuitive and heavily visual approach suitable for that level. its readers are expected to already have a solid background in linear algebra and some group theory. Reviewer Gizem Karaali recommends the book, both as a textbook for a "ca... | Mirrors and Reflections | 0.782532 |
86,375 | There are several other standard textbooks on reflection groups, including Groupes et algèbres de Lie, Chapitres 4, 5 et 6 (Bourbaki, 1968), Finite Reflection Groups (L. C. Grove and C. T. Benson, 1985), and Reflection Groups and Coxeter Groups (James E. Humphreys, 1990). However, these take a more algebraic and less g... | Mirrors and Reflections | 0.782532 |
86,376 | A Civil estimator is a construction professional who bids on civil projects that have gone to tender. Civil estimators typically have a background in civil engineering, construction project management, or construction supervision. Estimators are responsible for obtaining tenders, obtaining of material costs, calculatio... | Civil estimator | 0.78253 |
86,377 | A Stein discrepancy is a statistical divergence between two probability measures that is rooted in Stein's method. It was first formulated as a tool to assess the quality of Markov chain Monte Carlo samplers, but has since been used in diverse settings in statistics, machine learning and computer science. | Stein discrepancy | 0.78253 |
86,378 | Let X {\displaystyle X} be an arbitrary topological space. Let x ∼ y {\displaystyle x\sim y} if and only if y ∈ c o n n ( x ) {\displaystyle y\in \mathrm {conn} (x)} (where c o n n ( x ) {\displaystyle \mathrm {conn} (x)} denotes the largest connected subset containing x {\displaystyle x} ). This is obviously an equiva... | Totally path disconnected | 0.782528 |
86,379 | Paleozoological data is used in research concerning conservation biology. Conservation biology refers to biological study used for conservation, control, and preservation of various species and ecosystems. In this context, the paleozoological data used is obtained from recently deceased decomposing matter rather than p... | Paleozoology | 0.782528 |
86,380 | Palaeozoology, also spelled as Paleozoology (Greek: παλαιόν, palaeon "old" and ζῷον, zoon "animal"), is the branch of paleontology, paleobiology, or zoology dealing with the recovery and identification of multicellular animal remains from geological (or even archeological) contexts, and the use of these fossils in the ... | Paleozoology | 0.782528 |
86,381 | a b v a c w b a x b c y c d a z d c d {\displaystyle abvacwbaxbcycdazdcd} has avoidability index of 5. The repetitive threshold R T ( n ) {\displaystyle RT(n)} is the infimum of exponents k {\displaystyle k} such that x k {\displaystyle x^{k}} is avoidable on an alphabet of size n {\displaystyle n} . Also see Dejean's ... | Unavoidable pattern | 0.782528 |
86,382 | In mathematics and theoretical computer science, a pattern is an unavoidable pattern if it is unavoidable on any finite alphabet. | Unavoidable pattern | 0.782528 |
86,383 | In the above formulation, if the bit rate constraint is neglected by setting λ {\displaystyle \lambda } equal to 0, or equivalently if it is assumed that a fixed-length code (FLC) will be used to represent the quantized data instead of a variable-length code (or some other entropy coding technology such as arithmetic c... | Quantization (signal processing) | 0.782524 |
86,384 | The decision to establish a Norwegian national college of technology was made by the Norwegian parliament, the Storting, in 1900, after years of heated debate on where the institution should be located; many representatives felt that the capital Kristiania (now Oslo) was self-evident as the place for this nationally im... | Norwegian Institute of Technology | 0.782523 |
86,385 | The academic structure of NTH during the last years before its inclusion in NTNU was as follows: Faculty of Architecture, with 5 Departments: Form and Colour Studies Building Technology Architectural History Arch. Design Town and Regional Planning Faculty of Applied Earth Science and Metallurgy, with 3 Departments: Met... | Norwegian Institute of Technology | 0.782523 |
86,386 | To get the classical limit of the Caldeira–Leggett model, the bath must be integrated out (or traced out), which can be understood as taking the average over all the possible realizations of the bath and studying the effective dynamics of the quantum system. As a second step, the limit ℏ → 0 {\displaystyle \hbar \right... | Quantum dissipation | 0.782522 |
86,387 | Quantum dissipation is the branch of physics that studies the quantum analogues of the process of irreversible loss of energy observed at the classical level. Its main purpose is to derive the laws of classical dissipation from the framework of quantum mechanics. It shares many features with the subjects of quantum dec... | Quantum dissipation | 0.782522 |
86,388 | Notice that by virtue of the principle of universality, it is expected that the particular description of the bath will not affect the essential features of the dissipative process, as far as the model contains the minimal ingredients to provide the effect. The simplest way to model the bath was proposed by Feynman and... | Quantum dissipation | 0.782522 |
86,389 | The resulting classical equations of motion are: M d 2 d t 2 X ( t ) = − ∂ V ( X ) ∂ X − ∫ 0 T d t ′ α ( t − t ′ ) ( X ( t ) − X ( t ′ ) ) {\displaystyle M{\frac {d^{2}}{dt^{2}}}X(t)=-{\frac {\partial V(X)}{\partial X}}-\int _{0}^{T}dt'\alpha (t-t')(X(t)-X(t'))} where: α ( t − t ′ ) = 1 2 π ∫ 0 ∞ J ( ω ) e − ω | t − t ... | Quantum dissipation | 0.782522 |
86,390 | In this case, if s > 1 {\displaystyle s>1} the dissipation is called "super-ohmic", while if s < 1 {\displaystyle s<1} is sub-ohmic. An example of a super-ohmic bath is the electro-magnetic field under certain circumstances. As mentioned, the main idea in the field of quantum dissipation is to explain the way classical... | Quantum dissipation | 0.782522 |
86,391 | The physics of strings can be studied in various numbers of dimensions. In addition to three familiar dimensions from everyday experience (up/down, left/right, forward/backward), string theories may include one or more compact dimensions which are curled up into circles. A standard analogy for this is to consider multi... | T-duality | 0.782522 |
86,392 | Put differently, the two theories are mathematically different descriptions of the same phenomena. Like many of the dualities studied in theoretical physics, T-duality was discovered in the context of string theory. In string theory, particles are modeled not as zero-dimensional points but as one-dimensional extended o... | T-duality | 0.782522 |
86,393 | T-duality is a particular example of a general notion of duality in physics. The term duality refers to a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it e... | T-duality | 0.782522 |
86,394 | This led to the realization, in the mid-1990s, that all of the five consistent superstring theories are just different limiting cases of a single eleven-dimensional theory called M-theory. In general, T-duality relates two theories with different spacetime geometries. In this way, T-duality suggests a possible scenario... | T-duality | 0.782522 |
86,395 | In theoretical physics, T-duality (short for target-space duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories describes strings propagating in a spacetime shaped like a circle of some radius... | T-duality | 0.782522 |
86,396 | Instead, one finds that there are two Calabi–Yau manifolds that give rise to the same physics. These manifolds are said to be "mirror" to one another. This mirror duality is an important computational tool in string theory, and it has allowed mathematicians to solve difficult problems in enumerative geometry. | T-duality | 0.782522 |
86,397 | In string theory and algebraic geometry, the term "mirror symmetry" refers to a phenomenon involving complicated shapes called Calabi–Yau manifolds. These manifolds provide an interesting geometry on which strings can propagate, and the resulting theories may have applications in particle physics. In the late 1980s, it... | T-duality | 0.782522 |
86,398 | Quality and Reliability Engineering International is a scientific journal focusing on engineering quality and reliability. This includes the quality and reliability of components, equipment, and physics of failure. It covers the fields of electrical, mechanical, and systems engineering | Quality and Reliability Engineering International | 0.782521 |
86,399 | One may define additive functions with values in any additive monoid (for example any group or more commonly a vector space). For sigma-additivity, one needs in addition that the concept of limit of a sequence be defined on that set. For example, spectral measures are sigma-additive functions with values in a Banach al... | Sigma-additive set function | 0.782521 |
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