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Materials data management is not just about the avoidance of problems and risk. The MDMC reports that best practice materials data management can have very positive effects on innovation and quality. For example, Rolls-Royce Aerospace have described how the ongoing assessment and analysis of all of the materials proper... | Wikipedia - Materials data management | null | null | null |
Materials data management practitioners usually emphasize the need for a holistic approach. It is of limited use having a superb means to capture test data if that data disappears into a ‘black hole’ database that no-one accesses. Materials property analysis is a wasted investment if the results generated are not deplo... | Wikipedia - Materials data management | null | null | null |
The MDMC sees this process as having four stages: capture, analyze, deploy, and maintain. Key issues at each stage are: These issues need to be addressed through a combination of good practice, robust processes, and appropriate information systems. | Wikipedia - Materials data management | null | null | null |
MDMC members use a particular commercial-off-the-shelf (COTS) software solution. Whether an engineering enterprise applies such a solution or builds an in-house system, it needs to account for the issues above and to integrate into its wider product lifecycle management (PLM) systems. == References == | Wikipedia - Materials data management | null | null | null |
Materials exhibit myriad properties, including the following. Mechanical properties, see Strength of materials Chemical properties, see Chemistry Electrical properties, see Electricity Thermal properties, see Thermodynamics Optical properties, see Optics and Photonics Magnetic properties, see MagnetismThe properties of... | Wikipedia - Materials scientist | null | null | null |
Materials in certain cosmetics such as sun cream, moisturizer, and deodorant may have potentials benefits from the use of nanochemistry. Manufacturers are working to increase the effectiveness of various cosmetics by facilitating oil nanoemulsion. These particles have extended the boundaries in managing wrinkling, dehy... | Wikipedia - Nanochemistry | null | null | null |
Materials science is closely related to civil engineering. It studies fundamental characteristics of materials, and deals with ceramics such as concrete and mix asphalt concrete, strong metals such as aluminum and steel, and thermosetting polymers including polymethylmethacrylate (PMMA) and carbon fibers. Materials eng... | Wikipedia - Civil works | null | null | null |
It incorporates elements of applied physics and chemistry. With recent media attention on nanoscience and nanotechnology, materials engineering has been at the forefront of academic research. It is also an important part of forensic engineering and failure analysis. | Wikipedia - Civil works | null | null | null |
Materials science recognizes asperities ranging from the sub-visual (normally less than 0.1 mm) to the atomic scale. | Wikipedia - Asperity (Geotechnical engineering) | null | null | null |
Materials structures consist of intrinsic magnetic moments which are separated into domains called Weiss domains. This can result in ferromagnetic materials having no spontaneous magnetism as domains could potentially balance each other out. The position of particles can therefore have different orientations around the... | Wikipedia - Curie point | null | null | null |
An average total magnetism is taken from the bulk and surface temperatures to calculate the Curie temperature from the material, noting the bulk contributes more.The angular momentum of an electron is either +ħ/2 or −ħ/2 due to it having a spin of 1/2, which gives a specific size of magnetic moment to the electron; the... | Wikipedia - Curie point | null | null | null |
Angular momentum contributes twice as much to magnetic moments than orbital.For terbium which is a rare-earth metal and has a high orbital angular momentum the magnetic moment is strong enough to affect the order above its bulk temperatures. It is said to have a high anisotropy on the surface, that is it is highly dire... | Wikipedia - Curie point | null | null | null |
Materials supporting quantum spin liquid states may have applications in data storage and memory. In particular, it is possible to realize topological quantum computation by means of spin-liquid states. Developments in quantum spin liquids may also help in the understanding of high temperature superconductivity. == Ref... | Wikipedia - Quantum spin liquid | null | null | null |
Materials with high surface area to volume ratio (e.g. very small diameter, very porous, or otherwise not compact) react at much faster rates than monolithic materials, because more surface is available to react. An example is grain dust: while grain is not typically flammable, grain dust is explosive. Finely ground sa... | Wikipedia - Surface-to-volume ratio | null | null | null |
Materials, instrumentation, and measurement classes specific to biological systems Systems optimization Modeling and management of biological and physical systems Soil, water, conservation, and nutrient management engineering | Wikipedia - Natural resources engineering | null | null | null |
Maternal age has been shown to be related to intelligence with younger mothers tending have children of lower intelligence than older mothers. However, this relationship may be non-linear with older mothers being at increased risk of giving birth to children with down syndrome which greatly affects cognitive abilities. | Wikipedia - Environment and intelligence | null | null | null |
Maternal deprivation can be caused by the abandonment by a nurturing parent at a young age. In rodents or nonhuman primates, this leads to a higher vulnerability for stress-related illness. Research suggests that environmental enrichment can reverse the effects of maternal separation on stress reactivity, possibly by a... | Wikipedia - Environmental enrichment | null | null | null |
Maternal investment was "allometrically engineered" by surgically removing an ovary in cockroaches (Diploptera punctata). This effectively reduced number of progeny and increased resource allocation to each offspring. They coupled this manipulation with group effects (faster development in large groups), and found that... | Wikipedia - Allometric engineering | null | null | null |
Maternal mortality rates are extremely high worldwide. However, most women who die during or after pregnancy live in low and lower-middle income countries. Specifically, in 2017, 94% of all maternal deaths occurred in low and lower-middle income countries. The MMR in low-income countries was 462 in 2017 signifying that... | Wikipedia - Maternal health | null | null | null |
In many low and lower-middle income countries complications of pregnancy and childbirth are the leading causes of death among women of reproductive age. According to the World Health Organization, in its World Health Report 2005, poor maternal conditions account for the fourth leading cause of death for women worldwide... | Wikipedia - Maternal health | null | null | null |
Maternal stress experienced during labor and delivery can induce DOL. Stress levels can be influenced by factors including the way of labor, duration of labor and degree of post-surgical pain after a cesarean surgery (c-section). Unscheduled cesarean delivery and long labor duration place excessive pressure on the moth... | Wikipedia - Delayed onset of lactation | null | null | null |
The elevated level of the stress hormone affects the secretion of lactogenic hormones in the mother, which delays the onset of lactation.Women who underwent a c-section are more likely to experience DOL compared to women who delivered vaginally. This affiliation could be the result of post-surgical pain and stress asso... | Wikipedia - Delayed onset of lactation | null | null | null |
Maternal stress has been linked to a number of negative outcomes for the developing fetus. Pregnant women who firsthand experienced the devastation of the World Trade Center attack on September 11, 2001 were studied to observe the effects of PTSD (post-traumatic stress disorder) on their child's future health. Of the w... | Wikipedia - Fetal Origins Hypothesis | null | null | null |
The finding was strongest for the women who were in their third trimester during 9/11. Based on the findings that there was a trimester distinction in strength, conclusions can be drawn that the development of a vulnerability to stress was due at least in part to environment in utero. 9/11 is also correlated with lower... | Wikipedia - Fetal Origins Hypothesis | null | null | null |
Stress has also been linked to preterm birth, as shown by research studies conducted following the Tarapaca, Chile earthquake in 2005, as well as the Northridge, California earthquake in 1994. Similar findings have been replicated for stressful life experiences and fetal outcomes in the Hurricane Katrina population of ... | Wikipedia - Fetal Origins Hypothesis | null | null | null |
Experiencing loss during pregnancy also influences postnatal outcomes. Women who experienced the death of a close family member, friend, or spouse, or were pregnant during a wartime conflict, were more likely to have children prematurely, and the children of these women were significantly more likely than the general p... | Wikipedia - Fetal Origins Hypothesis | null | null | null |
Women who experienced the most stressful storm related events had children with detriments in cognitive, language, behavioral, and attention outcomes. Shockingly, the poorer performance by these children has persisted until the age of ten. Even job-related stress has been found to be associated with low birth weight an... | Wikipedia - Fetal Origins Hypothesis | null | null | null |
Working long hours, having temporarily employment, or reporting physically demanding job tasks showed "significant and strong" associations with poorer later birth outcomes. Findings for the job stress-birth association have been replicated by obstetricians at Cedars-Sinai Medical Center in Los Angeles. | Wikipedia - Fetal Origins Hypothesis | null | null | null |
However, some research has found that moderate amounts of stress and cortisol passed on to a developing fetus are actually beneficial, perhaps acting to give organs a "workout" prior to birth. Further cementing the theory that maternal emotional state can impact child development are the sound research findings that wo... | Wikipedia - Fetal Origins Hypothesis | null | null | null |
Out of the 389 workers detained, 270 served sentences and most were deported to primarily Mexico and Guatemala. Among those arrested 98% were Latino as they were suspected of being illegal immigrants. | Wikipedia - Fetal Origins Hypothesis | null | null | null |
Latino families feared future deportations and future raids creating psychological stress on Latinos in the area. In relation to maternal stress a study was conducted which found that Latino babies born 37 weeks after the event experienced a 24% greater risk of lower birth (about 5.5 pounds) weight than babies born in ... | Wikipedia - Fetal Origins Hypothesis | null | null | null |
Maternal stress levels may affect the developing child's intelligence. The timing and duration of stress can greatly alter the fetus' brain development which can have long-term effects on intelligence. Maternal reactions to stress such as increased heart rate are dampened during pregnancy in order to protect the fetus.... | Wikipedia - Environment and intelligence | null | null | null |
However, not all maternal stress has been perceived as bad as some has been seen to induce advantageous adaptions.Stress during early childhood may also affect the child's development and have negative consequences on neural systems underlying fluid intelligence. A 2006 study found that IQ scores were related to the nu... | Wikipedia - Environment and intelligence | null | null | null |
Maternity leave is usually fixed at 2 months post-partum, with no option of extending it. However, in the government, you may opt to take 3 months' post-partum leave (maternity), but on condition that you must not have more than 5 children (any child born after the 5th will only provide 2 months' post-partum leave). Th... | Wikipedia - Shared earning/shared parenting marriage | null | null | null |
Math Chemistry Physics Fluid Mechanics Chemical Reaction Engineering Thermodynamics Chemical Thermodynamics Engineering Mechanics Fluid Dynamics Heat Transfer Mass Transfer Transport Phenomena Green Chemistry and Sustainability Process Control Process Instrumentation Process Safety Unit Operation Process Design Chemica... | Wikipedia - Outline of chemical engineering | null | null | null |
Math League (grades 4–12) Mathematical Olympiads for Elementary and Middle Schools (MOEMS) (grades 4–6 and 7–8) | Wikipedia - Math competition | null | null | null |
Math Midway is a traveling exhibition of math-based interactive displays. The exhibits include a square-wheeled tricycle that travels smoothly over an undulating cycloidal track; the Ring of Fire, which uses lasers to intersect three-dimensional objects with a two-dimensional plane to uncover interesting shapes; and an... | Wikipedia - National Museum of Mathematics | null | null | null |
In 2016, the Math Midway exhibit was sold to the Science Centre Singapore. Math Midway 2 Go (MM2GO) is a spinoff of Math Midway. MM2GO includes six of the most popular Math Midway Exhibits. | Wikipedia - National Museum of Mathematics | null | null | null |
MM2GO began traveling to science festivals, schools, community centers, and libraries in the autumn of 2012. Math Encounters is a monthly speaker series presented by the Museum of Math and the Simons Foundation. | Wikipedia - National Museum of Mathematics | null | null | null |
The lectures initially took place at Baruch College in Manhattan on the first Wednesday of each month, but moved to MoMath's visitor center at 11 East 26th Street in March, 2013. Every month a different mathematician is invited to deliver a lecture. Lecturers have included Google's Director of Research Peter Norvig, jo... | Wikipedia - National Museum of Mathematics | null | null | null |
Examples of topics are "The Geometry of Origami", "The Patterns of Juggling", and "Mathematical Morsels from The Simpsons and Futurama". The lectures are meant to be accessible and engaging for high school students and adults. The first lecture occurred on March 3, 2011. Twenty unique lectures had been delivered as of ... | Wikipedia - National Museum of Mathematics | null | null | null |
Math, Philosophy, Comics and Bertrand Russell’s Search for Truth, Publishers Weekly, April 14, 2009 Bertrand Russell: The thinking person's superhero, The Independent, September 2, 2009 Logicomix, Financial Times, September 5, 2009 Essay review by Paolo Mancosu, pp. 1–14, U.C. Berkeley, January 2010 | Wikipedia - Logicomix | null | null | null |
Math: Swedish (titled "Matte Raketen") Finnish (titled "Matikkaraketti") Japanese (titled "算数戦士ブラスター(Sansū Senshi Burasutā)") | Wikipedia - Blaster Learning System | null | null | null |
Mathematica has an implementation as part of its support for stochastic processes Susa signal processing framework provides the C++ implementation for Forward error correction codes and channel equalization here. C++ C# Java Java 8 Julia (HMMBase.jl) Perl Prolog Haskell Go SFIHMM includes code for Viterbi decoding. | Wikipedia - Soft output Viterbi algorithm | null | null | null |
Mathematica is also integrated with Wolfram Alpha, an online answer engine that provides additional data, some of which is kept updated in real time, for users who use Mathematica with an internet connection. Some of the data sets include astronomical, chemical, geopolitical, language, biomedical, airplane, and weather... | Wikipedia - Wolfram Mathematica | null | null | null |
Mathematica: CylindricalDecomposition QEPCAD -- Quantifier Elimination by Partial Cylindrical Algebraic Decomposition redlog Maple: The RegularChains Library and ProjectionCAD | Wikipedia - Cylindrical algebraic decomposition | null | null | null |
Mathematical Introduction Review of Classical Mechanics All Is Not Well with Classical Mechanics The Postulates – a General Discussion Simple Problems in One Dimension The Classical Limit The Harmonic Oscillator The Path Integral Formulation of Quantum Theory The Heisenberg Uncertainty Relations Systems with N {\displa... | Wikipedia - Principles of Quantum Mechanics | null | null | null |
Mathematical Medicine and Biology received an impact factor of 1.854 in 2020. | Wikipedia - Mathematical Medicine and Biology | null | null | null |
Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. The term Platonism is used because such a view is seen to parallel Plato's T... | Wikipedia - Philosophy of mathematics | null | null | null |
A major question considered in mathematical Platonism is: Precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover trut... | Wikipedia - Philosophy of mathematics | null | null | null |
One proposed answer is the Ultimate Ensemble, a theory that postulates that all structures that exist mathematically also exist physically in their own universe. Kurt Gödel's Platonism postulates a special kind of mathematical intuition that lets us perceive mathematical objects directly. (This view bears resemblances ... | Wikipedia - Philosophy of mathematics | null | null | null |
Davis and Hersh have suggested in their 1999 book The Mathematical Experience that most mathematicians act as though they are Platonists, even though, if pressed to defend the position carefully, they may retreat to formalism. Full-blooded Platonism is a modern variation of Platonism, which is in reaction to the fact t... | Wikipedia - Philosophy of mathematics | null | null | null |
They may be provable, even if they cannot all be derived from a single consistent set of axioms.Set-theoretic realism (also set-theoretic Platonism) a position defended by Penelope Maddy, is the view that set theory is about a single universe of sets. This position (which is also known as naturalized Platonism because ... | Wikipedia - Philosophy of mathematics | null | null | null |
Mathematical Reviews – journal and online database published by the American Mathematical Society (AMS) that contains brief synopses (and occasionally evaluations) of many articles in mathematics, statistics and theoretical computer science. Zentralblatt MATH – service providing reviews and abstracts for articles in pu... | Wikipedia - Outline of mathematics | null | null | null |
Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno... | Wikipedia - Non-classical analysis | null | null | null |
Later, Greek mathematicians such as Eudoxus and Archimedes made more explicit, but informal, use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids. The explicit use of infinitesimals appears in Archimedes' The Method of Mechanical Theo... | Wikipedia - Non-classical analysis | null | null | null |
Mathematical analysis of this division-like process reveals how to select a divisor that guarantees good error-detection properties. In this analysis, the digits of the bit strings are taken as the coefficients of a polynomial in some variable x—coefficients that are elements of the finite field GF(2) (the integers mod... | Wikipedia - Cyclic redundancy | null | null | null |
Mathematical biology is one of the fastest expanding areas of mathematics at the beginning of the 21st century. "Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better" is an essay by Joel E. Cohen. | Wikipedia - Future of mathematics | null | null | null |
Mathematical biology is the use of mathematical models of living organisms to examine the systems that govern structure, development, and behavior in biological systems. This entails a more theoretical approach to problems, rather than its more empirically-minded counterpart of experimental biology. Mathematical biolog... | Wikipedia - Computational biologist | null | null | null |
Gathering and analyzing large datasets have made room for growing research fields such as data mining, and computational biomodeling, which refers to building computer models and visual simulations of biological systems. This allows researchers to predict how such systems will react to different environments, which is ... | Wikipedia - Computational biologist | null | null | null |
A majority of researchers believe this will be essential in developing modern medical approaches to creating new drugs and gene therapy. A useful modeling approach is to use Petri nets via tools such as esyN.Along similar lines, until recent decades theoretical ecology has largely dealt with analytic models that were d... | Wikipedia - Computational biologist | null | null | null |
Mathematical chemistry Mathematical physics Analytical mechanics Mathematical fluid dynamics Numerical analysis Control theory Dynamical systems Mathematical optimization Operations research Probability Statistics Game theory Engineering mathematics Mathematical economics Financial mathematics Information theory Crypto... | Wikipedia - Outline of mathematics | null | null | null |
Mathematical considerations, such as symmetry and complexity, are used for analysis in theoretical aesthetics. This is different from the aesthetic considerations of applied aesthetics used in the study of mathematical beauty. Aesthetic considerations such as symmetry and simplicity are used in areas of philosophy, suc... | Wikipedia - Aesthetic judgment | null | null | null |
The fact that judgments of beauty and judgments of truth both are influenced by processing fluency, which is the ease with which information can be processed, has been presented as an explanation for why beauty is sometimes equated with truth. Recent research found that people use beauty as an indication for truth in m... | Wikipedia - Aesthetic judgment | null | null | null |
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. The applied methods usually refer to nontrivial mathematical techniques or approaches. Mathematical economics is based on statistics, probability, mathematical programming (as well as other computa... | Wikipedia - Applied geometry | null | null | null |
Mathematical expressions are written in Hebrew using the same symbols as in English, including Western numerals, which are written left to right. The only variant that exists is an alternative plus sign, which is a plus sign which looks like an inverted capital T. Unicode has this symbol at position U+FB29 "Hebrew lett... | Wikipedia - Hebrew punctuation | null | null | null |
Mathematical formulas or models (also known as algorithms), may be applied to the data in order to identify relationships among the variables; for example, using correlation or causation. In general terms, models may be developed to evaluate a specific variable based on other variable(s) contained within the dataset, w... | Wikipedia - Information analysis | null | null | null |
Mathematical modeling is a powerful tool that is used in ecological economic analysis. Various approaches and techniques include: evolutionary, input-output, neo-Austrian modeling, entropy and thermodynamic models, multi-criteria, and agent-based modeling, the environmental Kuznets curve, and Stock-Flow consistent mode... | Wikipedia - Ecological economics | null | null | null |
Mathematical models are based on mathematical equations and random events. The most common way to create compositions through mathematics is stochastic processes. In stochastic models a piece of music is composed as a result of non-deterministic methods. The compositional process is only partially controlled by the com... | Wikipedia - Algorithmic music | null | null | null |
Prominent examples of stochastic algorithms are Markov chains and various uses of Gaussian distributions. Stochastic algorithms are often used together with other algorithms in various decision-making processes. Music has also been composed through natural phenomena. | Wikipedia - Algorithmic music | null | null | null |
These chaotic models create compositions from the harmonic and inharmonic phenomena of nature. For example, since the 1970s fractals have been studied also as models for algorithmic composition. As an example of deterministic compositions through mathematical models, the On-Line Encyclopedia of Integer Sequences provid... | Wikipedia - Algorithmic music | null | null | null |
(It is initially set to convert each integer to a note on an 88-key musical keyboard by computing the integer modulo 88, at a steady rhythm. Thus 123456, the natural numbers, equals half of a chromatic scale.) As another example, the all-interval series has been used for computer-aided composition. | Wikipedia - Algorithmic music | null | null | null |
Mathematical models can be used to study the spread of technological innovations among individuals connected to each other by a network of peer-to-peer influences, such as in a physical community or neighborhood.Complex system (particularly complex network) models can be used to represent a system of individuals as nod... | Wikipedia - Sociological theory of diffusion | null | null | null |
Computer models have been developed to investigate the balance between the social aspects of diffusion and perceived intrinsic benefit to the individuals. When the effect of each individual node was analyzed along with its influence over the entire network, the expected level of adoption was seen to depend on the numbe... | Wikipedia - Sociological theory of diffusion | null | null | null |
Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models. In many case... | Wikipedia - Mathematical model | null | null | null |
Mathematical models of evolution, pioneered by the likes of Sewall Wright, Ronald Fisher and J. B. S. Haldane and extended via diffusion theory by Motoo Kimura, allow predictions about the genetic structure of evolving populations. Direct examination of the genetic structure of modern populations via DNA sequencing has... | Wikipedia - Evidence of common descent | null | null | null |
Mathematical models used in multiphysics simulations are generally a set of coupled equations. The equations can be divided into three categories according to the nature and intended role: governing equation, auxiliary equations and boundary/initial conditions. A governing equation describes a major physical mechanisms... | Wikipedia - Multiphysics simulation | null | null | null |
Mathematical notation is used to represent various kinds of mathematical ideas. All types of notation in probability Cartesian coordinate system, for representing position and other spatial concepts in analytic geometry Notation for differentiation, common representations of the derivative in calculus Big O notation, u... | Wikipedia - Notation system | null | null | null |
Mathematical notations as shown in the table do not fit into the scheme of a first-order term as defined above, as they all introduce an own local, or bound, variable that may not appear outside the notation's scope, e.g. t ⋅ ∫ a b sin ( k ⋅ t ) d t {\displaystyle t\cdot \int _{a}^{b}\sin(k\cdot t)\;dt} doesn't make ... | Wikipedia - Term (logic) | null | null | null |
As another example, a C function to implement the second example from the table, Σ, would have a function pointer argument (see box below). Lambda terms can be used to denote anonymous functions to be supplied as arguments to lim, Σ, ∫, etc. For example, the function square from the C program below can be written anony... | Wikipedia - Term (logic) | null | null | null |
The general sum operator Σ can then be considered as a ternary function symbol taking a lower bound value, an upper bound value and a function to be summed-up. Due to its latter argument, the Σ operator is called a second-order function symbol. As another example, the lambda term λn. | Wikipedia - Term (logic) | null | null | null |
x/n denotes a function that maps 1, 2, 3, ... to x/1, x/2, x/3, ..., respectively, that is, it denotes the sequence (x/1, x/2, x/3, ...). The lim operator takes such a sequence and returns its limit (if defined). The rightmost column of the table indicates how each mathematical notation example can be represented by a ... | Wikipedia - Term (logic) | null | null | null |
Mathematical object — an abstract concept in mathematics; an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. Each branch of mathematics has its own objects. Mathematical structure — a set endowed with some additional features on the... | Wikipedia - Outline of mathematics | null | null | null |
Mathematical optimization is a technique that can be used to calculate a mathematical optimum by minimizing or maximizing a function. | Wikipedia - Algorithmic technique | null | null | null |
Mathematical optimization is used in much modern controller design. High-level controllers such as model predictive control (MPC) or real-time optimization (RTO) employ mathematical optimization. These algorithms run online and repeatedly determine values for decision variables, such as choke openings in a process plan... | Wikipedia - Numerical optimization | null | null | null |
Mathematical optimization — algorithm for finding maxima or minima of a given function | Wikipedia - List of numerical analysis topics | null | null | null |
Mathematical papers about the Riemann hypothesis tend to be cautiously noncommittal about its truth. Of authors who express an opinion, most of them, such as Riemann (1859) and Bombieri (2000), imply that they expect (or at least hope) that it is true. The few authors who express serious doubt about it include Ivić (20... | Wikipedia - Critical line theorem | null | null | null |
Some of the arguments for and against the Riemann hypothesis are listed by Sarnak (2005), Conrey (2003), and Ivić (2008), and include the following: Several analogues of the Riemann hypothesis have already been proved. The proof of the Riemann hypothesis for varieties over finite fields by Deligne (1974) is possibly th... | Wikipedia - Critical line theorem | null | null | null |
Similarly Selberg zeta functions satisfy the analogue of the Riemann hypothesis, and are in some ways similar to the Riemann zeta function, having a functional equation and an infinite product expansion analogous to the Euler product expansion. But there are also some major differences; for example, they are not given ... | Wikipedia - Critical line theorem | null | null | null |
In contrast to these positive examples, some Epstein zeta functions do not satisfy the Riemann hypothesis even though they have an infinite number of zeros on the critical line. These functions are quite similar to the Riemann zeta function, and have a Dirichlet series expansion and a functional equation, but the ones ... | Wikipedia - Critical line theorem | null | null | null |
But analytic number theory has had many conjectures supported by substantial numerical evidence that turned out to be false. See Skewes number for a notorious example, where the first exception to a plausible conjecture related to the Riemann hypothesis probably occurs around 10316; a counterexample to the Riemann hypo... | Wikipedia - Critical line theorem | null | null | null |
Such functions occur in the theory of the zeta function controlling the behavior of its zeros; for example the function S(T) above has average size around (log log T)1/2. As S(T) jumps by at least 2 at any counterexample to the Riemann hypothesis, one might expect any counterexamples to the Riemann hypothesis to start ... | Wikipedia - Critical line theorem | null | null | null |
Denjoy's probabilistic argument for the Riemann hypothesis is based on the observation that if μ(x) is a random sequence of "1"s and "−1"s then, for every ε > 0, the partial sums (the values of which are positions in a simple random walk) satisfy the bound with probability 1. The Riemann hypothesis is equivalent to thi... | Wikipedia - Critical line theorem | null | null | null |
When μ(x) is nonzero its sign gives the parity of the number of prime factors of x, so informally the Riemann hypothesis says that the parity of the number of prime factors of an integer behaves randomly. Such probabilistic arguments in number theory often give the right answer, but tend to be very hard to make rigorou... | Wikipedia - Critical line theorem | null | null | null |
The calculations in Odlyzko (1987) show that the zeros of the zeta function behave very much like the eigenvalues of a random Hermitian matrix, suggesting that they are the eigenvalues of some self-adjoint operator, which would imply the Riemann hypothesis. All attempts to find such an operator have failed. | Wikipedia - Critical line theorem | null | null | null |
There are several theorems, such as Goldbach's weak conjecture for sufficiently large odd numbers, that were first proved using the generalized Riemann hypothesis, and later shown to be true unconditionally. This could be considered as weak evidence for the generalized Riemann hypothesis, as several of its "predictions... | Wikipedia - Critical line theorem | null | null | null |
Mathematical physics is an enormous and diverse subject. Some indications of future research directions are given in "New Trends in Mathematical Physics: Selected Contributions of the XVth International Congress on Mathematical Physics". | Wikipedia - Future of mathematics | null | null | null |
Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".1 List of mathematical topics in classical mechanics List of mathematical topics in quantum theory List o... | Wikipedia - Lists of mathematics topics | null | null | null |
Mathematical programming and in particular Mixed integer programming models are another approach to solve MSA problems. The advantage of such optimization models is that they can be used to find the optimal MSA solution more efficiently compared to the traditional DP approach. This is due in part, to the applicability ... | Wikipedia - Multiple Sequence Alignment | null | null | null |
Mathematical reasoning requires rigor. This means that the definitions must be absolutely unambiguous and the proofs must be reducible to a succession of applications of inference rules, without any use of empirical evidence and intuition. Rigorous reasoning is not specific to mathematics, but, in mathematics, the stan... | Wikipedia - Fields of mathematics | null | null | null |
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