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The exterior product of two vectors can be identified with the signed area enclosed by a parallelogram the sides of which are the vectors. The cross product of two vectors in 3 {\displaystyle 3} dimensions with positive-definite quadratic form is closely related to their exterior product. Most instances of geometric al...
Geometric algebra
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Transmission electron microscopy images are projections of the object showing the distribution of density through the object, similar to medical X-rays. By making use of the projection-slice theorem a three-dimensional reconstruction of the object can be generated by combining many images (2D projections) of the object...
Single particle analysis
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87,502
', 'Yes, I see only whales, but I hope they are only big waves. '", is one of humorous scenes when the author, Bohr and other friends were sailing in a dark night. The book provides a first-hand account about how science is done and how quantum physics, especially the Copenhagen interpretation, emerged.
Physics and Beyond
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Bioswales are benchmarked to meet a specific level of infiltration to determine if maintenance is required. A staff gauge is used to measure the infiltration rate. Soil chemistry testing is also required to determine if the soil has a certain off-level of any pollutant.
Bioretention swales
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This contains only results, and there is no indication of the method by which they were obtained, so that, according to L. O. Hosse, they are, like Fermat's theorems, riddles to the present and future generations. Eminent analysts succeeded in proving some of the theorems, but it was reserved to Luigi Cremona to prove ...
Jakob Steiner
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Brouwer's insistence on "constructibility" in the search for a "consistency proof for arithmetic" resulted in sensitivity to the issue as reflected by the work of Finsler and Gödel. Ultimately Gödel would "numeralize" his formulae; Gödel then used primitive recursion (and its instantiation of the intuitive, constructiv...
Brouwer–Hilbert controversy
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This algorithm finds the prime factorization of an n-bit integer in O ~ ( n 3 ) {\displaystyle {\tilde {O}}(n^{3})} time whereas the best known classical algorithm requires 2 O ( n 1 / 3 ) {\displaystyle 2^{O(n^{1/3})}} time and the best upper bound for the complexity of this problem is O ( 2 n / 3 + o ( 1 ) ) {\displa...
Quantum speedup
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{\displaystyle \Delta (x)=f(x+1)-f(x).} A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods.
Difference calculus
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87,508
Between 1985 and 1993, the Naval Civil Engineering Laboratory (NCEL) (now the Naval Facilities Engineering Service Center (NFESC)) of Port Hueneme, California developed controllable horizontal drilling technologies. These technologies are capable of reaching 10,000–15,000 ft (3000–4500 m) and may reach 25,000 ft (7500 ...
Horizontal drilling
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In quantum field theory, a sum rule is a relation between a static quantity and an integral over a dynamical quantity. Therefore, they have a form such as: ∫ A ( x ) d x = B {\displaystyle \int A(x)dx=B} where A ( x ) {\displaystyle A(x)} is the dynamical quantity, for example a structure function characterizing a part...
Sum rules (Quantum Field Theory)
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Spherical aberration The difference in focal length between paraxial rays and marginal rays, proportional to the square of the objective diameter. Coma A defect by which points appear as comet-like asymmetrical patches of light with tails, which makes measurement very imprecise. Its magnitude is usually deduced from th...
Optical telescope
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There is a canonical involutive automorphism on any superalgebra called the grade involution. It is given on homogeneous elements by x ^ = ( − 1 ) | x | x {\displaystyle {\hat {x}}=(-1)^{|x|}x} and on arbitrary elements by x ^ = x 0 − x 1 {\displaystyle {\hat {x}}=x_{0}-x_{1}} where xi are the homogeneous parts of x. I...
Even subalgebra
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There is also much interest in the size of the smallest prime in an arithmetic progression; Linnik's theorem gives an estimate. The twin prime conjecture, namely that there are an infinity of primes p such that p+2 is also prime, is the subject of active research. Chen's theorem shows that there are an infinity of prim...
Multiplicative number theory
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Existence of a reflective layer was predicted in 1902 independently and almost simultaneously by the American electrical engineer Arthur Edwin Kennelly (1861–1939) and the British polymath Oliver Heaviside (1850–1925), as an explanation for the propagation of radio waves beyond the horizon observed by Guglielmo Marconi...
Kennelly–Heaviside layer
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Human antimicrobial peptides which are toxic to viruses, fungi, bacteria and cancerous cells are considered a part of the immune system.In nuclear physics, a poison is a substance that obstructs or inhibits a nuclear reaction. Environmentally hazardous substances are not necessarily poisons, and vice versa. For example...
Toxic Substances
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On the other hand, Hardy denigrates much of the applied mathematics as either being "trivial", "ugly", or "dull", and contrasts it with "real mathematics", which is how he ranks the higher, pure mathematics. Hardy expounds by commenting about a phrase attributed to Carl Friedrich Gauss that "Mathematics is the queen of...
A Mathematician's Apology
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Regina Barzilay (born 1970) is an Israeli-American computer scientist. She is a professor at the Massachusetts Institute of Technology and a faculty lead for artificial intelligence at the MIT Jameel Clinic. Her research interests are in natural language processing and applications of deep learning to chemistry and onc...
Regina Barzilay
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A permutation matrix is itself a doubly stochastic matrix, but it also plays a special role in the theory of these matrices. The Birkhoff–von Neumann theorem says that every doubly stochastic real matrix is a convex combination of permutation matrices of the same order and the permutation matrices are precisely the ext...
Permutation matrices
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(2004). Categorical foundations. Special topics in order, topology, algebra, and sheaf theory.
Complete Heyting algebra
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87,519
Poor and intermediate metabolizers have reduced metabolism of the drug as compared to extensive metabolizers; patients with these metabolizer types may have an increased probability of experiencing side effects. Ultrarapid metabolizers use nortriptyline much faster than extensive metabolizers; patients with this metabo...
Nortriptyline
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The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) and National Center for Biotechnology Information (NCBI). Note: * paraphyletic Halobacteriaceae
Haloarchaea
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Samuel J. Danishefsky was born in 1936 in the United States. He completed his B.S. from Yeshiva University in 1956. He earned his Ph.D. in chemistry from Harvard University in 1962 with Peter Yates, which partially overlapped with a National Institutes of Health postdoctoral fellowship in the laboratory of Gilbert Stor...
Samuel J. Danishefsky
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A Software Development Kit is available from NEC for developers and customers. It contains proprietary products and must be purchased from NEC. The SDK contains: C, C++ and Fortran compilers that support automatic vectorization and automatic parallelization as well as OpenMP. Performance optimization tools: ftraceviewe...
NEC SX-Aurora TSUBASA
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In graph theory, the extended natural numbers are used to define distances in graphs, with ∞ {\displaystyle \infty } being the distance between two unconnected vertices. They can be used to show the extension of some results, such as the max-flow min-cut theorem, to infinite graphs.In topology, the topos of right actio...
Extended natural numbers
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An electron–ion collider (EIC) is a type of particle accelerator collider designed to collide spin-polarized beams of electrons and ions, in order to study the properties of nuclear matter in detail via deep inelastic scattering. In 2012, a whitepaper was published, proposing the developing and building of an EIC accel...
Electron-ion collider
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Bounded completeness also occurs in Bahadur's theorem. In the case where there exists at least one minimal sufficient statistic, a statistic which is sufficient and boundedly complete, is necessarily minimal sufficient. Another form of Bahadur's theorem states that any sufficient and boundedly complete statistic over a...
Completeness (statistics)
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87,526
Bulk ground conductivity typically uses transmitter/receiver pairs to obtain primary/secondary EM signals from the surrounding environment (note potential difficulty in urban areas with above-ground EM sources of interference), with collection areas depending upon the antennae spacing and equipment used. There are airb...
Near-surface geophysics
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They simply indicate the need to run the optimization with an additional set of mathematically expressed constraints that would not normally apply to financial portfolios. Furthermore, some of the simplest elements of Modern Portfolio Theory are applicable to virtually any kind of portfolio. The concept of capturing th...
Modern Portfolio Theory
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87,528
In May 2001, the Center for Astrophysics | Harvard & Smithsonian hosted "Donald H. Menzel: Scientist, Educator, Builder," a symposium in honor of the 100th anniversary of the birth of Donald H. Menzel. Menzel traveled with several expeditions to view solar eclipses to obtain scientific data. On 19 June 1936, he led the...
Donald Howard Menzel
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Klaus Schmiegel (born June 28, 1939), is a German chemist best known for his work in organic chemistry, which led to the invention of Prozac, a widely used antidepressant.
Klaus Schmiegel
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In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of plasma wave in which ions oscillate in response to a restoring force provided by an effective tension on the magnetic field lines.
Alfvén waves
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Derived from the Greek ἀνατομή anatomē "dissection" (from ἀνατέμνω anatémnō "I cut up, cut open" from ἀνά aná "up", and τέμνω témnō "I cut"), anatomy is the scientific study of the structure of organisms including their systems, organs and tissues. It includes the appearance and position of the various parts, the mater...
Vertebrate anatomy
0.798367
87,532
In mathematics and computer science, the middle-square method is a method of generating pseudorandom numbers. In practice it is a highly flawed method for many practical purposes, since its period is usually very short and it has some severe weaknesses; repeated enough times, the middle-square method will either begin ...
Middle-square method
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Imidazolate is a common bridging ligand in coordination chemistry. In the zeolitic imidazolate frameworks, the metals are interconnected via imidazolates. In the enzyme superoxide dismutase, imidazolate links copper and zinc centers. == References ==
Imidazolate
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87,534
Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall...
Observer (relativity)
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In quantum field theory, quantities like coupling constant and mass "run" with the energy scale of high energy physics. The running mass of a fermion or massive boson depends on the energy scale at which the observation occurs, in a way described by a renormalization group equation (RGE) and calculated by a renormaliza...
Pole mass
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In this regard, theoretical particle physics forms a good example. For instance: "phenomenologists" might employ (semi-) empirical formulas and heuristics to agree with experimental results, often without deep physical understanding. "Modelers" (also called "model-builders") often appear much like phenomenologists, but...
Theoretical Physics
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Indeed, the Riesz diagram of T is the collection of all points (1/p, 1/q) in the unit square × such that T is of type (p, q). The interpolation theorem states that the Riesz diagram of T is a convex set: given two points in the Riesz diagram, the line segment that connects them will also be in the diagram. The interp...
Riesz-Thorin theorem
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87,538
The smallest r {\displaystyle r} that makes the last statement valid for each x {\displaystyle x} in the convex hull of P is defined as the Carathéodory's number of P {\displaystyle P} . Depending on the properties of P {\displaystyle P} , upper bounds lower than the one provided by Carathéodory's theorem can be obtain...
Constantin Carathéodory
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Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents. What makes belief revision non-trivial is that several different w...
Belief revision
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87,540
The laws of physics are invariant with respect to space-translation—for example, the laws of physics in Brazil are the same as the laws of physics in Argentina. This symmetry leads to the continuity equation for conservation of momentum. The laws of physics are invariant with respect to orientation—for example, floatin...
Continuity principle
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87,541
Astronomy: both positional and clock synchronization data is used in astrometry and celestial mechanics and precise orbit determination. GPS is also used in both amateur astronomy with small telescopes as well as by professional observatories for finding extrasolar planets. Automated vehicle: applying location and rout...
GPS monitoring
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87,542
Problem-Oriented Software Engineering provides a formal definition of problems, and a framework for associating problems with solutions through formal, logical arguments; Problem Frames provide a framework for defining empirical models of software engineering problems which are grounded in the physical world. The Probl...
Problem-oriented development
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87,543
In theoretical physics, a dual resonance model arose during the early investigation (1968–1973) of string theory as an S-matrix theory of the strong interaction.
Dual resonance model
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In some cases, the homology of the group G ∞ = ⋃ n G n {\displaystyle G_{\infty }=\bigcup _{n}G_{n}} can be computed by other means or is related to other data. For example, the Barratt–Priddy theorem relates the homology of the infinite symmetric group agrees with mapping spaces of spheres. This can also be stated as ...
Homological stability
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87,545
Data science and data analysis are both important disciplines in the field of data management and analysis, but they differ in several key ways. While both fields involve working with data, data science is more of an interdisciplinary field that involves the application of statistical, computational, and machine learni...
Data scientist
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Benter; O. J. Schmitz (2007). "Ultrasensitive Determination of Polycyclic Aromatic Compounds with Atmospheric-Pressure Laser Ionization as an Interface for GC/MS". Analytical Chemistry.
Atmospheric-pressure laser ionization
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87,547
For functions of one variable, such an equation differs from a differential equation primarily through a change of variable substituting the function by its derivative, however this is not the case when the integral is taken over an open surface An integro-differential equation is a functional equation involving both t...
Equation
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87,548
Auxiliary normed spaces Finest locally convex topology Finest vector topology Helly space Mackey topology Polar topology Vague topology
List of topologies
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In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer n, not depending on special form or properties. It was described by D. H. Lehmer and R. E. Powers in 1931, and developed a...
Continued fraction factorization
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87,550
He was a member of several scientific organisations including IEEE, SIAM, EURASIP, ISCA and a chair of several conferences. He is a coauthor of pioneer publications from mathematical optimization models in biology. His works had also an important impact on Polish speech recognition technologies.
Mariusz Ziółko
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The four color theorem states that the vertices of every planar graph can be colored with four colors, so that no two adjacent vertices have equal colors. An erroneous proof was published in 1879 by Alfred Kempe, but it was discovered to be erroneous by 1890. The four color theorem was not given a valid proof until 197...
Errera graph
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His findings were independently confirmed by Robin Warren and Barry Marshall, who received the Nobel Prize in 2005. Witold Hurewicz, Polish mathematician; Hurewicz space, Hurewicz theorem.
Timeline of Polish science and technology
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He then went on to Yale University where he worked in the laboratory of Kenneth B. Wiberg on the thermochemistry of organic compounds. He received his M.Phil. degree in 1977 and a Ph.D. in 1980. He took a postdoctoral position with Charles DePuy and Veronica Bierbaum at the University of Colorado, Boulder where he stud...
Robert R. Squires
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If the axiom of choice holds, then every cardinal κ has a successor, denoted κ+, where κ+ > κ and there are no cardinals between κ and its successor. (Without the axiom of choice, using Hartogs' theorem, it can be shown that for any cardinal number κ, there is a minimal cardinal κ+ such that κ + ≰ κ . {\displaystyle \k...
Cardinal arithmetic
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Since there are not many explicitly parametrized distribution families (all the classical distribution families, such as the normal distribution, the Gumbel distribution, etc, are far too simplistic to model the true distribution), we consider implicitly parametrized probability distributions: First, define a simple di...
Variational free energy
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87,556
It has been shown that one can crosslink the DNA strands at their base, and subsequently dissolve the inorganic core with KCN or I2 to create a core-less (hollow) form of SNA (Fig. 3, right), which exhibits many of the same properties as the original polyvalent DNA gold nanoparticle conjugate (Fig. 3, left). Due to the...
Spherical nucleic acid
0.798361
87,557
In other words, the term o p e n ∘ o n {\displaystyle \mathrm {open} \circ \mathrm {on} } represent a possible state, and does not by itself mean that this is the current state. A separate condition can be stated to specify that this is actually the state at a given time, e.g., s t a t e ( o p e n ∘ o n , 10 ) {\displa...
Frame problem
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87,558
Benjamin Widom (born 13 October 1927) is the Goldwin Smith Professor of Chemistry at Cornell University. His research interests include physical chemistry and statistical mechanics. In 1998, Widom was awarded the Boltzmann Medal "for his illuminating studies of the statistical mechanics of fluids and fluid mixtures and...
Benjamin Widom
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XLAB Research is among largest Slovenian private computer science research departments and 1st SME in Slovenia in terms of H2020 funded research projects. It has been involved in more than 80 research projects and has coordinated 2 of them, earning the title of the first Slovenian coordinator of a Horizon 2020 project....
XLAB d.o.o
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87,560
In chemistry and biochemistry, the Henderson–Hasselbalch equation relates the pH of a chemical solution of a weak acid to the numerical value of the acid dissociation constant, Ka, of acid and the ratio of the concentrations, {\displaystyle {\frac {}{}}} of the acid and its conjugate base in an equilibrium. H A ( a c...
Henderson-Hasselbalch equation
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87,561
In the 1980s, when the Characteristic set Method was introduced, polynomial factorization was an active research area and certain fundamental questions on this subject were solved recentlyNowadays, decomposing an algebraic variety into irreducible components is not essential to process most application problems, since ...
Triangular decomposition
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87,562
In mathematics, a generalized conic is a geometrical object defined by a property which is a generalization of some defining property of the classical conic. For example, in elementary geometry, an ellipse can be defined as the locus of a point which moves in a plane such that the sum of its distances from two fixed po...
Generalized conic
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87,563
A biconcave disc — also referred to as a discocyte — is a geometric shape resembling an oblate spheroid with two concavities on the top and on the bottom. Biconcave discs appear in the study of cell biology, where it is meta-stable, and involves the continuous adjustment of the asymmetric transbilayer lipid distributio...
Biconcave disc
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87,564
In the late 1920s, Cramér became interested in the field of probability, which at the time was not an accepted branch of mathematics. Cramér knew that a radical change was needed in this field, and in a paper in 1926 said, "The probability concept should be introduced by a purely mathematical definition, from which its...
Harald Cramér
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ISTE provides professional development opportunities on a range of educational topics, including digital citizenship, computational thinking, artificial intelligence, and online teaching. The organization offers professional learning for a wide variety of educator roles, including ed tech coaches, library media special...
International Society for Technology in Education
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87,566
Search engine technology Search algorithm Search engine image protection Search engine indexing Search engine optimization Search engine results page Search engine software Search engine submission Search engine optimization copywriting Web crawler
Outline of search engines
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87,567
When normal forces are low, the solid bodies vibratory modes are weakly excited. The resulting noise generated is known as roughness noise. This noise is largely broad-band near the surface, and radiation efficiency and material geometry dictates which frequency content is radiated into the far field. Surfaces that are...
Friction Acoustics
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87,568
By mimicking a lifelike appearance or automating movements, a robot may convey a sense of intelligence or thought of its own. Autonomous things are expected to proliferate in the future, with home robotics and the autonomous car as some of the main drivers.The branch of technology that deals with the design, constructi...
Robot
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87,569
In mathematics, the AKNS system is an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, Alan C. Newell, and Harvey Segur from their publication in Studies in Applied Mathematics: Ablowitz, Kaup, and Newell et al. (1974).
AKNS system
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87,570
Here is a context-free grammar for syntactically correct infix algebraic expressions in the variables x, y and z: S → x S → y S → z S → S + S S → S – S S → S * S S → S / S S → (S)This grammar can, for example, generate the string (x + y) * x – z * y / (x + x)as follows: S → S – S (by rule 5) → S * S – S (by rule 6, app...
Context-free grammars
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87,571
In 1988, he became head of a research team at the Institute of Genetics and Microbiology (IGM) in Orsay and directed research on Archaea, the new living area discovered in 1977 by Carl Woese. In 2004, he joined the Pasteur Institute as Director of Microbiology . Patrick Forterre is particularly known for his theories o...
Patrick Forterre
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Solving systems of multivariate polynomial equations is proven to be NP-complete. That's why those schemes are often considered to be good candidates for post-quantum cryptography. Multivariate cryptography has been very productive in terms of design and cryptanalysis. Overall, the situation is now more stable and the ...
Multivariate cryptography
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87,573
The historical development of geophysics has been motivated by two factors. One of these is the research curiosity of humankind related to planet Earth and its several components, its events and its problems. The second is economical usage of Earth's resources (ore deposits, petroleum, water resources, etc.) and Earth-...
History of geophysics
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Neuroevolution involves the use of both neural networks and evolutionary algorithms. Instead of using gradient descent like most neural networks, neuroevolution models make use of evolutionary algorithms to update neurons in the network. Researchers claim that this process is less likely to get stuck in a local minimum...
Machine learning in video games
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87,575
The k × k {\displaystyle k\times k} submatrix of R ( q ) E ′ {\displaystyle R(q)_{E'}} induced the y 1 , … , y k {\displaystyle y_{1},\dots ,y_{k}} is invertible, so by the implicit function theorem, there exists a continuously differentiable function g {\displaystyle g} such that y = g ( x ) {\displaystyle y=g(x)} and...
Geiringer–Laman theorem
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87,576
European Journal of Biochemistry. E Biszku, M Sajgo, M Solti, G Szabolcsi, 1973. On the mechanism of formation of a partially active aldolase by tryptic digestion.
Gertrud Szabolcsi
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Pittendrigh used this model to demonstrate that the circadian clock in drosophila is temperature-compensated (meaning its period is stable over a broad range of temperatures) and to design an early theoretical model for phase response curves. The bang box was the primary means of investigation in chronobiology in the 1...
Eclosion assay
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87,578
Until the end of the 19th century and the foundational crisis of mathematics, all mathematical theories were built from a few basic properties that were considered as self-evident; for example, the facts that every natural number has a successor, and that there is exactly one line that passes through two given distinct...
Formal theorem
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87,579
In the natural sciences, especially in atmospheric and Earth sciences involving applied statistics, an anomaly is a persisting deviation in a physical quantity from its expected value, e.g., the systematic difference between a measurement and a trend or a model prediction. Similarly, a standardized anomaly equals an an...
Atmospheric anomaly
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87,580
Let A be a quadratic Jordan algebra over a field k of characteristic ≠ 2. Following Jacobson (1969), a linear Jordan algebra structure can be associated with A such that, if L(a) is Jordan multiplication, then the quadratic structure is given by Q(a) = 2L(a)2 − L(a2). Firstly the axiom Q(a)R(b,a) = R(a,b)Q(a) can be st...
Isotope (Jordan algebra)
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87,581
Their expertise made their positions difficult to replace with returning soldiers.These early programmers were drawn from a group of about two hundred women employed as computers at the Moore School of Electrical Engineering at the University of Pennsylvania. The job of computers was to produce the numeric result of ma...
Electronic Numerical Integrator and Computer
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87,582
Scotobiology is the study of the role darkness plays in living organisms and shows that interrupting darkness by light pollution creates drastic effects for most organisms; changing their food gathering and feeding habits, their mating and reproduction behavior, migration behaviour (birds and insects) and social behavi...
Dark-sky movement
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87,583
Ekeland has contributed to mathematical analysis, particularly to variational calculus and mathematical optimization.
Ivar Ekeland
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87,584
The 2m Bubble Chamber was a device used in conjunction with CERN’s 25 GeV Proton Synchrotron (PS) machine to study high-energy physics. It was decided to build this chamber in 1958 with a large team of physicists, engineers, technicians and designers led by Charles Peyrou. This project was of considerable magnitude, th...
2 m Bubble Chamber (CERN)
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87,585
Electrochemical engineering is applied in industrial water electrolysis, electrolysis, electrosynthesis, electroplating, fuel cells, flow batteries, decontamination of industrial effluents, electrorefining, electrowinning, etc. The primary example of an electrolysis-based process is the Chloralkali process for caustic ...
Electrochemical engineering
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87,586
In particular, many of the basic spectroscopic and spectrometric techniques were discovered in the early 20th century and refined in the late 20th century.The separation sciences follow a similar time line of development and also became increasingly transformed into high performance instruments. In the 1970s many of th...
Analytic chemistry
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87,587
The College of Agricultural, Life, and Physical Sciences consists of six constituent schools and several pre-health professional programs. It is based in the Agricultural Building, which was constructed in 1957. The college offers experiential opportunities for students in the form of a 2,000+ acre working farm, tree i...
Southern Illinois University Carbondale
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87,588
Journal of Algebraic Combinatorics is a peer-reviewed scientific journal covering algebraic combinatorics. It was established in 1992 and is published by Springer Science+Business Media. The editor-in-chief is Ilias S. Kotsireas (Wilfrid Laurier University). In 2017, the journal's four editors-in-chief and editorial bo...
Journal of Algebraic Combinatorics
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87,589
Energy exists in two basic modes: "Tangential Energy": energy that can be measured by physics. "Radial Energy": spiritual energy which accumulates into a higher state as time progresses.Teilhard defines Radial Energy as becoming more concentrated and available as it is a critical element in man's evolution. The theory ...
Omega Point
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His prediction was based on the difficulties and failures of computer use he had observed in 1981, including a candid horror story of his own Princeton University library's attempt to computerize its operations. His computers of the future, represented by the robot butler his visitor to Earth encounters in 2081, includ...
2081: A Hopeful View of the Human Future
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87,591
This theorem was first proved by L.E.J. Brouwer, by use of the Lebesgue covering theorem (a result based on compactness). It served to put the homology theory of the time—the first decade of the twentieth century—on a rigorous basis, since it showed that the topological effect (on homology groups) of continuous mapping...
Simplicial approximation theorem
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87,592
Among other things, HBE attempts to explain variation in human behavior as adaptive solutions to the competing life-history demands of growth, development, reproduction, parental care, and mate acquisition. HBE overlaps with evolutionary psychology, human or cultural ecology, and decision theory. It is most prominent i...
Human behavioural ecology
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87,593
Except their abilities in catalyzing organic reactions, palladacycles have also shown their potential in medicinal and biological chemistry after the success of cis-Pt(NH3)2Cl2 as an anticancer agent. Additionally, they can also be used in CO/SCN- sensing.
Palladacycle
0.798353
87,594
Desserts, ice cream, cream, milkshakes, yogurts, salad dressings, sweetened condensed milks Sauces: to increase viscosity Beer: clarifier to remove haze-causing proteins Pâtés and processed meats (e.g., ham): substitute for fat, increase water retention, increase volume, or improve slicing Toothpaste: stabilizer to pre...
Carrageenan
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87,595
Dives with multiple twists and somersaults are some of the most spectacular movements, as well as the most challenging to perform. The rules state that twisting "must not be generated manifestly on take-off". Consequently, divers must use some of the somersaulting angular momentum to generate twisting movements. The ph...
Synchronized diving
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87,596
In 2004, Chilcutt and Tabashnik found Bt protein in kernels of a refuge crop (a conventional crop planted to harbor pests that might otherwise become resistant a pesticide associated with the GMO) implying that gene flow had occurred.In 2005, scientists at the UK Centre for Ecology and Hydrology reported the first evid...
GMO labeling
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In graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability graph is a...
Comparability graph
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Substituting these values into the last equation yields the main result of Bertrand's theorem: β 2 ( 1 − β 2 ) ( 4 − β 2 ) = 0. {\displaystyle \beta ^{2}(1-\beta ^{2})(4-\beta ^{2})=0.} Hence, the only potentials that can produce stable closed non-circular orbits are the inverse-square force law (β = 1) and the radial ...
Bertrand theorem
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Now suppose that a consistent linear multistep method is applied to a sufficiently smooth differential equation and that the starting values y 1 , … , y s − 1 {\displaystyle y_{1},\ldots ,y_{s-1}} all converge to the initial value y 0 {\displaystyle y_{0}} as h → 0 {\displaystyle h\to 0} . Then, the numerical solution ...
Adams–Bashforth method
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