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28,000 | These were beginning steps for proof of principle regarding Veselago's original 1967 proposal. In 2000, a team of UCSD researchers produced and demonstrated metamaterials, which exhibited unusual physical properties that were never before produced in nature. These materials obey the laws of physics, but behave differen... | History of metamaterials | 0.806306 |
28,001 | Not until thirty-three years later did the properties of this material, a metamaterial, became a subdiscipline of physics and engineering. However, there were certain observations, demonstrations, and implementations that closely preceded this work. Permittivity of metals, with values that could be stretched from the p... | History of metamaterials | 0.806306 |
28,002 | In 1967, Victor Veselago produced an often cited, seminal work on a theoretical material that could produce extraordinary effects that are difficult or impossible to produce in nature. At that time he proposed that a reversal of Snell's law, an extraordinary lens, and other exceptional phenomena can occur within the la... | History of metamaterials | 0.806306 |
28,003 | This was followed by the first proof of principle for metamaterial cloaking (shielding an object from view), also in the microwave range, about six years later. However, a cloak that can conceal objects across the entire electromagnetic spectrum is still decades away. Many physics and engineering problems need to be so... | History of metamaterials | 0.806306 |
28,004 | However, the basic cause was not known. Louis Pasteur solved the problem (chirality of the molecules) originating a new discipline known as stereochemistry. At the macroscopic scale, Lindman applied microwaves to the problem with wire spirals (wire helices) in 1920 and 1922.Karl F. Lindman, from 1914 and into the 1920s... | History of metamaterials | 0.806306 |
28,005 | At the time, Pendry didn't realize the significance of the two materials he had engineered. By combining the electrical properties of Marconi's radar-absorbing material with his new man-made magnetic material he had unwittingly placed in his hands a new way to manipulate electromagnetic radiation. In 1999, Pendry publi... | History of metamaterials | 0.806306 |
28,006 | He realized rather than conventionally altering a material through its chemistry, as lead does with glass, the behavior of a material can be altered by changing a material's internal structure on a very fine scale. The very fine scale was less than the wavelength of the electromagnetic radiation that is applied. The th... | History of metamaterials | 0.806306 |
28,007 | However, the company did not understand the physics of the material. The company asked Pendry if he could understand how the material worked.Pendry discovered that the radiation absorption property did not come from the molecular or chemical structure of the material, i.e. the carbon per se. This property came from the... | History of metamaterials | 0.806306 |
28,008 | However, at the end of the 20th century this description was expanded by John Pendry, a physicist from Imperial College in London. In the 1990s he was consulting for a British company, Marconi Materials Technology, as a condensed matter physics expert. The company manufactured a stealth technology made of a radiation-a... | History of metamaterials | 0.806306 |
28,009 | Historically, and conventionally, the function or behavior of materials can be altered through their chemistry. This has long been known. For example, adding lead changes the color or hardness of glass. | History of metamaterials | 0.806306 |
28,010 | Agranovich and V.L. Ginzburg (1966) reported the repercussions of negative permittivity, negative permeability, and negative group velocity in their study of crystals and excitons.In 1967, V.G. Veselago from Moscow Institute of Physics and Technology considered the theoretical model of medium that known now as a metama... | History of metamaterials | 0.806306 |
28,011 | Jagadish Chandra Bose was a scientist involved in original microwave research during the 1890s. As officiating professor of physics at Presidency College he involved himself with laboratory experiments and studies involving refraction, diffraction and polarization, as well as transmitters, receivers and various microwa... | History of metamaterials | 0.806306 |
28,012 | This situation can be modeled as a bipartite graph ( P , J , E ) {\displaystyle (P,J,E)} where an edge connects each job-seeker with each suitable job. A perfect matching describes a way of simultaneously satisfying all job-seekers and filling all jobs; Hall's marriage theorem provides a characterization of the biparti... | Bipartite graphs | 0.806306 |
28,013 | Moreover, this is achieved by using local evolution rules instead of global evolution rules. Theorem. S M 3 ( l e v o l , e n d o , e x o ) = R E {\displaystyle SM_{3}(levol,endo,exo)=RE} . The proof of this result uses a similar technique to that used in . | Mobile membranes | 0.806306 |
28,014 | If this is an optimal construction remains an open problem. Theorem. E M 9 ( e n d o , e x o , f e n d o , f e x o ) = R E {\displaystyle EM_{9}(endo,exo,fendo,fexo)=RE} . The proof is similar to that presented in . | Mobile membranes | 0.806306 |
28,015 | E M 12 ( e n d o , e x o , f e n d o , f e x o ) = R E {\displaystyle EM_{12}(endo,exo,fendo,fexo)=RE} . When proving the result of the previous theorem the authors have not used an optimal construction of a membrane system. In what follows it is proven that using the same types of rules (endo, exo, fendo, fexo) a memb... | Mobile membranes | 0.806306 |
28,016 | Theorem. E M 3 ( e n d o , e x o ) = E M 3 ( f e n d o , f e x o ) {\displaystyle EM_{3}(endo,exo)=EM_{3}(fendo,fexo)} . Theorem. | Mobile membranes | 0.806306 |
28,017 | The structural congruence relation is a way of rearranging the system such that the interacting parts come together, as illustrated in what follows: In what follows the reduction rules of the calculus are presented: The action p i n o ( ρ ) {\displaystyle pino(\rho )} creates an empty bubble within the membrane where t... | Mobile membranes | 0.806306 |
28,018 | Actions often come in complementary pairs which cause the interaction between membranes. The names n {\displaystyle n} are used to pair-up actions and co-actions. Cardelli motivates that the replication operator is used to model the notion of a "multitude" of components of the same kind, which is in fact a standard sit... | Mobile membranes | 0.806306 |
28,019 | Brane calculus deals with membranes representing the sites of activity; thus a computation happens on the membrane surface. The operations of the two basic brane calculi, pino, exo, phago (PEP) and mate, drip, bud (MBD) are directly inspired by biologic processes such as endocytosis, exocytosis and mitosis. The latter... | Mobile membranes | 0.806306 |
28,020 | Theorem. M M 3 ( m e n d o , m e x o ) = R E {\displaystyle MM_{3}(mendo,mexo)=RE} . In systems of simple mobile membranes with local evolution rules and mobility rules it is known that systems of degree three have the same power as a Turing machine, while in systems of enhanced mobile membranes using only mobility rul... | Mobile membranes | 0.806306 |
28,021 | As it is expressed in , "at the first sight the role of objects placed on membranes is different in membrane and brane systems: in membrane computing the focus is on the evolution of objects themselves, while in brane calculi the objects ("proteins") mainly control the evolution of membranes". By defining an encoding o... | Mobile membranes | 0.806306 |
28,022 | A fragment of brane calculus called PEP, and mutual mobile membranes with objects on surface as a variant of systems with mobile membranes are considered. The mobile membranes with objects on surface is inspired by a model of membrane system introduced in having objects attached to membranes. A simulation of the PEP f... | Mobile membranes | 0.806306 |
28,023 | It is proven in that systems of nine membranes with objects on surface and using phago and exo operations of weight four and three (or five and two) are universal. The number of membranes can be reduced from nine to four, but in order to do this the weight of the phago and exo operations are increased from four and th... | Mobile membranes | 0.806306 |
28,024 | This means that in order to construct a universal system of mobile membranes with objects on surface by using pino and exo operations, one needs to decide either he wants to minimize the number of membranes, or the weights of the operations. Theorem. M M O S m ( p i n o ( r ) , e x o ( s ) ) = R E {\displaystyle MMOS_{... | Mobile membranes | 0.806306 |
28,025 | Membrane systems and brane calculus start from the same observations; however, they are built having in mind different goals: membrane systems investigate formally the computational nature and power of various features of membranes, while the brane calculus is capable to give a faithful and intuitive representation o... | Mobile membranes | 0.806306 |
28,026 | Theorem. (Operational correspondence) If A ⇒ a m b B {\displaystyle A\Rightarrow _{amb}B} , then T ( A ) ⇒ m e m T ( B ) {\displaystyle {\mathcal {T}}(A)\Rightarrow _{mem}{\mathcal {T}}(B)} . If T ( A ) ⇒ m e m M {\displaystyle {\mathcal {T}}(A)\Rightarrow _{mem}M} , then exists B {\displaystyle B} such that A ⇒ a m b ... | Mobile membranes | 0.806306 |
28,027 | ( ν n ) A {\displaystyle (\nu n)A} creates a new unique name n {\displaystyle n} within the scope of A {\displaystyle A} . The structural congruence ≡ a m b {\displaystyle \equiv _{amb}} over ambients is the least congruence such that ( A , ∣ , 0 ) {\displaystyle ({\mathcal {A}},\mid ,0)} is a commutative monoid. The o... | Mobile membranes | 0.806306 |
28,028 | A specific feature of the mobile membranes is that this new rule-based model is appropriate to prove computability results in terms of Turing machines rather by reduction to the lambda calculus as in the case of process calculi with mobility. In this section are defined four classes of membranes inspired from biologica... | Mobile membranes | 0.806306 |
28,029 | This network, called the Radio Solar Telescope Network (RSTN), uses a bandwidth from 25 MHz to 85 MHz. The prototype was assembled and operated at the Sagamore Hill Solar Radio Observatory during the early 1960s. The Sagamore Hill Solar Radio Observatory began operating solar patrols in 1966. The Air Force Geophysics L... | Radio Solar Telescope Network | 0.806306 |
28,030 | The symmetric algebra is a functor from the category of K-modules to the category of K-commutative algebra, since the universal property implies that every module homomorphism f: V → W {\displaystyle f:V\to W} can be uniquely extended to an algebra homomorphism S ( f ): S ( V ) → S ( W ) . {\displaystyle S(f):S(V)\to S... | Symmetric square | 0.806304 |
28,031 | Given a module V over a commutative ring K, the symmetric algebra S(V) can be defined by the following universal property: For every K-linear map f from V to a commutative K-algebra A, there is a unique K-algebra homomorphism g: S ( V ) → A {\displaystyle g:S(V)\to A} such that f = g ∘ i , {\displaystyle f=g\circ i,} w... | Symmetric square | 0.806304 |
28,032 | The Sk are functors comparable to the exterior powers; here, though, the dimension grows with k; it is given by dim ( S k ( V ) ) = ( n + k − 1 k ) {\displaystyle \operatorname {dim} (S^{k}(V))={\binom {n+k-1}{k}}} where n is the dimension of V. This binomial coefficient is the number of n-variable monomials of degre... | Symmetric square | 0.806304 |
28,033 | The symmetric algebra can be given the structure of a Hopf algebra. See Tensor algebra for details. | Symmetric square | 0.806304 |
28,034 | One can analogously construct the symmetric algebra on an affine space. The key difference is that the symmetric algebra of an affine space is not a graded algebra, but a filtered algebra: one can determine the degree of a polynomial on an affine space, but not its homogeneous parts. For instance, given a linear polyno... | Symmetric square | 0.806304 |
28,035 | Because of the universal property of the tensor algebra, a linear map f from V to a commutative algebra A extends to an algebra homomorphism T ( V ) → A {\displaystyle T(V)\rightarrow A} , which factors through S(V) because A is commutative. The extension of f to an algebra homomorphism S ( V ) → A {\displaystyle S(V)\... | Symmetric square | 0.806304 |
28,036 | It is possible to use the tensor algebra T(V) to describe the symmetric algebra S(V). In fact, S(V) can be defined as the quotient algebra of T(V) by the two-sided ideal generated by the commutators v ⊗ w − w ⊗ v . {\displaystyle v\otimes w-w\otimes v.} It is straightforward to verify that the resulting algebra satisfi... | Symmetric square | 0.806304 |
28,037 | In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is a commutative algebra over K that contains V, and is, in some sense, minimal for this property. Here, "minimal" means that S(V) satisfies the following universal property: for every linear map f from V to a commutativ... | Symmetric square | 0.806304 |
28,038 | Residual value is one of the constituents of a leasing calculus or operation. It describes the future value of a good in terms of absolute value in monetary terms, and it is sometimes abbreviated into a percentage of the initial price when the item was new. Example: A car is sold at a list price of $20,000 today. After... | Residual value | 0.806302 |
28,039 | In some restricted instances, the Tutte polynomial can be computed in polynomial time, ultimately because Gaussian elimination efficiently computes the matrix operations determinant and Pfaffian. These algorithms are themselves important results from algebraic graph theory and statistical mechanics. T G ( 1 , 1 ) {\dis... | Flow polynomial | 0.806299 |
28,040 | In Tutte’s words, “This may be unfair to Hassler Whitney who knew and used analogous coefficients without bothering to affix them to two variables.” (There is “notable confusion” about the terms dichromate and dichromatic polynomial, introduced by Tutte in different paper, and which differ only slightly.) The generalis... | Flow polynomial | 0.806299 |
28,041 | Define the hyperbola in the xy−plane: H 2: ( x − 1 ) ( y − 1 ) = 2 , {\displaystyle H_{2}:\quad (x-1)(y-1)=2,} the Tutte polynomial specialises to the partition function, Z ( ⋅ ) , {\displaystyle Z(\cdot ),} of the Ising model studied in statistical physics. Specifically, along the hyperbola H 2 {\displaystyle H_{2}} t... | Flow polynomial | 0.806299 |
28,042 | This is computable in polynomial time as the determinant of a maximal principal submatrix of the Laplacian matrix of G, an early result in algebraic graph theory known as Kirchhoff’s Matrix–Tree theorem. Likewise, the dimension of the bicycle space at T G ( − 1 , − 1 ) {\displaystyle T_{G}(-1,-1)} can be computed in po... | Flow polynomial | 0.806299 |
28,043 | The Mirsky–Newman theorem, a special case of the Herzog–Schönheim conjecture, states that there is no disjoint distinct covering system. This result was conjectured in 1950 by Paul Erdős and proved soon thereafter by Leon Mirsky and Donald J. Newman. However, Mirsky and Newman never published their proof. The same proo... | Covering system | 0.806294 |
28,044 | Population control is the practice of artificially maintaining the size of any population. It simply refers to the act of limiting the size of an animal population so that it remains manageable, as opposed to the act of protecting a species from excessive rates of extinction, which is referred to as conservation biolog... | Control of populations | 0.806288 |
28,045 | The four points can be ordered in any of three distinct ways (counting reversals as not distinct) to form three different quadrilaterals, for each of which the sum of the products of opposite sides is at least as large as the product of the diagonals. Thus the three product terms in the inequality can be additively per... | Ptolemy's inequality | 0.806288 |
28,046 | In Euclidean geometry, Ptolemy's inequality relates the six distances determined by four points in the plane or in a higher-dimensional space. It states that, for any four points A, B, C, and D, the following inequality holds: A B ¯ ⋅ C D ¯ + B C ¯ ⋅ D A ¯ ≥ A C ¯ ⋅ B D ¯ . {\displaystyle {\overline {AB}}\cdot {\overli... | Ptolemy's inequality | 0.806288 |
28,047 | For four points in order around a circle, Ptolemy's inequality becomes an equality, known as Ptolemy's theorem: A B ¯ ⋅ C D ¯ + A D ¯ ⋅ B C ¯ = A C ¯ ⋅ B D ¯ . {\displaystyle {\overline {AB}}\cdot {\overline {CD}}+{\overline {AD}}\cdot {\overline {BC}}={\overline {AC}}\cdot {\overline {BD}}.} In the inversion-based pro... | Ptolemy's inequality | 0.806288 |
28,048 | Ptolemy's inequality is often stated for a special case, in which the four points are the vertices of a convex quadrilateral, given in cyclic order. However, the theorem applies more generally to any four points; it is not required that the quadrilateral they form be convex, simple, or even planar. For points in the pl... | Ptolemy's inequality | 0.806288 |
28,049 | For a superposition of two or more structures, SuperPose generates sequence alignments, structure alignments, PDB (Protein Data Bank) coordinates and RMSD statistics, as well as difference distance plots and images (both static and interactive) of the superimposed molecules. All superimposed structure images can be ref... | SuperPose | 0.806284 |
28,050 | For example, a multiple-choice exam designed to assess knowledge of key concepts in natural selection does not meet a number of standards of quality control. One problem with the exam is that the two members of each of several pairs of parallel items, with each pair designed to measure exactly one key concept in natura... | Concept inventory | 0.806284 |
28,051 | For a discussion of how a number of concept inventories were developed see Beichner.In addition to physics, concept inventories have been developed in statistics, chemistry, astronomy, basic biology, natural selection, genetics, engineering, geoscience. and computer science.In many areas, foundational scientific concep... | Concept inventory | 0.806284 |
28,052 | Since the development of the FCI, other physics instruments have been developed. These include the Force and Motion Conceptual Evaluation concept and the Brief Electricity and Magnetism Assessment. | Concept inventory | 0.806284 |
28,053 | By the FEE the two following series are calculated fast: f 1 = f 1 ( z ) = ∑ j = 0 ∞ a ( j ) b ( j ) z j , {\displaystyle f_{1}=f_{1}(z)=\sum _{j=0}^{\infty }{\frac {a(j)}{b(j)}}z^{j},} f 2 = f 2 ( z ) = ∑ j = 0 ∞ a ( j ) b ( j ) z j j ! , {\displaystyle f_{2}=f_{2}(z)=\sum _{j=0}^{\infty }{\frac {a(j)}{b(j)}}{\frac {z... | FEE method | 0.806281 |
28,054 | The algorithms based on the method FEE include the algorithms for fast calculation of any elementary transcendental function for any value of the argument, the classical constants e, π , {\displaystyle \pi ,} the Euler constant γ , {\displaystyle \gamma ,} the Catalan and the Apéry constants, such higher transcendental... | FEE method | 0.806281 |
28,055 | Using the FEE, it is possible to prove the following theorem: Theorem: Let y = f ( x ) {\displaystyle y=f(x)} be an elementary transcendental function, that is the exponential function, or a trigonometric function, or an elementary algebraic function, or their superposition, or their inverse, or a superposition of the ... | FEE method | 0.806281 |
28,056 | In the thermodynamical limit, the specific entropy becomes independent on the choice of δE. An important result, known as Nernst's theorem or the third law of thermodynamics, states that the entropy of a system at zero absolute temperature is a well-defined constant. This is because a system at zero temperature exists ... | Entropy (statistical thermodynamics) | 0.806281 |
28,057 | (As we will see, the thermodynamic definition of entropy is also defined only up to a constant.) To avoid coarse graining one can take the entropy as defined by the H-theorem. S = − k B H B := − k B ∫ f ( q i , p i ) ln f ( q i , p i ) d q 1 d p 1 ⋯ d q N d p N {\displaystyle S=-k_{\rm {B}}H_{\rm {B}}:=-k_{\rm {B}}\i... | Entropy (statistical thermodynamics) | 0.806281 |
28,058 | The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The s... | Entropy (statistical thermodynamics) | 0.806281 |
28,059 | Discontinuities in acceleration do not occur in real-world environments because of deformation, quantum mechanics effects, and other causes. However, a jump-discontinuity in acceleration and, accordingly, unbounded jerk are feasible in an idealized setting, such as an idealized point mass moving along a piecewise smoot... | Jerk (physics) | 0.806277 |
28,060 | As a vector, jerk j can be expressed as the first time derivative of acceleration, second time derivative of velocity, and third time derivative of position: Where: a is acceleration v is velocity r is position t is timeThird-order differential equations of the form are sometimes called jerk equations. When converted t... | Jerk (physics) | 0.806277 |
28,061 | In physics, jerk (also known as jolt) is the rate of change of an object's acceleration over time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s3 (SI units) or standard gravities per second (g0/s). | Jerk (physics) | 0.806277 |
28,062 | The Extreme-Ultraviolet Explorer (EUVE) was a spinning spacecraft designed to rotate about the Earth/Sun line. EUVE was a part of NASA's Explorer spacecraft series, and designed to operate in the extreme ultraviolet (EUV) range of the spectrum, from 70 to 760 Ångström (Å). This spacecraft's objective was to carry out a... | Extreme Ultraviolet Explorer | 0.806276 |
28,063 | The Extreme Ultraviolet Explorer (EUVE or Explorer 67) was a NASA space telescope for ultraviolet astronomy. EUVE was a part of NASA's Explorer spacecraft series. Launched on 7 June 1992. With instruments for ultraviolet (UV) radiation between wavelengths of 7 and 76 nm (equivalent to 0.016–0.163 keV in energy), the EU... | Extreme Ultraviolet Explorer | 0.806276 |
28,064 | In particle physics, dimensional transmutation is a physical mechanism providing a linkage between a dimensionless parameter and a dimensionful parameter. In classical field theory, such as gauge theory in four-dimensional spacetime, the coupling constant is a dimensionless constant. However, upon quantization, logarit... | Dimensional transmutation | 0.806274 |
28,065 | The first iteration of the Energy Logic model was introduced by Emerson Network Power on November 29, 2007. Described as a “new approach to energy optimization,” the model was developed in response to industry feedback suggesting a growing emphasis on promoting efficiency initiatives, without compromising the performan... | Energy Logic | 0.806274 |
28,066 | The Energy Logic model proposes ten vendor-neutral actions that are forecast to reduce cumulative energy consumption by up to 50 percent (reducing energy consumption to 585 kW from the data center's initial 1,127 kW load). The ten recommended actions prescribed in the Energy Logic model are: Integrating IT equipment wi... | Energy Logic | 0.806274 |
28,067 | The Physics Aptitude Test (PAT) is a 2-hour subject-specific admissions test for applicants to the University of Oxford for undergraduate degree courses in engineering, materials science and physics undergraduate degree courses. The PAT is held pre-interview stage at the beginning of November. Test results are not publ... | History Aptitude Test | 0.806273 |
28,068 | The Mathematics Admissions Test (MAT) is a 2-hour 30-minute subject-specific admissions test for applicants to the University of Oxford, the University of Warwick and Imperial College London for undergraduate degree courses in mathematics, computer science and their joint degrees. It is set with the aim of being approa... | History Aptitude Test | 0.806273 |
28,069 | In proof theory, proof nets are a geometrical method of representing proofs that eliminates two forms of bureaucracy that differentiate proofs: (A) irrelevant syntactical features of regular proof calculi, and (B) the order of rules applied in a derivation. In this way, the formal properties of proof identity correspon... | Proof net | 0.806273 |
28,070 | In biochemical reactions involving phosphate groups (e.g. adenosine triphosphate), a "phosphoryl" group is usually transferred between the substrates by the "phosphoryl transfer reactions" (see phosphorylation). Examples of molecules containing those groups in biology, biochemistry and biomedicine are adenosine monopho... | Phosphoryl group | 0.806267 |
28,071 | A phosphoryl group is a trivalent >P(=O)− group, consisting of a phosphorus atom (symbol P) and an oxygen atom (symbol O), where the three free valencies are on the phosphorus atom. Despite that, the meaning of the term "phosphoryl" varies, depending on the branch of scientific discipline. In biology, biochemistry and ... | Phosphoryl group | 0.806267 |
28,072 | The institute also administers the Skaggs-Oxford Scholarship program, which enables students to pursue a joint Ph.D./D.Phil. with the University of Oxford. The most recent graduate school rankings by U.S. News & World Report places Scripps Research's program as 6th in chemistry (2nd in biochemistry, 5th in organic chem... | Scripps Research | 0.806267 |
28,073 | The graduate program at Scripps Research started in 1989 as the Macromolecular and Cellular Structure and Chemistry (MCSC) Program. A program in Chemistry followed three years after the establishment of the MCSC Program. In 2003, the institute redefined the curriculum to allow and encourage students to build course loa... | Scripps Research | 0.806267 |
28,074 | According to the 2017 Nature Innovation Index, Scripps Research is the #1 most influential research institution in the world (LENS score of 18.1), followed by The Rockefeller University (LENS score of 15.4) and the Massachusetts Institute of Technology (MIT) (LENS score of 9.4).Scripps Research was noted as a standout ... | Scripps Research | 0.806267 |
28,075 | The Florida campus of Scripps Research operates a 350,000-square-foot (33,000 m2) state-of-the-art biomedical research facility focusing on neuroscience, cancer biology, medicinal chemistry, drug discovery, biotechnology, and alternative energy development. More than 500 faculty, staff and students occupy Scripps Resea... | Scripps Research | 0.806267 |
28,076 | Among the 173 members of faculty are Nobel laureates Ardem Patapoutian, K. Barry Sharpless, and Kurt Wüthrich, as well as many other notable scientists, including Phil S. Baran, Donna Blackmond, Dale L. Boger, Benjamin Cravatt III, William R. Roush, Paul Schimmel, Peter G. Schultz, Gary Siuzdak, Eric Topol, Charles Wei... | Scripps Research | 0.806267 |
28,077 | Scripps Research, previously known as The Scripps Research Institute (TSRI), is a nonprofit American medical research facility that focuses on research and education in the biomedical sciences. Headquartered in San Diego, California, the institute has over 170 laboratories employing 2,100 scientists, technicians, gradu... | Scripps Research | 0.806267 |
28,078 | Scripps Research emphasizes interdisciplinary studies. Scripps Research scientists possess deep expertise in a range of scientific fields and are organized into five interrelated departments: Chemistry, Immunology and Microbiology, Integrative Structural and Computational Biology, Molecular Medicine, and Neuroscience. ... | Scripps Research | 0.806267 |
28,079 | Harvard biochemist A. Baird Hastings joined the institute in 1959, followed by immunologist Frank J. Dixon and colleagues William Weigle, Joseph Feldman, Charles Cochrane, and Jacinto Vazquez in 1961, biochemist Frank Huennekens and microbiologist John Spizizen in 1962. Dixon was appointed director of research operatio... | Scripps Research | 0.806267 |
28,080 | The edges of the drawing may be depicted as chords of the circle, as circular arcs (possibly perpendicular to the vertex circle, so that the edges model lines of the Poincaré disk model of hyperbolic geometry), or as other types of curve.The visual distinction between the inside and the outside of the vertex circle in ... | Circular layout | 0.806266 |
28,081 | Na⁺/K⁺-ATPase was discovered by Jens Christian Skou in 1957 while working as assistant professor at the Department of Physiology, University of Aarhus, Denmark. He published his work that year.In 1997, he received one-half of the Nobel Prize in Chemistry "for the first discovery of an ion-transporting enzyme, Na⁺,K⁺-AT... | Sodium-potassium ATPase | 0.806266 |
28,082 | Circular layouts are a good fit for communications network topologies such as star or ring networks, and for the cyclic parts of metabolic networks. For graphs with a known Hamiltonian cycle, a circular layout allows the cycle to be depicted as the circle, and in this way circular layouts form the basis of the LCF nota... | Circular layout | 0.806266 |
28,083 | Instead, the best approximation known for the balanced cut problem has ρ = O ( log n ) {\displaystyle \rho =O({\sqrt {\log n}})} , giving this circular layout algorithm an approximation ratio of O ( log 3 n ) {\displaystyle O(\log ^{3}n)} on graphs that have a large number of crossings relative to their vertex degr... | Circular layout | 0.806266 |
28,084 | In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms of linear maps. The module construction is analogous to the construction of the tensor product of vector spaces, but can be carried out for a pair of modules over a ... | Tensor product of abelian groups | 0.806265 |
28,085 | Hon, Giora; Goldstein, Bernard R, "Symmetry and asymmetry in electrodynamics from Rowland to Einstein", Studies in History and Philosophy of Modern Physics, vol. 37, iss. 4, pp. 635–660, Elsevier December 2006. | Magnetomotive force | 0.80626 |
28,086 | The Penguin Dictionary of Physics, 1977, ISBN 0-14-051071-0 A Textbook of Electrical Technology, 2008, ISBN 81-219-2440-5 | Magnetomotive force | 0.80626 |
28,087 | In physics, the magnetomotive force (abbreviated mmf or MMF, symbol F {\displaystyle {\mathcal {F}}} ) is a quantity appearing in the equation for the magnetic flux in a magnetic circuit, Hopkinson's law. It is the property of certain substances or phenomena that give rise to magnetic fields: where Φ is the magnetic fl... | Magnetomotive force | 0.80626 |
28,088 | The VIP2 experiment (Violation of the Pauli Principle) is an atomic physics experiment studying the possible violation of the Pauli exclusion principle for electrons. The experiment is located in the underground laboratory of Gran Sasso, LNGS-INFN, near the town L'Aquila in Italy. It is run by an international collabor... | VIP2 experiment | 0.806255 |
28,089 | The Van der Waals surface of a molecule is an abstract representation or model of that molecule, illustrating where, in very rough terms, a surface might reside for the molecule based on the hard cutoffs of Van der Waals radii for individual atoms, and it represents a surface through which the molecule might be conceiv... | Van der Waals surface | 0.806255 |
28,090 | The contrapositive of the third condition exactly expresses that the associated relation x ≤ y {\displaystyle x\leq y} (the partial order) is transitive. So that property is called co-transitivity. Using the asymmetry condition, one quickly derives the theorem that a pseudo-order is actually transitive as well. Transit... | Pseudo-order | 0.806255 |
28,091 | {\displaystyle {\begin{aligned}M_{x}M_{z}=-M_{z}M_{x}\,\\M_{y}M_{z}=-M_{z}M_{y}\,\\\\M_{x}^{2}=M_{y}^{2}=M_{z}^{2}=I\,\\\\M_{x}M_{y}=-M_{y}M_{x}={\rm {i}}M_{z}\,\\M_{y}M_{z}=-M_{z}M_{y}={\rm {i}}M_{x}\,\\M_{z}M_{x}=-M_{x}M_{z}={\rm {i}}M_{y}\,.\end{aligned}}} The (Ψ±, M) are not unique. Different choices of Ψ± would gi... | Matrix representation of Maxwell's equations | 0.806252 |
28,092 | The first three give the y, x, and z components of the curl and the last one gives the divergence conditions. The matrices M are all non-singular and all are Hermitian. Moreover, they satisfy the usual (quaternion-like) algebra of the Dirac matrices, including, M x M z = − M z M x M y M z = − M z M y M x 2 = M y 2 = M ... | Matrix representation of Maxwell's equations | 0.806252 |
28,093 | Within Earth Science Division and Heliophysics Division, the large strategic missions are usually in excess of US$500 million. "Strategic" refers to their role advancing multiple strategic priorities set forth in plans such as the Decadal Surveys. "Science" marks these missions as primarily scientific in nature, under ... | Large strategic science mission | 0.806249 |
28,094 | NASA's large strategic science missions or large strategic missions, formerly known as Flagship missions or Flagship-class missions, are the costliest and most capable NASA science spacecraft. Flagship missions exist within all four divisions of NASA's Science Mission Directorate (SMD): the astrophysics, Earth science,... | Large strategic science mission | 0.806249 |
28,095 | Although crucial to the understanding of nonadiabatic processes, direct evaluation of vibronic couplings has been very limited until very recently. Evaluation of vibronic couplings is often associated with severe difficulties in mathematical formulation and program implementations. As a result, the algorithms to evalua... | Vibronic coupling | 0.806248 |
28,096 | The computational cost of evaluating the vibronic coupling using (multireference) wave function theory has led to the idea of evaluating them at the TDDFT level, which indirectly describes the excited states of a system without describing its excited state wave functions. However, the derivation of the TDDFT vibronic c... | Vibronic coupling | 0.806248 |
28,097 | Compounds with oxidation states +5 are somewhat elusive, one example is the blue anion hypomanganate 3-. Compounds with Mn in oxidation state +5 are rarely encountered and often found associated with an oxide (O2-) or nitride (N3-) ligand.Mn(IV) is somewhat enigmatic because it is common in nature but far rarer in synt... | Manganese compounds | 0.806246 |
28,098 | Methylcyclopentadienyl manganese tricarbonyl is an additive in some unleaded gasoline to boost octane rating and reduce engine knocking. Manganese(IV) oxide (manganese dioxide, MnO2) is used as a reagent in organic chemistry for the oxidation of benzylic alcohols (where the hydroxyl group is adjacent to an aromatic rin... | Manganese compounds | 0.806246 |
28,099 | Phonons obey Bose–Einstein statistics. Their distribution is given by the famous Bose–Einstein statistics formula ⟨ N ⟩ B E = 1 e E / k T − 1 . {\displaystyle \langle N\rangle _{BE}={1 \over e^{E/kT}-1}\,.} | Debye frequency | 0.806245 |
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