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25,200 | Gerhard Herzberg, who won the Nobel prize for his research into the electron structure and geometry of radicals, suggested a looser definition of free radicals: "any transient (chemically unstable) species (atom, molecule, or ion)". The main point of his suggestion is that there are many chemically unstable molecules t... | Single electron transfer | 0.807765 |
25,201 | This species was discovered by Moses Gomberg in 1900. In 1933 Morris S. Kharasch and Frank Mayo proposed that free radicals were responsible for anti-Markovnikov addition of hydrogen bromide to allyl bromide.In most fields of chemistry, the historical definition of radicals contends that the molecules have nonzero elec... | Single electron transfer | 0.807765 |
25,202 | Until late in the 20th century the word "radical" was used in chemistry to indicate any connected group of atoms, such as a methyl group or a carboxyl, whether it was part of a larger molecule or a molecule on its own. A radical is often known as an R group. The qualifier "free" was then needed to specify the unbound c... | Single electron transfer | 0.807765 |
25,203 | Radicals play important roles in biology. Many of these are necessary for life, such as the intracellular killing of bacteria by phagocytic cells such as granulocytes and macrophages. Radicals are involved in cell signalling processes, known as redox signaling. For example, radical attack of linoleic acid produces a se... | Single electron transfer | 0.807765 |
25,204 | A common example of backpressure is that caused by the exhaust system (consisting of the exhaust manifold, catalytic converter, muffler and connecting pipes) of an automotive four-stroke engine, which has a negative effect on engine efficiency, resulting in a decrease of power output that must be compensated by increas... | Back pressure | 0.80776 |
25,205 | In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency e... | Transmission lines | 0.807756 |
25,206 | These modes are classified into two groups, transverse electric (TE) and transverse magnetic (TM) waveguide modes. When more than one mode can exist, bends and other irregularities in the cable geometry can cause power to be transferred from one mode to another. The most common use for coaxial cables is for television ... | Transmission lines | 0.807755 |
25,207 | Alternatively, the complex square root can be evaluated algebraically, to yield: α = ± b 2 ( − a + a 2 + b 2 ) , {\displaystyle \alpha ={\frac {\pm b}{\sqrt {2\left(-a+{\sqrt {a^{2}+b^{2}}}\right)~}}},} and β = ± 1 2 ( − a + a 2 + b 2 ) , {\displaystyle \beta =\pm {\sqrt {{\tfrac {1}{2}}\left(-a+{\sqrt {a^{2}+b^{2}}}\r... | Transmission lines | 0.807755 |
25,208 | In both naturally occurring and synthetic porous structures, the geometry of pores and capillaries is almost never perfectly cylindrical. Often, porous media contain networks of capillaries, much like a sponge. Since pore geometry affects the shape and curvature of an equilibrium meniscus, the Kelvin equation could be ... | Capillary condensation | 0.807754 |
25,209 | Capillary condensation is an important factor in both naturally occurring and synthetic porous structures. In these structures, scientists use the concept of capillary condensation to determine pore size distribution and surface area through adsorption isotherms. Synthetic applications such as sintering of materials ar... | Capillary condensation | 0.807754 |
25,210 | Capillary condensation bridges two surfaces together, with the formation of a meniscus, as is stated above. In the case of atomic-force microscopy (AFM) a capillary bridge of water can form between the tip and the surface, especially in cases of a hydrophilic surface in a humid environment when the AFM is operated in c... | Capillary condensation | 0.807754 |
25,211 | In a parallel situation, where the capillary radius is constant throughout its height, vapor condensation would occur much more rapidly, reaching the equilibrium radius of curvature (Kelvin radius) as quickly as possible. This dependence on pore geometry and curvature can result in hysteresis and vastly different liqui... | Capillary condensation | 0.807754 |
25,212 | The case Δ = 2 is straightforward (any union of paths and cycles may be equitably colored by using a repeated pattern of three colors, with minor adjustments to the repetition when closing a cycle) and the case Δ + 1= n/3 had previously been solved by Corrádi & Hajnal (1963). The full conjecture was proven by Hajnal & ... | Equitable coloring | 0.807754 |
25,213 | Brooks' theorem states that any connected graph with maximum degree Δ has a Δ-coloring, with two exceptions (complete graphs and odd cycles). However, this coloring may in general be far from equitable. Paul Erdős (1964) conjectured that an equitable coloring is possible with only one more color: any graph with maximum... | Equitable coloring | 0.807754 |
25,214 | Because K1,5 has maximum degree five, the number of colors guaranteed for it by the Hajnal–Szemerédi theorem is six, achieved by giving each vertex a distinct color. Another interesting phenomenon is exhibited by a different complete bipartite graph, K2n + 1,2n + 1. This graph has an equitable 2-coloring, given by its ... | Equitable coloring | 0.807754 |
25,215 | The equitable chromatic number of a graph G is the smallest number k such that G has an equitable coloring with k colors. But G might not have equitable colorings for some larger numbers of colors; the equitable chromatic threshold of G is the smallest k such that G has equitable colorings for any number of colors grea... | Equitable coloring | 0.807754 |
25,216 | In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that No two adjacent vertices have the same color, and The numbers of vertices in any two color classes differ by at most one.That is, the partition of vertices among the diffe... | Equitable coloring | 0.807754 |
25,217 | Yet another generalization of the Hajnal–Szemerédi theorem is the Bollobás–Eldridge–Catlin conjecture (or BEC-conjecture for short). This states that if G1 and G2 are graphs on n vertices with maximum degree Δ1 and Δ2 respectively, and if (Δ1 + 1)(Δ2 + 1) ≤ n+1, then G1 and G2 can be packed. That is, G1 and G2 can be r... | Equitable coloring | 0.807754 |
25,218 | Seymour's conjecture has been approximately proven, i.e. for graphs where every vertex has at least kn/(k + 1)+o(n) neighbors. The proof uses several deep tools including the Hajnal–Szemerédi theorem itself. | Equitable coloring | 0.807754 |
25,219 | A strengthened version of the conjecture states that each such graph has an equitable coloring with exactly Δ colors, with one additional exception, a complete bipartite graph in which both sides of the bipartition have the same odd number of vertices.Seymour (1974) proposed a strengthening of the Hajnal–Szemerédi theo... | Equitable coloring | 0.807754 |
25,220 | A polynomial time algorithm for finding equitable colorings with this many colors was described by Kierstead and Kostochka; they credit Marcelo Mydlarz and Endre Szemerédi with a prior unpublished polynomial time algorithm. Kierstead and Kostochka also announce but do not prove a strengthening of the theorem, to show t... | Equitable coloring | 0.807754 |
25,221 | Furmańczyk (2006) mentions a specific application of this type of scheduling problem, assigning university courses to time slots in a way that spreads the courses evenly among the available time slots and avoids scheduling incompatible pairs of courses at the same time as each other. The Hajnal-Szemerédi theorem has al... | Equitable coloring | 0.807754 |
25,222 | The Journal of Zhejiang University Science A: Applied Physics & Engineering is a monthly peer-reviewed scientific journal covering applied physics and engineering. It was established in 2000 and is published by Zhejiang University Press and Springer Science+Business Media. | Journal of Zhejiang University Science A | 0.807751 |
25,223 | One form of HWT is known as a Gun Tunnel or hot shot tunnel (up to M=27), which can be used for analysis of flows past ballistic missiles, space vehicles in atmospheric entry, and plasma physics or heat transfer at high temperatures. It runs intermittently, but has a very low running time (less than a second). The meth... | Hypersonic wind tunnel | 0.807751 |
25,224 | Since 2000, logical independence has become understood as having crucial significance in the foundations of physics. | Logical independence | 0.807751 |
25,225 | If nanofactories could be built, severe disruption to the world economy would be one of many possible negative impacts, though it could be argued that this disruption would have little negative effect, if everyone had such nanofactories. Great benefits also would be anticipated. Various works of science fiction have ex... | Molecular assembler | 0.807744 |
25,226 | Such visions have been the subject of much debate, on several intellectual levels. No one has discovered an insurmountable problem with the underlying theories and no one has proved that the theories can be translated into practice. However, the debate continues, with some of it being summarized in the molecular nanote... | Molecular assembler | 0.807744 |
25,227 | A nanofactory is a proposed system in which nanomachines (resembling molecular assemblers, or industrial robot arms) would combine reactive molecules via mechanosynthesis to build larger atomically precise parts. These, in turn, would be assembled by positioning mechanisms of assorted sizes to build macroscopic (visibl... | Molecular assembler | 0.807744 |
25,228 | Trans-organismic communication is when organisms of different species interact. In biology the relationships formed between different species is known as symbiosis. These relationships come in two main forms mutualistic and parasitic. Mutualistic Relationships are when both species benefit from their interactions. | Biocommunication (science) | 0.807743 |
25,229 | Biocommunication theory may be considered to be a branch of biosemiotics. Whereas Biosemiotics studies the production and interpretation of signs and codes, biocommunication theory investigates concrete interactions mediated by signs. Accordingly, syntactic, semantic, and pragmatic aspects of biocommunication processes... | Biocommunication (science) | 0.807743 |
25,230 | Interpreting stimuli from an organism's environment is an essential part of life for any individual. Abiotic things that an organism must interpret include climate (weather, temperature, rainfall), geology (rocks, soil type), and geography (location of vegetation communities, exposure to elements, location of food and ... | Biocommunication (science) | 0.807743 |
25,231 | The conditional change model in statistics is the analytic procedure in which change scores are regressed on baseline values, together with the explanatory variables of interest (often including indicators of treatment groups). The method has some substantial advantages over the usual two-sample t-test recommended in t... | Conditional change model | 0.807743 |
25,232 | Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation g x = h {\displaystyle g^{x}=h} given elements g and h of a finite cyclic group G. The difficulty of this problem is the basis for the security of sever... | Discrete logarithm records | 0.807741 |
25,233 | Certicom Corp. has issued a series of Elliptic Curve Cryptography challenges. Level I involves fields of 109-bit and 131-bit sizes. Level II includes 163, 191, 239, 359-bit sizes. | Discrete logarithm records | 0.807741 |
25,234 | The team used a new variation of the function field sieve for the medium prime case to compute a discrete logarithm in a field of 3334135357 elements (a 1425-bit finite field). The same technique had been used a few weeks earlier to compute a discrete logarithm in a field of 3355377147 elements (an 1175-bit finite fiel... | Discrete logarithm records | 0.807741 |
25,235 | The computation took less than 220 core hours.The current record (as of 2014) in a finite field of characteristic 2 of prime degree was announced by Thorsten Kleinjung on 17 October 2014. The calculation was done in a field of 21279 elements and followed essentially the path sketched for F 2 4 ⋅ 1223 {\displaystyle \ma... | Discrete logarithm records | 0.807741 |
25,236 | His team was able to compute discrete logarithms in the field with 26168 = (2257)24 elements using less than 550 CPU-hours. This computation was performed using the same index calculus algorithm as in the recent computation in the field with 24080 elements. Robert Granger, Faruk Göloğlu, Gary McGuire, and Jens Zumbräge... | Discrete logarithm records | 0.807741 |
25,237 | Under the condition of a barotropic fluid with a constant projection area A e {\displaystyle A_{e}} , the Bjerknes circulation theorem reduces to Kelvin's theorem. However, in the context of atmospheric dynamics, such conditions are not a good approximation: if the fluid circuit moves from the equatorial region to the ... | Potential vorticity | 0.807735 |
25,238 | Vilhelm Bjerknes generalized Helmholtz's vorticity equation (1858) and Kelvin's circulation theorem (1869) to inviscid, geostrophic, and baroclinic fluids, i.e., fluids of varying density in a rotational frame which has a constant angular speed. If we define circulation as the integral of the tangent component of veloc... | Potential vorticity | 0.807735 |
25,239 | Using the Ertel PV conservation theorem has led to various advances in understanding the general circulation. One of them was "tropopause folding" process described in Reed et al., (1950). For the upper-troposphere and stratosphere, air parcels follow adiabatic movements during a synoptic period of time. | Potential vorticity | 0.807735 |
25,240 | The Ertel PV conservation theorem, equation (12), states that for a dry atmosphere, if an air parcel conserves its potential temperature, its potential vorticity is also conserved following its full three-dimensional motions. In other words, in adiabatic motion, air parcels conserve Ertel PV on an isentropic surface. R... | Potential vorticity | 0.807735 |
25,241 | In September 2009, a live attenuated influenza vaccine for the novel H1N1 influenza virus was approved and the seasonal intranasal vaccine was approved by the European Medicines Agency (EMA) for use in the European Union in 2011. The quadrivalent version was approved for use in the European Union in 2013.As of 2007, th... | Live attenuated influenza vaccine | 0.807734 |
25,242 | In mathematical set theory, a Cohen algebra, named after Paul Cohen, is a type of Boolean algebra used in the theory of forcing. A Cohen algebra is a Boolean algebra whose completion is isomorphic to the completion of a free Boolean algebra (Koppelberg 1993). | Cohen algebra | 0.807733 |
25,243 | In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as φ ( n ) {\displaystyle \varphi (n)} or ϕ ( n ) {\displaystyle \phi (n)} , and may also be called Euler's phi function. In other words, it is the num... | Euler totient | 0.807732 |
25,244 | The characterization of the capacity of a set as the minimum of an energy functional achieving particular boundary values, given above, can be extended to other energy functionals in the calculus of variations. | Capacity of a set | 0.807732 |
25,245 | The search for the optimal autoencoder can be accomplished by any mathematical optimization technique, but usually by gradient descent. This search process is referred to as "training the autoencoder". In most situations, the reference distribution is just the empirical distribution given by a dataset { x 1 , . | Autoencoder | 0.807732 |
25,246 | The autoencoder was first proposed as a nonlinear generalization of principal components analysis (PCA) by Kramer. The autoencoder has also been called the autoassociator, or Diabolo network. Its first applications date to early 1990s. Their most traditional application was dimensionality reduction or feature learning,... | Autoencoder | 0.807732 |
25,247 | The encoder-decoder architecture, often used in natural language processing and neural networks, can be scientifically applied in the field of SEO (Search Engine Optimization) in various ways: Text Processing: By using an autoencoder, it's possible to compress the text of web pages into a more compact vector representa... | Autoencoder | 0.807732 |
25,248 | . . , x N } ⊂ X {\displaystyle \{x_{1},...,x_{N}\}\subset {\mathcal {X}}} , so that where and δ x i {\displaystyle \delta _{x_{i}}} is the Dirac measure, and the quality function is just L2 loss: d ( x , x ′ ) = ‖ x − x ′ ‖ 2 2 {\displaystyle d(x,x')=\|x-x'\|_{2}^{2}} . Then the problem of searching for the optimal aut... | Autoencoder | 0.807732 |
25,249 | Dimensionality reduction was one of the first deep learning applications.For Hinton's 2006 study, he pretrained a multi-layer autoencoder with a stack of RBMs and then used their weights to initialize a deep autoencoder with gradually smaller hidden layers until hitting a bottleneck of 30 neurons. The resulting 30 dime... | Autoencoder | 0.807732 |
25,250 | Studies with human pharmacology and genetics, genetically manipulated rodents, and other animal models and randomized trials indicate that this is due to suppression of PTGS2 (COX-2)-dependent cardioprotective prostaglandins, prostacyclin in particular.The expression of PTGS2 (COX-2) is upregulated in many cancers. The... | Prostaglandin-endoperoxide synthase 2 | 0.807731 |
25,251 | Renewable energy resources exist over wide geographical areas, in contrast to fossil fuels, which are concentrated in a limited number of countries. Deployment of renewable energy and energy efficiency technologies is resulting in significant energy security, climate change mitigation, and economic benefits. However re... | Renewable power | 0.807729 |
25,252 | Renewable energy is energy from renewable resources that are naturally replenished on a human timescale. Renewable resources include sunlight, wind, the movement of water, and geothermal heat. Although most renewable energy sources are sustainable, some are not. For example, some biomass sources are considered unsustai... | Renewable power | 0.807729 |
25,253 | The International Renewable Energy Agency (IRENA) stated that ~86% (187 GW) of renewable capacity added in 2022 had lower costs than electricity generated from fossil fuels. IRENA also stated that capacity added since 2000 reduced electricity bills in 2022 by at least $520 billion, and that in non-OECD countries, the l... | Renewable power | 0.807729 |
25,254 | Solar energy can be harnessed anywhere that receives sunlight; however, the amount of solar energy that can be harnessed for electricity generation is influenced by weather conditions, geographic location and time of day. According to chapter 6 of the IPCC 2022 climate mitigation report, the global potential of direct ... | Renewable power | 0.807729 |
25,255 | Solar energy, radiant light and heat from the sun, is harnessed using a range of ever-evolving technologies such as solar heating, photovoltaics, concentrated solar power (CSP), concentrator photovoltaics (CPV), solar architecture and artificial photosynthesis. Most new renewable energy is solar. Solar technologies are... | Renewable power | 0.807729 |
25,256 | According to the IEA, to achieve net zero emissions by 2050, 90% of global electricity generation will need to be produced from renewable sources. Some studies have shown that a global transition to 100% renewable energy across all sectors – power, heat, transport and industry – is feasible and economically viable. | Renewable power | 0.807729 |
25,257 | In most countries, photovoltaic solar or onshore wind are the cheapest new-build electricity.Many nations around the world already have renewable energy contributing more than 20% of their total energy supply, with some generating over half their electricity from renewables. A few countries generate all their electrici... | Renewable power | 0.807729 |
25,258 | There are 3,146 gigawatts installed in 135 countries, while 156 countries have laws regulating the renewable energy sector. In 2021, China accounted for almost half of the global increase in renewable electricity.Globally there are over 10 million jobs associated with the renewable energy industries, with solar photovo... | Renewable power | 0.807729 |
25,259 | Renewable energy is often used for electricity generation, heating and cooling. Renewable energy projects are typically large-scale, but they are also suited to rural and remote areas and developing countries, where energy is often crucial in human development. Renewable energy is often deployed together with further e... | Renewable power | 0.807729 |
25,260 | The Jacobi Bound Problem concerns the veracity of Jacobi's inequality which is an inequality on the absolute dimension of a differential algebraic variety in terms of its defining equations.The inequality is the differential algebraic analog of Bezout's theorem in affine space. Although first formulated by Jacobi, In 1... | Jacobi bound problem | 0.807725 |
25,261 | Let ( K , ∂ ) {\displaystyle (K,\partial )} be a differential field of characteristic zero and consider Γ {\displaystyle \Gamma } a differential algebraic variety determined by the vanishing of differential polynomials u 1 , … , u n ∈ K ∂ {\displaystyle u_{1},\ldots ,u_{n}\in K_{\partial }} . If Γ 1 {\displaystyle \Ga... | Jacobi bound problem | 0.807725 |
25,262 | The detector was a 6-chamber cylindrical assembly 5.8 m long and 2.3 m in diameter, the largest imaging drift chamber of its day. It recorded the tracks of charged particles curving in a 0.7 Tesla magnetic field, measuring their momentum, the sign of their electric charge and their rate of energy loss (dE/dx). Atoms in... | UA1 experiment | 0.807724 |
25,263 | It was named as the first experiment in a CERN "Underground Area" (UA), i.e. located underground, outside of the two main CERN sites, at an interaction point on the SPS accelerator, which had been modified to operate as a collider. The UA1 central detector was crucial to understanding the complex topology of proton-ant... | UA1 experiment | 0.807724 |
25,264 | The UA1 experiment (an abbreviation of Underground Area 1) was a high-energy physics experiment that ran at CERN's Proton-Antiproton Collider (SppS), a modification of the one-beam Super Proton Synchrotron (SPS). The data was recorded between 1981 and 1990. The joint discovery of the W and Z bosons by this experiment a... | UA1 experiment | 0.807724 |
25,265 | However, their topographical distribution is different, and the delta power of K-complexes is higher.They are created by the occurrence in widespread cortical areas of outward dendritic currents from the middle (III) to the upper (I) layers of the cerebral cortex. This is accompanied by a decrease in broadband EEG powe... | K complex | 0.807724 |
25,266 | The Corps of Engineers initiated the use of CBA in the US, after the Federal Navigation Act of 1936 mandated cost–benefit analysis for proposed federal-waterway infrastructure. The Flood Control Act of 1939 was instrumental in establishing CBA as federal policy, requiring that "the benefits to whomever they accrue in ... | Cost-benefit Analysis | 0.807723 |
25,267 | In order to mitigate rapid climate change, renewable energy sources, such as solar and wind energy are adopted by the building industry to support electricity generation. However, the electricity demand profile shows imbalance between supply and demand, which is known as the ‘duck curve’. This could impact on maintaini... | Building science | 0.807719 |
25,268 | With the improvement from computational performance and machine learning algorithms, model prediction on cooling and heating load with optimal control can further improve occupants comfort by pre-operating the HVAC system. It is recognized that advanced control strategies implementation is under the scope of developing... | Building science | 0.807719 |
25,269 | These measurements can be used to evaluate how the mechanical system is operating and if there are areas of anomalous heat gain or heat loss through the building envelope.Measurements of conditions in existing buildings are used as part of post occupancy evaluations. Post occupancy evaluations may also include surveys ... | Building science | 0.807719 |
25,270 | Building science is the science and technology-driven collection of knowledge in order to provide better indoor environmental quality (IEQ), energy-efficient built environments, and occupant comfort and satisfaction. Building physics, architectural science, and applied physics are terms used for the knowledge domain th... | Building science | 0.807719 |
25,271 | Impact Factor (2019): 4.739 Architectural Science Review: Founded at the University of Sydney, Australia in 1958, this journal aims to promote the development, accumulation, and application of scientific knowledge on a wide range of environmental topics. According to the journal description, the topics may include but ... | Building science | 0.807719 |
25,272 | The aim is to present new research results, and new proven practice aimed at reducing the energy needs of a building and improving indoor air quality. The journal's most cited articles cover topics such as prediction models for building energy consumption, optimization models of HVAC systems, and life cycle assessment.... | Building science | 0.807719 |
25,273 | Building and Environment: This international journal publishes original research papers and review articles related to building science, urban physics, and human interaction with the indoor and outdoor built environment. The journal's most cited articles cover topics such as occupant behavior in buildings, green buildi... | Building science | 0.807719 |
25,274 | These tools are valuable for evaluating a design and ensuring it will perform within an acceptable range before construction begins. Many of the available computational tools have the capability to analyze building performance goals and perform design optimization. The accuracy of the models is influenced by the modele... | Building science | 0.807719 |
25,275 | Python (programming language) Interspace -A package for finding the distance between two vectors, numbers and strings. SciPy -Distance computations (scipy.spatial.distance) Julia (programming language) Julia Statistics Distance -A Julia package for evaluating distances (metrics) between vectors. | Distance | 0.807718 |
25,276 | Most of the notions of distance between two points or objects described above are examples of the mathematical idea of a metric. A metric or distance function is a function d which takes pairs of points or objects to real numbers and satisfies the following rules: The distance between an object and itself is always zer... | Distance | 0.807718 |
25,277 | In statistics and information geometry, statistical distances measure the degree of difference between two probability distributions. There are many kinds of statistical distances, typically formalized as divergences; these allow a set of probability distributions to be understood as a geometrical object called a stati... | Distance | 0.807718 |
25,278 | In Euclidean geometry, the distance between two points A and B is often denoted | A B | {\displaystyle |AB|} . In coordinate geometry, Euclidean distance is computed using the Pythagorean theorem. The distance between points (x1, y1) and (x2, y2) in the plane is given by: Similarly, given points (x1, y1, z1) and (x2, y... | Distance | 0.807718 |
25,279 | The distance between two points in physical space is the length of a straight line between them, which is the shortest possible path. This is the usual meaning of distance in classical physics, including Newtonian mechanics. Straight-line distance is formalized mathematically as the Euclidean distance in two- and three... | Distance | 0.807718 |
25,280 | The two copper atoms are coordinated by two histidines, one methionine, a protein backbone carbonyl oxygen, and two bridging cysteine residues. Copper B centres (CuB) are found in cytochrome c oxidase. The copper atom is coordinated by three histidines in trigonal pyramidal geometry. A tetranuclear Copper Z centre (CuZ... | Copper protein | 0.807718 |
25,281 | This is the proper geometry of the blue copper protein. This shows that there is no presence of the Jahn-Teller effect. The energy diagram shows that the asymmetry of the short Cu-S(Cys) bond and the highly distorted Cu-L bond angles causes the degeneracy of the orbitals to be removed and thereby removing the Jahn-Tell... | Copper protein | 0.807718 |
25,282 | The C3v geometry was formed by the elongated methionine thioether bond at the reduced site. The unpaired electrons leads to the Jahn-Teller effect. (iii) shows the ground state energy level splitting diagram of the Cs geometry with a longer thioester bond and a subsequently shorter thiolate bond. | Copper protein | 0.807718 |
25,283 | (i) shows the tetrahedral geometry energy level diagram with a that is degenerate. The tetrahedral structure can undergo Jahn-Teller distortion because of the degenerate orbitals. (ii) shows the C3v symmetric geometry energy level splitting diagram with an 2E ground state that is degenerate. | Copper protein | 0.807718 |
25,284 | Cu2+ complexes normally have slow transfer rates. An example is the Cu2+/+ aquo, which is 5 x 10−7 M−1.sec−1 compared to the blue copper protein which is 1ms-01μs. Upon electron transfer the oxidized Cu2+ state at the blue copper protein active site will be minimized because the Jahn-Teller effect is minimized. The dis... | Copper protein | 0.807718 |
25,285 | The geometry of the Cu center has a major impact on its redox properties. The Jahn-Teller distortion does not apply to the blue copper proteins because the copper site has low symmetry that does not support degeneracy in the d-orbital manifold. The absence of large reorganizational changes enhances the rate of their el... | Copper protein | 0.807718 |
25,286 | Operating systems that are sensitive to BIOS-reported drive geometry include Solaris, DOS and Windows NT family, where NTLDR (NT, 2000, XP, Server 2003) or WINLOAD (Vista, Server 2008, Windows 7 and Server 2008 R2) use Master boot record which addresses the disk using CHS; x86-64 and Itanium versions of Windows can par... | Logical Block Address | 0.807717 |
25,287 | In stellar astronomy, the Algol paradox is a paradoxical situation when elements of a binary star seem to evolve in discord with the established theories of stellar evolution. A fundamental feature of these theories is that the rate of evolution of stars depends on their mass: The greater the mass, the faster this evol... | Algol paradox | 0.807717 |
25,288 | The minimum feedback arc set and maximum acyclic subgraph are equivalent for the purposes of exact optimization, as one is the complement set of the other. However, for parameterized complexity and approximation, they differ, because the analysis used for those kinds of algorithms depends on the size of the solution an... | Feedback arc set | 0.807715 |
25,289 | The complexity class APX is defined as consisting of optimization problems that have a polynomial time approximation algorithm that achieves a constant approximation ratio. Although such approximations are not known for the feedback arc set problem, the problem is known to be APX-hard, meaning that accurate approximati... | Feedback arc set | 0.807715 |
25,290 | This problem is NP-complete, implying that neither it nor the optimization problem are expected to have polynomial time algorithms. It was one of Richard M. Karp's original set of 21 NP-complete problems; its NP-completeness was proved by Karp and Eugene Lawler by showing that inputs for another hard problem, the verte... | Feedback arc set | 0.807715 |
25,291 | In order to apply the theory of NP-completeness to the minimum feedback arc set, it is necessary to modify the problem from being an optimization problem (how few edges can be removed to break all cycles) to an equivalent decision version, with a yes or no answer (is it possible to remove k {\displaystyle k} edges). Th... | Feedback arc set | 0.807715 |
25,292 | The remaining terms of their sum are (with common factors removed) ∑ i = 0 n ( 2 n 2 i ) − ∑ i = 0 n − 1 ( 2 n 2 i + 1 ) = ∑ j = 0 2 n ( − 1 ) j ( 2 n j ) = ( 1 − 1 ) 2 n = 0 {\displaystyle \sum _{i=0}^{n}{2n \choose 2i}-\sum _{i=0}^{n-1}{2n \choose 2i+1}=\sum _{j=0}^{2n}(-1)^{j}{2n \choose j}=(1-1)^{2n}=0} by the bino... | Pythagorean identity | 0.807714 |
25,293 | {\displaystyle \sec \theta ={\frac {c}{a}}.} In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the le... | Pythagorean identity | 0.807714 |
25,294 | c and reflecting our triangle in the y axis and setting a = x {\displaystyle a=x} and b = y {\displaystyle b=y} . Alternatively, the identities found at Trigonometric symmetry, shifts, and periodicity may be employed. | Pythagorean identity | 0.807714 |
25,295 | Any similar triangles have the property that if we select the same angle in all of them, the ratio of the two sides defining the angle is the same regardless of which similar triangle is selected, regardless of its actual size: the ratios depend upon the three angles, not the lengths of the sides. Thus for either of th... | Pythagorean identity | 0.807714 |
25,296 | The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. The identity is sin 2 θ + cos 2 θ... | Pythagorean identity | 0.807714 |
25,297 | A calculation confirms that z(0) = 1, and z is a constant so z = 1 for all x, so the Pythagorean identity is established. A similar proof can be completed using power series as above to establish that the sine has as its derivative the cosine, and the cosine has as its derivative the negative sine. In fact, the definit... | Pythagorean identity | 0.807714 |
25,298 | Sine and cosine can be defined as the two solutions to the differential equation: y ″ + y = 0 {\displaystyle y''+y=0} satisfying respectively y(0) = 0, y′(0) = 1 and y(0) = 1, y′(0) = 0. It follows from the theory of ordinary differential equations that the first solution, sine, has the second, cosine, as its derivativ... | Pythagorean identity | 0.807714 |
25,299 | This example of the Pareto principle (or 80–20 rule) allows search engines to employ optimization techniques such as index or database partitioning, caching and pre-fetching. In addition, studies have been conducted into linguistically-oriented attributes that can recognize if a web query is navigational, informational... | Web query | 0.807713 |
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