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So too do the multiplications by characters: ( M χ f ) ( y ) = χ ( y ) f ( y ) {\displaystyle (M_{\chi }f)(y)=\chi (y)f(y)} for χ ∈ K ^ {\displaystyle \chi \in {\hat {K}}} . These operators do not commute, and instead satisfy ( T x M χ T x − 1 M χ − 1 f ) ( y ) = χ ( x ) ¯ f ( y ) {\displaystyle \left(T_{x}M_{\chi }T_{... | Wikipedia - Heisenberg group | null | null | null |
{\displaystyle 1\to U(1)\to H(K)\to K\times {\hat {K}}\to 0.} More general Heisenberg groups are described by 2-cocyles in the cohomology group H 2 ( K , U ( 1 ) ) {\displaystyle H^{2}(K,U(1))} . | Wikipedia - Heisenberg group | null | null | null |
The existence of a duality between K {\displaystyle K} and K ^ {\displaystyle {\hat {K}}} gives rise to a canonical cocycle, but there are generally others. The Heisenberg group acts irreducibly on L 2 ( K ) {\displaystyle L^{2}(K)} . Indeed, the continuous characters separate points so any unitary operator of L 2 ( K ... | Wikipedia - Heisenberg group | null | null | null |
But commuting with translations implies that the multiplier is constant.A version of the Stone–von Neumann theorem, proved by George Mackey, holds for the Heisenberg group H ( K ) {\displaystyle H(K)} . The Fourier transform is the unique intertwiner between the representations of L 2 ( K ) {\displaystyle L^{2}(K)} and... | Wikipedia - Heisenberg group | null | null | null |
It is much more difficult, on a technical and political level to jam a satellite signal compared to blocking a website. Data streams can be transmitted alongside television channels. An attempt to jam the data stream will end up jamming the TV stations as well. | Wikipedia - Internet Protocol Datacasting | null | null | null |
It is natural to ask why ordinary everyday objects and events do not seem to display quantum mechanical features such as superposition. Indeed, this is sometimes regarded as "mysterious", for instance by Richard Feynman. In 1935, Erwin Schrödinger devised a well-known thought experiment, now known as Schrödinger's cat,... | Wikipedia - Superposition (quantum mechanics) | null | null | null |
One modern view is that this mystery is explained by quantum decoherence. A macroscopic system (such as a cat) may evolve over time into a superposition of classically distinct quantum states (such as "alive" and "dead"). The mechanism that achieves this is a subject of significant research. | Wikipedia - Superposition (quantum mechanics) | null | null | null |
One mechanism suggests that the state of the cat is entangled with the state of its environment (for instance, the molecules in the atmosphere surrounding it). When averaged over the possible quantum states of the environment (a physically reasonable procedure unless the quantum state of the environment can be controll... | Wikipedia - Superposition (quantum mechanics) | null | null | null |
It is natural to classify control problems by their control goals. Five kinds are listed below. Regulation (often called stabilization or positioning) is the most common and simple control goal. Regulation is understood as driving the state vector x ( t ) {\displaystyle x(t)} (or the output vector y ( t ) {\displaystyl... | Wikipedia - Cybernetical Physics | null | null | null |
Tracking. State tracking is driving a solution x ( t ) {\displaystyle x(t)} to the prespecified function of time x ∗ ( t ) {\displaystyle x*(t)} . Similarly, output tracking is driving the output y ( t ) {\displaystyle y(t)} to the desired output function y ∗ ( t ) {\displaystyle y*(t)} . | Wikipedia - Cybernetical Physics | null | null | null |
The problem is more complex if the desired equilibrium x ∗ {\displaystyle x*} or trajectory x ∗ ( t ) {\displaystyle x*(t)} is unstable in the absence of control action. For example, a typical problem of chaos control can be formulated as tracking an unstable periodic solution (orbit). The key feature of the control pr... | Wikipedia - Cybernetical Physics | null | null | null |
A limit case is stabilization of a system by an arbitrarily small control. The solvability of this task is not obvious if the trajectory x ∗ ( t ) {\displaystyle x*(t)} is unstable, for example in the case of chaotic systems. See.Generation (excitation) of oscillations. | Wikipedia - Cybernetical Physics | null | null | null |
The third class of control goals corresponds to the problems of "excitation" or "generation" of oscillations. Here, it is assumed that the system is initially at rest. The problem is to find out if it is possible to drive it into an oscillatory mode with the desired characteristics (energy, frequency, etc.) In this cas... | Wikipedia - Cybernetical Physics | null | null | null |
Moreover, the goal trajectory may be unknown, or may even be irrelevant to the achievement of the control goal. Such problems are well known in electrical, radio engineering, acoustics, laser, and vibrational technologies, and indeed wherever it is necessary to create an oscillatory mode for a system. Such a class of c... | Wikipedia - Cybernetical Physics | null | null | null |
Sometimes such problems can be reduced to tracking, but the reference trajectories x ∗ ( t ) {\displaystyle x*(t)} in these cases are not necessarily periodic and may be unstable. Besides, the goal trajectory x ∗ ( t ) {\displaystyle x*(t)} may be known only partially. Synchronization. | Wikipedia - Cybernetical Physics | null | null | null |
The fourth important class of control goals corresponds to synchronization (more accurately, "controlled synchronization" as distinct from "autosynchronization" or "self-synchronization"). Generally speaking, synchronization is understood as concurrent change of the states of two or more systems or, perhaps, concurrent... | Wikipedia - Cybernetical Physics | null | null | null |
If synchronization does not exist in the system without control the problem may be posed as finding the control function which ensures synchronization in the closed-loop system, i.e., synchronization may be a control goal. Synchronization problem differs from the model reference control problem in that some phase shift... | Wikipedia - Cybernetical Physics | null | null | null |
In such cases the limit mode (synchronous mode) in the overall system is not known in advance. Modification of the limit sets (attractors) of the systems. The last class of control goals is related to the modification of some quantitative characteristics that limit the behavior of the system. | Wikipedia - Cybernetical Physics | null | null | null |
It includes such specific goals as changing the type of the equilibrium (e.g., transforming an unstable equilibrium into a stable one, or vice versa); changing the type of the limit set (e.g., transforming a limit cycle into a chaotic attractor, or vice versa, changing the fractal dimension of the limit set, etc.); cha... | Wikipedia - Cybernetical Physics | null | null | null |
Additionally, the desired degree of chaoticity may be specified by specifying the Lyapunov exponent, fractal dimension, entropy, etc. See.In addition to the main control goal, some additional goals or constraints may be specified. A typical example is the "small control" requirement: the control function should have li... | Wikipedia - Cybernetical Physics | null | null | null |
Such a restriction is needed to avoid "violence" and preserve the inherent properties of the system under control. This is important for ensuring the elimination of artefacts and for an adequate study of the system. Three types of control are used in physical problems: constant control, feedforward control and feedback... | Wikipedia - Cybernetical Physics | null | null | null |
Implementation of a feedback control requires additional measurement devices working in real time, which are often hard to install. Therefore, studying the system may start with the application of inferior forms of control: time-constant and then feedforward control. The possibilities of changing system behavior by mea... | Wikipedia - Cybernetical Physics | null | null | null |
It is natural to try to understand the relationship between the objects D χ E {\displaystyle D\chi _{E}} , | D χ E | {\displaystyle |D\chi _{E}|} , and the topological boundary ∂ E {\displaystyle \partial E} . There is an elementary lemma that guarantees that the support (in the sense of distributions) of D χ E {\displ... | Wikipedia - Caccioppoli set | null | null | null |
It is near impossible for a healthy person to become intoxicated drinking low-alcohol drinks. The low concentration severely limits the rate of intake, which is easily dispatched by human metabolism. Quickly drinking 1.5 L of 0.4% ABV beer in an hour resulted in a maximum of 0.0056% BAC in a study of German volunteers. | Wikipedia - Alcohol content | null | null | null |
Healthy human kidneys can only excrete 0.8–1.0 L of water per hour, making water intoxication likely to set in before any alcoholic intoxication.The process of ethanol fermentation will slow down and eventually come to a halt as the alcohol produced becomes too concentrated for the yeast to tolerate, defining an upper ... | Wikipedia - Alcohol content | null | null | null |
It is nocturnal and roosts in sheltered places during the day, such as human structures, tree hollows, and rock crevices. | Wikipedia - Angolan free-tailed bat | null | null | null |
It is non-trivial to implement the random selection of r-regular graphs efficiently and in an unbiased way, since most graphs are not regular. The pairing model (also configuration model) is a method which takes nr points, and partitions them into n buckets with r points in each of them. Taking a random matching of the... | Wikipedia - Random regular graph | null | null | null |
If this object has no multiple edges or loops (i.e. it is a graph), then it is the required result. If not, a restart is required.A refinement of this method was developed by Brendan McKay and Nicholas Wormald. == References == | Wikipedia - Random regular graph | null | null | null |
It is normal for infants have hepatic EMH as they are developing up until roughly 5 weeks of age. On the other hand, hepatic EMH in adults can indicate a pathological state. This includes transplantation, hepatic tumors, hepatic disorders, or sepsis. Hepatoblastoma, adenomas and hepatocellular carcinomas can also lead ... | Wikipedia - Extramedullary hematopoiesis | null | null | null |
It is normal to correlate the erection of the penis with male sexual arousal. Physical or psychological stimulation, or both, leads to vasodilation and the increased blood flow engorges the three spongy areas that run along the length of the penis (the two corpora cavernosa and the corpus spongiosum). The penis grows e... | Wikipedia - Sexual arousal | null | null | null |
However, the relationship between erection and arousal is not one-to-one (arousal non-concordance). After their mid-forties, some men report that they do not always have an erection when they are sexually aroused. Equally, a male erection can occur during sleep (nocturnal penile tumescence) without conscious sexual aro... | Wikipedia - Sexual arousal | null | null | null |
A young man—or one with a strong libido—may experience enough sexual arousal for an erection to result from a passing thought, or just the sight of a passerby. Once erect, his penis may gain enough stimulation from contact with the inside of his clothing to maintain and encourage it for some time.As sexual arousal and ... | Wikipedia - Sexual arousal | null | null | null |
With further sexual stimulation, their heart rate increases, blood pressure rises and breathing becomes quicker. The increase in blood flow in the genital and other regions may lead to a sex flush in some men.As sexual stimulation continues, orgasm begins, when the muscles of the pelvic floor, the vas deferens (between... | Wikipedia - Sexual arousal | null | null | null |
Equally, if sexual stimulation stops before orgasm, the physical effects of the stimulation, including the vasocongestion, will subside in a short time. Repeated or prolonged stimulation without orgasm and ejaculation can lead to discomfort in the testes (corresponding to the slang term "blue balls"). After orgasm and ... | Wikipedia - Sexual arousal | null | null | null |
It is not difficult to establish the basic properties of the product numerical range which are independent of the partition of the Hilbert space and of the structure of the operator. We list them below leaving some simple items without a proof. | Wikipedia - Product numerical range | null | null | null |
It is not feasible to determine FCD using chemical analysis for every nutrient in every food type due to insufficient resources. Therefore, compilers of FCDB use other approaches to determine the required FCD within a FCDB. For example, to estimate values for a cooked food values for a raw food or dish can often be use... | Wikipedia - Food composition | null | null | null |
It is not immediately obvious why verification even functions correctly. To see why, denote as C the curve point computed in step 5 of verification, C = u 1 × G + u 2 × Q A {\displaystyle C=u_{1}\times G+u_{2}\times Q_{A}} From the definition of the public key as Q A = d A × G {\displaystyle Q_{A}=d_{A}\times G} , C = ... | Wikipedia - Elliptic Curve DSA | null | null | null |
It is not known if the complex lasso motif is functional in general. However, in some cases the importance of the motif for the protein function was reported. In particular, in case of lasso peptides, the motif allows to act like a plug for specific NTP-uptake channels. | Wikipedia - Complex lasso proteins | null | null | null |
On the other hand, the motif was shown to be functional in case of leptin - the obesity-related protein. The analysis of the shape of complex lasso proteins compared to the polymeric models with similar size shows, that some classes of complex lasso proteins may also be functional. This concerns toxic, antimicrobial, d... | Wikipedia - Complex lasso proteins | null | null | null |
It is not possible to consider time as an additional spatial dimension. To illustrate this suppose we map the dimension of time onto an axis of space. The data structure we will use to add the spatial time dimension is a min-heap. Let the y axis represent the key values of the items within the heap and the x axis is th... | Wikipedia - Retroactive data structure | null | null | null |
After several insertions and delete-min operations (all done non-retroactively) our min-heap would appear like in figure 1. Now suppose we retroactively insert zero to the beginning of the operation list. | Wikipedia - Retroactive data structure | null | null | null |
Our min-heap would appear like in figure 2. Notice how the single operation produces a cascading effect which affects the entire data structure. Thus we can see that while time can be drawn as a spatial dimension, operations with time involved produces dependence which have a ripple when modifications are made with res... | Wikipedia - Retroactive data structure | null | null | null |
It is not possible to form a black hole with vanishing surface gravity. That is, κ = 0 {\displaystyle \kappa =0} cannot be achieved. | Wikipedia - Bekenstein–Hawking entropy equation | null | null | null |
It is not possible to get pregnant from semen released in a commercial swimming pool without penetration. The sperm cells would be quickly killed by the chlorinated water and would not survive long enough to reach the vagina. Lack of a visible hymen is not a reliable indicator that a female has had penetrative sex, bec... | Wikipedia - Historical myth | null | null | null |
Hand size and foot size do not correlate with human penis size, but finger length ratio may. While pregnancies from sex between first cousins do carry a slightly elevated risk of birth defects, this risk is often exaggerated. The risk is 5–6% (similar to that of a woman in her early 40s giving birth), compared with a b... | Wikipedia - Historical myth | null | null | null |
The effects of inbreeding depression, while still relatively small compared to other factors (and thus difficult to control for in a scientific experiment), become more noticeable if isolated and maintained for several generations. Having sex before a sporting event or contest is not physiologically detrimental to perf... | Wikipedia - Historical myth | null | null | null |
There is no definitive proof of the existence of the vaginal G-spot, and the general consensus is that no such spot exists on the female body. Closeted or latent homosexuality is not correlated with internalized homophobia. A 1996 study claiming a connection in men has not been verified by subsequent studies, including... | Wikipedia - Historical myth | null | null | null |
It is not possible to produce gamma sources that emit all the energies needed to calculate accurately the response of a TAS detector. For this reason, it is better to perform a Montecarlo simulation of the response. For this simulation to be reliable, the interactions of all the particles emitted in the decay (γ, e−/e+... | Wikipedia - Total absorption spectroscopy | null | null | null |
The way to perform this simulation is explained in detail in paper by D. Cano-Ott et al. GEANT3 and GEANT4 are well suited for these kind of simulations. If the scintillator material of the TAS detector suffers from a non proportionality in the light production, the peaks produced by a cascade will be displaced further... | Wikipedia - Total absorption spectroscopy | null | null | null |
During the measurement there are additional statistical processes that affect the energy collection and are not included in the Montecarlo. The effect of this is an extra widening of the TAS experimental peaks. | Wikipedia - Total absorption spectroscopy | null | null | null |
Since the peaks reproduced with the Montecarlo do not have the correct width, a convolution with an empirical instrumental resolution distribution has to be applied to the simulated response. Finally, if the data to be analyzed comes from electron capture events, a simulated gamma response matrix must be built using th... | Wikipedia - Total absorption spectroscopy | null | null | null |
It is not sufficiently recognized that Peirce's career was that of a scientist, not a philosopher; and that during his lifetime he was known and valued chiefly as a scientist, only secondarily as a logician, and scarcely at all as a philosopher. Even his work in philosophy and logic will not be understood until this fa... | Wikipedia - Logic of relatives | null | null | null |
His writings bear on a wide array of disciplines, including mathematics, logic, philosophy, statistics, astronomy, metrology, geodesy, experimental psychology, economics, linguistics, and the history and philosophy of science. This work has enjoyed renewed interest and approval, a revival inspired not only by his antic... | Wikipedia - Logic of relatives | null | null | null |
In his work, fallibilism and pragmatism may seem to work somewhat like skepticism and positivism, respectively, in others' work. However, for Peirce, fallibilism is balanced by an anti-skepticism and is a basis for belief in the reality of absolute chance and of continuity, and pragmatism commits one to anti-nominalist... | Wikipedia - Logic of relatives | null | null | null |
It is not true that the join operation defined above is associative up to homeomorphism for arbitrary topological spaces. However, for locally compact Hausdorff spaces A , B , C {\displaystyle A,B,C} we have ( A ⋆ B ) ⋆ C ≅ A ⋆ ( B ⋆ C ) . {\displaystyle (A\star B)\star C\cong A\star (B\star C).} Therefore, one can def... | Wikipedia - Join (topology) | null | null | null |
It is not uncommon for patients to be anxious about being tested; explaining that tests are designed so that they will challenge everyone and that no one is expected to answer all questions correctly may be helpful. An important consideration of any neuropsychological assessment is a basic coverage of all major cogniti... | Wikipedia - Clinical neuropsychology | null | null | null |
It is not yet known what exactly is measured by DNA methylation age. Horvath hypothesized that DNA methylation age measures the cumulative effect of an epigenetic maintenance system but details are unknown. The fact that DNA methylation age of blood predicts all-cause mortality in later life has been used to argue that... | Wikipedia - Epigenetics of aging | null | null | null |
It is not yet understood why the universe has more matter than antimatter. It is generally assumed that when the universe was young and very hot it was in statistical equilibrium and contained equal numbers of baryons and antibaryons. However, observations suggest that the universe, including its most distant parts, is... | Wikipedia - Big-Bang singularity | null | null | null |
For baryogenesis to occur, the Sakharov conditions must be satisfied. These require that baryon number is not conserved, that C-symmetry and CP-symmetry are violated and that the universe depart from thermodynamic equilibrium. All these conditions occur in the Standard Model, but the effects are not strong enough to ex... | Wikipedia - Big-Bang singularity | null | null | null |
It is notable that EBEC is starting to be recognised from universities as a project of high quality that contributes to the education of the participants. University of Porto was the first university to recognise the competition by attributing ECTS to the participants. | Wikipedia - European BEST Engineering Competition | null | null | null |
It is now believed that Flourens may have removed more than just the parts of the hemispheres that he claimed because his experiments can be replicated without his same drastic results. At the time, extraction methods were very crude and little was understood about the stages of recovery. These things contributed to th... | Wikipedia - Mass Action Principle (neuroscience) | null | null | null |
François Pourfour du Petit demonstrated that localization of motor movements on one side of the body was contained in the hemisphere on the opposite side. In the 1860s, Hughlings Jackson also came to these conclusions after connecting convulsions on one side of the body to the disease of the opposite side of the brain ... | Wikipedia - Mass Action Principle (neuroscience) | null | null | null |
His findings were under the umbrella of field theory, but he didn't completely agree with Flourens. He determined that only the more elementary functions are localized, with the more complex ones not being bound to certain structures. | Wikipedia - Mass Action Principle (neuroscience) | null | null | null |
Shepherd Ivory Franz contributed to this field greatly by using better methods to study live animals. Lashley used these methods in combination with a large sample of animals to get results that can be statistically analyzed, and therefore came up with his equipotentiality and mass action theories. However, many others... | Wikipedia - Mass Action Principle (neuroscience) | null | null | null |
It is now believed that quantum mechanics should underlie all physical phenomena, so that a classical field theory should, at least in principle, permit a recasting in quantum mechanical terms; success yields the corresponding quantum field theory. For example, quantizing classical electrodynamics gives quantum electro... | Wikipedia - Internal group | null | null | null |
In quantum chromodynamics, the color field lines are coupled at short distances by gluons, which are polarized by the field and line up with it. This effect increases within a short distance (around 1 fm from the vicinity of the quarks) making the color force increase within a short distance, confining the quarks withi... | Wikipedia - Internal group | null | null | null |
General relativity, the Einsteinian field theory of gravity, has yet to be successfully quantized. However an extension, thermal field theory, deals with quantum field theory at finite temperatures, something seldom considered in quantum field theory. In BRST theory one deals with odd fields, e.g. Faddeev–Popov ghosts. | Wikipedia - Internal group | null | null | null |
There are different descriptions of odd classical fields both on graded manifolds and supermanifolds. As above with classical fields, it is possible to approach their quantum counterparts from a purely mathematical view using similar techniques as before. The equations governing the quantum fields are in fact PDEs (spe... | Wikipedia - Internal group | null | null | null |
It is now generally accepted that the description of quantum mechanics in which all self-adjoint operators represent observables is untenable. For this reason, observables are identified with elements of an abstract C*-algebra A (that is one without a distinguished representation as an algebra of operators) and states ... | Wikipedia - Quantum Liouville equation | null | null | null |
The C*-algebraic formulation can be seen to include both classical and quantum systems. When the system is classical, the algebra of observables become an abelian C*-algebra. In that case the states become probability measures. | Wikipedia - Quantum Liouville equation | null | null | null |
It is now possible to use computers to search for routes using the nonlinearities in the gravity of the planets and moons of the Solar System. For example, it is possible to plot an orbit from high earth orbit to Mars, passing close to one of the Earth's Trojan points. Collectively referred to as the Interplanetary Tra... | Wikipedia - Reversibility of orbits | null | null | null |
In addition launch windows can be very far apart. They have, however, been employed on projects such as Genesis. This spacecraft visited the Earth-Sun L1 point and returned using very little propellant. | Wikipedia - Reversibility of orbits | null | null | null |
It is often desirable to consider curves in the projective space. An algebraic curve in the projective plane or plane projective curve is the set of the points in a projective plane whose projective coordinates are zeros of a homogeneous polynomial in three variables P(x, y, z). Every affine algebraic curve of equation... | Wikipedia - Plane projective curve | null | null | null |
This implies that an affine curve and its projective completion are the same curves, or, more precisely that the affine curve is a part of the projective curve that is large enough to well define the "complete" curve. This point of view is commonly expressed by calling "points at infinity" of the affine curve the point... | Wikipedia - Plane projective curve | null | null | null |
It is often difficult to precisely define yielding due to the wide variety of stress–strain curves exhibited by real materials. In addition, there are several possible ways to define yielding: True elastic limit The lowest stress at which dislocations move. This definition is rarely used since dislocations move at very... | Wikipedia - Elastic Limit | null | null | null |
Elastic limit (yield strength) Beyond the elastic limit, permanent deformation will occur. The elastic limit is, therefore, the lowest stress point at which permanent deformation can be measured. This requires a manual load-unload procedure, and the accuracy is critically dependent on the equipment used and operator sk... | Wikipedia - Elastic Limit | null | null | null |
For elastomers, such as rubber, the elastic limit is much larger than the proportionality limit. Also, precise strain measurements have shown that plastic strain begins at very low stresses. Yield point The point in the stress-strain curve at which the curve levels off and plastic deformation begins to occur. | Wikipedia - Elastic Limit | null | null | null |
Offset yield point (proof stress) When a yield point is not easily defined on the basis of the shape of the stress-strain curve an offset yield point is arbitrarily defined. The value for this is commonly set at 0.1% or 0.2% plastic strain. The offset value is given as a subscript, e.g., R p0.1 = 310 {\displaystyle R_{... | Wikipedia - Elastic Limit | null | null | null |
For most practical engineering uses, R p0.2 {\displaystyle R_{\text{p0.2}}} is multiplied by a factor of safety to obtain a lower value of the offset yield point. High strength steel and aluminum alloys do not exhibit a yield point, so this offset yield point is used on these materials. Upper and lower yield points Som... | Wikipedia - Elastic Limit | null | null | null |
It is often illegal for a practicing engineer to jeopardize public safety in any way. This means that an engineer must hold herself or himself to the highest level of technical and moral conduct reasonable or suffer litigation if an engineering system fails causing harm to the public, including maintenance technicians.... | Wikipedia - Professional engineering | null | null | null |
It is often noted that green criminology is interdisciplinary and as a result, lacks its own unique theory or any preferred theoretical approach. Moreover, significant portions of the green criminological literature are qualitative and descriptive, and those studies have generally not proposed a unique or unifying theo... | Wikipedia - Green criminology | null | null | null |
For example, as noted, the political economic approach to green criminology develops explanations of green crime, victimization and environmental justice consistent with several existing strains of political economic analysis. Beirne's approach takes an interdisciplinary view of theory with respect to various animal ri... | Wikipedia - Green criminology | null | null | null |
It is often possible to multiply a group element by several small integers more quickly than by their product, generally by difference-based methods; one calculates differences between consecutive primes and adds consecutively by the d i r {\displaystyle d_{i}r} . This means that a two-step procedure becomes sensible, ... | Wikipedia - Algebraic-group factorization algorithm | null | null | null |
It is often required to delay a command's execution until a certain time. This is often because the spacecraft is not in view of the ground station, but may also be for reasons of precision. The OBC will store the TC until the required time in a queue, and then execute it. | Wikipedia - Command and data handling | null | null | null |
It is often the case that the canonical minterm form can be simplified to an equivalent SoP form. This simplified form would still consist of a sum of product terms. However, in the simplified form, it is possible to have fewer product terms and/or product terms that contain fewer variables. For example, the following ... | Wikipedia - Canonical disjunctive normal form | null | null | null |
In this trivial example, it is obvious that b c = a ′ b c + a b c {\displaystyle bc=a'bc+abc} , but the simplified form has both fewer product terms, and the term has fewer variables. The most simplified SoP representation of a function is referred to as a minimal SoP form. | Wikipedia - Canonical disjunctive normal form | null | null | null |
In a similar manner, a canonical maxterm form can have a simplified PoS form. While this example was simplified by applying normal algebraic methods , in less obvious cases a convenient method for finding the minimal PoS/SoP form of a function with up to four variables is using a Karnaugh map. The minimal PoS and SoP f... | Wikipedia - Canonical disjunctive normal form | null | null | null |
It is often useful to be able to compute the variance in a single pass, inspecting each value x i {\displaystyle x_{i}} only once; for example, when the data is being collected without enough storage to keep all the values, or when costs of memory access dominate those of computation. For such an online algorithm, a re... | Wikipedia - Algorithms for calculating variance | null | null | null |
It is also common to denote M k = x ¯ k {\displaystyle M_{k}={\bar {x}}_{k}} and S k = M 2 , k {\displaystyle S_{k}=M_{2,k}} .An example Python implementation for Welford's algorithm is given below. This algorithm is much less prone to loss of precision due to catastrophic cancellation, but might not be as efficient be... | Wikipedia - Algorithms for calculating variance | null | null | null |
It is one of the earliest fast block matching algorithms. It runs as follows: Start with search location at center Set step size S = 4 and search parameter p = 7 Search 8 locations +/- S pixels around location (0,0) and the location (0,0) Pick among the 9 locations searched, the one with minimum cost function Set the n... | Wikipedia - Block-matching algorithm | null | null | null |
It is pointed out by W.T. Grandy Jr, that entropy, though it may be defined for a non-equilibrium system is—when strictly considered—only a macroscopic quantity that refers to the whole system, and is not a dynamical variable and in general does not act as a local potential that describes local physical forces. Under s... | Wikipedia - Non-equilibrium thermodynamics | null | null | null |
It is possible for some polyhedra to change their overall shape, while keeping the shapes of their faces the same, by varying the angles of their edges. A polyhedron that can do this is called a flexible polyhedron. By Cauchy's rigidity theorem, flexible polyhedra must be non-convex. The volume of a flexible polyhedron... | Wikipedia - Polyhedral surface | null | null | null |
It is possible that data obtained during biometric enrollment may be used in ways for which the enrolled individual has not consented. For example, most biometric features could disclose physiological and/or pathological medical conditions (e.g., some fingerprint patterns are related to chromosomal diseases, iris patte... | Wikipedia - Biometric authentication | null | null | null |
It is possible to add more supercharges. That is, we fix a number which by convention is labelled N {\displaystyle {\mathcal {N}}} , and define supercharges Q α I , Q ¯ α ˙ I {\displaystyle Q_{\alpha }^{I},{\bar {Q}}_{\dot {\alpha }}^{I}} with I = 1 , ⋯ , N . {\displaystyle I=1,\cdots ,{\mathcal {N}}.} These can be tho... | Wikipedia - Super-Poincaré algebra | null | null | null |
It is possible to arrange multiple beams of laser light such that destructive quantum interference suppresses the vacuum fluctuations. Such a squeezed vacuum state involves negative energy. The repetitive waveform of light leads to alternating regions of positive and negative energy. | Wikipedia - Negative kinetic energy | null | null | null |
It is possible to borrow the initialization methodology to generate compound structure and array literals: Compound literals are often combined with designated initializers to make the declaration more readable: | Wikipedia - Storage class specifier | null | null | null |
It is possible to calculate eigenvalues, one for each of the four state variables (lean angle, lean rate, steer angle, and steer rate), from the linearized equations in order to analyze the normal modes and self-stability of a particular bike design. In the plot to the right, eigenvalues of one particular bicycle are c... | Wikipedia - Bike physics | null | null | null |
The eigenvalues are point symmetric about the origin and so any bike design with a self-stable region in forward speeds will not be self-stable going backwards at the same speed.There are three forward speeds that can be identified in the plot to the right at which the motion of the bike changes qualitatively: The forw... | Wikipedia - Bike physics | null | null | null |
Below this speed, oscillations increase until the uncontrolled bike falls over. Above this speed, oscillations eventually die out. The forward speed at which non-oscillatory leaning increases, where the capsize mode eigenvalues switch from negative to positive in a pitchfork bifurcation at about 8 m/s (18 mph) in this ... | Wikipedia - Bike physics | null | null | null |
Above this speed, this non-oscillating lean eventually causes the uncontrolled bike to fall over.Between these last two speeds, if they both exist, is a range of forward speeds at which the particular bike design is self-stable. In the case of the bike whose eigenvalues are shown here, the self-stable range is 5.3–8.0 ... | Wikipedia - Bike physics | null | null | null |
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