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On present-day computers, performance is determined more by cache and CPU pipeline considerations than by strict operation counts, and a slight difference in arithmetic cost is unlikely to be significant. Since FHT and real-input FFT algorithms have similar computational structures, neither appears to have a substantia... | Wikipedia - Discrete Hartley transform | null | null | null |
As a practical matter, highly optimized real-input FFT libraries are available from many sources (e.g. from CPU vendors such as Intel), whereas highly optimized DHT libraries are less common. On the other hand, the redundant computations in FFTs due to real inputs are more difficult to eliminate for large prime N, desp... | Wikipedia - Discrete Hartley transform | null | null | null |
Just as imposing the classical simplicity constraint recovers general relativity from BF theory, one expects an appropriate quantum simplicity constraint will recover quantum gravity from quantum BF theory. Much progress has been made with regard to this issue by Engle, Pereira, and Rovelli, Freidel and Krasnov and Liv... | Wikipedia - Loop gravity | null | null | null |
Just as in all of life, the likely benefits of a procured product come with possible non-beneficial qualities. Procurement is a careful activity attempting to achieve the best value for money. The benefits of the product must be satisfactorily delivered as specified for performance in the law of contract. Just as in fo... | Wikipedia - Child protection | null | null | null |
Welfare defines the process by which proper consent or agreement is given when procuring products that will be beneficial and safe in the procurer's particular circumstances. If a child is the ultimate consumer of a procured product then the child's welfare (health, safety and happiness) is the paramount consideration ... | Wikipedia - Child protection | null | null | null |
The calculus of negligence is a legal approach, in the spirit of procurement efficiency, that attempts to strike that balance on economic grounds. This is most easily understood in terms of insurance liability. Should a car driver have a duty of care towards unlit cyclists at night or should the cyclist have a duty of ... | Wikipedia - Child protection | null | null | null |
Just as in metals, when the stress at the crack tip approaches infinity, a yield zone will form at this crack tip front. Craze yielding is the most common yielding method at the crack front under tension due to the high triaxial stresses being applied in this local region. The Dugdale- Barenblatt strip-yield model is u... | Wikipedia - Fracture in polymers | null | null | null |
ρ = π / 8 ( K I / σ c ) {\displaystyle \rho =\pi /8(K_{I}/\sigma _{c})} Dugdale-Barenblatt strip-yield model The equation for stress intensity factor for a specimen with a single crack is given in the following equation where Y is a geometric parameter, s is the stress being applied and a is the crack length. For an ed... | Wikipedia - Fracture in polymers | null | null | null |
To accurately determine the stability of a crack growth and R curve plot should be constructed. A unique tip of fracture mode is called stick/slip crack growth. This occurs when an entire crack zone ruptures at some critical crack tip opening displacement (CTOD) followed by a crack arrest and then the formation of a ne... | Wikipedia - Fracture in polymers | null | null | null |
Just as integer sorting can be faster than comparison sorting for small-enough integers, the same is true for X + Y {\displaystyle X+Y} sorting. In particular, with integer inputs in the range from 0 {\displaystyle 0} to some upper limit M {\displaystyle M} , the problem can be solved in O ( n + M log M ) {\displayst... | Wikipedia - X + Y sorting | null | null | null |
Just as it sounds, a logical security audit follows a format in an organized procedure. The first step in an audit of any system is to seek to understand its components and its structure. When auditing logical security the auditor should investigate what security controls are in place, and how they work. In particular,... | Wikipedia - IT security auditors | null | null | null |
Passwords should not be shared and employees should have mandatory scheduled changes. Employees should have user rights that are in line with their job functions. They should also be aware of proper log on/ log off procedures. | Wikipedia - IT security auditors | null | null | null |
Also helpful are security tokens, small devices that authorized users of computer programs or networks carry to assist in identity confirmation. They can also store cryptographic keys and biometric data. The most popular type of security token (RSA's SecurID) displays a number that changes every minute. | Wikipedia - IT security auditors | null | null | null |
Users are authenticated by entering a personal identification number and the number on the token. Termination Procedures: Proper termination procedures so that, old employees can no longer access the network. This can be done by changing passwords and codes. | Wikipedia - IT security auditors | null | null | null |
Also, all id cards and badges that are in circulation should be documented and accounted for. Special User Accounts: Special User Accounts and other privileged accounts should be monitored and have proper controls in place. Remote Access: Remote access is often a point where intruders can enter a system. The logical se... | Wikipedia - IT security auditors | null | null | null |
Just as light is a wave motion that is considered as composed of particles called photons, we can think of the normal modes of vibration in a solid as being particle-like. The quantum of lattice vibration is called phonon. In lattice dynamics we want to find the normal modes of vibration of a crystal. In other words, w... | Wikipedia - Phonon laser | null | null | null |
The relationship between frequency ω and wave vector k is called phonon dispersion. Light and sound are similar in various ways. They both can be thought of in terms of waves, and they both come in quantum mechanical units. | Wikipedia - Phonon laser | null | null | null |
In the case of light we have photons while in sound we have phonons. Both sound and light can be produced as random collections of quanta (e.g. light emitted by a light bulb) or orderly waves that travel in a coordinated form (e.g. laser light). This parallelism implies that lasers should be as feasible with sound as t... | Wikipedia - Phonon laser | null | null | null |
In the 21st century, it is easy to produce low frequency sound in the range that humans can hear (~20 kHz), in either a random or orderly form. However, at the terahertz frequencies in the regime of phonon laser applications, more difficulties arise. The problem stems from the fact that sound travels much slower than l... | Wikipedia - Phonon laser | null | null | null |
This means that the wavelength of sound is much shorter than light at a given frequency. Instead of resulting in orderly, coherent phonons, laser structures that can produce terahertz sound tend to emit phonons randomly. Researchers have overcome the problem of terahertz frequencies by following various approaches. | Wikipedia - Phonon laser | null | null | null |
Scientists in Caltech have overcome this problem by assembling a pair of microscopic cavities that only permit specific frequencies of phonons to be emitted. This system can be also tuned to emit phonons of different frequencies by changing the relative separation of the microcavities. | Wikipedia - Phonon laser | null | null | null |
On the other hand, the group from the University of Nottingham took a different approach. They have built their device out of electrons moving through a series of structures known as quantum wells. Briefly, as an electron hops from one quantum well to another neighbouring well it produces a phonon. | Wikipedia - Phonon laser | null | null | null |
External energy pumping (e.g. a light beam or voltage) can help to the excitation of an electron. Relaxation of an electron from one of the upper states may occur by emission of either a photon or a phonon. This is determined by the density of states of phonons and photons. | Wikipedia - Phonon laser | null | null | null |
Density of states is the number of states per volume unit in an interval of energy (E, E + dE) that are available to be occupied by electrons. Both phonons and photons are bosons and thus, they obey Bose–Einstein statistics. This means that, since bosons with the same energy can occupy the same place in space, phonons ... | Wikipedia - Phonon laser | null | null | null |
There are more allowed states available for occupancy in a phonon field than in a photon field. Therefore, since the density of terminal states in the phonon field exceeds that in a photon field (by up to ~105), phonon emission is by far the more likely event. We could also imagine a concept where the excitation of an ... | Wikipedia - Phonon laser | null | null | null |
The vibration energy of the lattice can take discrete values for every excitation. Every one of this "excitation packages" is called phonon. An electron does not stay in an excited state for too long. | Wikipedia - Phonon laser | null | null | null |
It readily releases energy to return to its stable low energy state. The electrons release energy in any random direction and at any time (after their excitation). At some particular times, some electrons get excited while others lose energy in a way that the average energy of system is the lowest possible. | Wikipedia - Phonon laser | null | null | null |
By pumping energy into the system we can achieve a population inversion. This means that there are more excited electrons than electrons in the lowest energy state in the system. As electron releases energy (e.g. phonon) it interacts with another excited electron to release its energy too. | Wikipedia - Phonon laser | null | null | null |
Therefore, we have a stimulated emission, which means a lot of energy (e.g., acoustic radiation, phonons) is released at the same time. One can mention that the stimulated emission is a procedure where we have a spontaneous and an induced emission at the same time. The induced emission comes from the pumping procedure ... | Wikipedia - Phonon laser | null | null | null |
A SASER device should consist of a pumping mechanism and an active medium. The pumping procedure can be induced for example by an alternating electric field or with some mechanical vibrations of resonators, followed by acoustic amplification in the active medium. The fact that a SASER operates on principles remarkably ... | Wikipedia - Phonon laser | null | null | null |
Instead of a feedback-built potent wave of electromagnetic radiation, a SASER delivers a potent sound wave. Some methods for sound amplification of GHz–THz have been proposed so far. Some have been explored only theoretically and others have been explored in non-coherent experiments. | Wikipedia - Phonon laser | null | null | null |
We note that acoustic waves of 100 GHz to 1 THz have wavelengths in nanometre range. Sound amplification according to the experiment taken in the University of Nottingham could be based on an induced cascade of electrons in semiconductor superlattices. The energy levels of electrons are confined in the superlattice lay... | Wikipedia - Phonon laser | null | null | null |
As the electrons hop between gallium arsenide quantum wells in the superlattice they emit phonons. Then, one phonon going in, produces two phonons coming out of the superlattice. This process can be stimulated by other phonons and then give rise to an acoustic amplification. | Wikipedia - Phonon laser | null | null | null |
Upon the addition of electrons, short-wavelength (in the terahertz range) phonons are produced. Since the electrons are confined to the quantum wells existing within the lattice, the transmission of their energy depends upon the phonons they generate. As these phonons strike other layers in the lattice, they excite ele... | Wikipedia - Phonon laser | null | null | null |
Eventually, a very narrow beam of high-frequency ultrasound exits the device. Semiconductor superlattices are used as acoustic mirrors. These superlattice structures must be in the right size obeying the theory of multilayer distributed Bragg reflector, in similarity with multilayer dielectric mirrors in optics. | Wikipedia - Phonon laser | null | null | null |
Just as order relations are grounded in ordered sets, sets closed under pairwise supremum and infimum, equivalence relations are grounded in partitioned sets, which are sets closed under bijections that preserve partition structure. Since all such bijections map an equivalence class onto itself, such bijections are als... | Wikipedia - Equivalence relations | null | null | null |
Let G denote the set of bijective functions over A that preserve the partition structure of A, meaning that for all x ∈ A {\displaystyle x\in A} and g ∈ G , g ( x ) ∈ . {\displaystyle g\in G,g(x)\in .} Then the following three connected theorems hold: ~ partitions A into equivalence classes. | Wikipedia - Equivalence relations | null | null | null |
(This is the Fundamental Theorem of Equivalence Relations, mentioned above); Given a partition of A, G is a transformation group under composition, whose orbits are the cells of the partition;Given a transformation group G over A, there exists an equivalence relation ~ over A, whose equivalence classes are the orbits o... | Wikipedia - Equivalence relations | null | null | null |
{\displaystyle a\sim b{\text{ if and only if }}ab^{-1}\in H.} The equivalence classes of ~—also called the orbits of the action of H on G—are the right cosets of H in G. Interchanging a and b yields the left cosets. Related thinking can be found in Rosen (2008: chpt. 10). | Wikipedia - Equivalence relations | null | null | null |
Just as quantum physics differs in fundamental ways from classical physics, quantum economics differs from neoclassical economics in a number of key respects. Neoclassical economics is based on expected utility theory, which combines utility theory to model people’s preferences, and probability theory to model expectat... | Wikipedia - Quantum economics | null | null | null |
In quantum economics, price fluctuations are seen as being due to fundamental uncertainty.Neoclassical economics assumes that people act independently while making economic decisions. Quantum economics notes that financial actors are part of an entangled system, as in quantum game theory. | Wikipedia - Quantum economics | null | null | null |
Quantum economics also stresses the importance of financial transactions and in particular the role of money as an active force in the economy, for example in the way that it entangles debtors and creditors through loans. Quantum economics can therefore be viewed as an alternative to neoclassical economics which begins... | Wikipedia - Quantum economics | null | null | null |
Just as the Poincaré algebra generates the Poincaré group of isometries of Minkowski space, the super-Poincaré algebra, an example of a Lie super-algebra, generates what is known as a supergroup. This can be used to define superspace with N {\displaystyle {\mathcal {N}}} supercharges: these are the right cosets of the ... | Wikipedia - Super-Poincare algebra | null | null | null |
The supercharge Q α I {\displaystyle Q_{\alpha }^{I}} generates translations in the direction labelled by the coordinate θ α I . {\displaystyle \theta _{\alpha }^{I}.} By counting, there are 4 N {\displaystyle 4{\mathcal {N}}} spin dimensions. | Wikipedia - Super-Poincare algebra | null | null | null |
Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function and the plane that contains... | Wikipedia - Definite integral | null | null | null |
This reduces the problem of computing a double integral to computing one-dimensional integrals. Because of this, another notation for the integral over R uses a double integral sign: ∬ R f ( x , y ) d A . {\displaystyle \iint _{R}f(x,y)\,dA.} | Wikipedia - Definite integral | null | null | null |
Integration over more general domains is possible. The integral of a function f, with respect to volume, over an n-dimensional region D of R n {\displaystyle \mathbb {R} ^{n}} is denoted by symbols such as: ∫ D f ( x ) d n x = ∫ D f d V . {\displaystyle \int _{D}f(\mathbf {x} )d^{n}\mathbf {x} \ =\int _{D}f\,dV.} | Wikipedia - Definite integral | null | null | null |
Just as the delays talking to memory while its price fell suggested a radical change in ISA (Instruction Set Architecture) from CISC to RISC, designers are considering whether the problems scaling in parallelism and the increasing delays talking to registers demands another switch in basic ISA. Among the ways to introd... | Wikipedia - Explicit Data Graph Execution | null | null | null |
An instruction that might take five cycles if the data is in the cache could take hundreds if it is not, but the compiler has no way to know whether that data will be in the cache at runtime – that's determined by overall system load and other factors that have nothing to do with the program being compiled. The key per... | Wikipedia - Explicit Data Graph Execution | null | null | null |
Just as the exterior algebra (and tensor algebra) of vector fields on a manifold form a Lie algebra (over the base field K), the de Rham complex of differential forms on a manifold form a Lie coalgebra (over the base field K). Further, there is a pairing between vector fields and differential forms. However, the situat... | Wikipedia - Lie coalgebra | null | null | null |
Just as the formulas for the roots of second, third, and fourth degree polynomials suggest extending real numbers to the more algebraically complete setting of the complex numbers, many properties of algebraic varieties suggest extending affine space to a more geometrically complete projective space. Whereas the comple... | Wikipedia - Algebraic Geometry | null | null | null |
If we draw it, we get a parabola. As x goes to positive infinity, the slope of the line from the origin to the point (x, x2) also goes to positive infinity. | Wikipedia - Algebraic Geometry | null | null | null |
As x goes to negative infinity, the slope of the same line goes to negative infinity. Compare this to the variety V(y − x3). This is a cubic curve. | Wikipedia - Algebraic Geometry | null | null | null |
As x goes to positive infinity, the slope of the line from the origin to the point (x, x3) goes to positive infinity just as before. But unlike before, as x goes to negative infinity, the slope of the same line goes to positive infinity as well; the exact opposite of the parabola. So the behavior "at infinity" of V(y −... | Wikipedia - Algebraic Geometry | null | null | null |
The consideration of the projective completion of the two curves, which is their prolongation "at infinity" in the projective plane, allows us to quantify this difference: the point at infinity of the parabola is a regular point, whose tangent is the line at infinity, while the point at infinity of the cubic curve is a... | Wikipedia - Algebraic Geometry | null | null | null |
Furthermore, the introduction of projective techniques made many theorems in algebraic geometry simpler and sharper: For example, Bézout's theorem on the number of intersection points between two varieties can be stated in its sharpest form only in projective space. For these reasons, projective space plays a fundament... | Wikipedia - Algebraic Geometry | null | null | null |
When a coordinate system has been chosen in the space of dimension n + 1, all the points of a line have the same set of coordinates, up to the multiplication by an element of k. This defines the homogeneous coordinates of a point of Pn as a sequence of n + 1 elements of the base field k, defined up to the multiplicatio... | Wikipedia - Algebraic Geometry | null | null | null |
This allows us to define a projective algebraic set in Pn as the set V(f1, ..., fk), where a finite set of homogeneous polynomials {f1, ..., fk} vanishes. Like for affine algebraic sets, there is a bijection between the projective algebraic sets and the reduced homogeneous ideals which define them. The projective varie... | Wikipedia - Algebraic Geometry | null | null | null |
In other words, a projective variety is a projective algebraic set, whose homogeneous coordinate ring is an integral domain, the projective coordinates ring being defined as the quotient of the graded ring or the polynomials in n + 1 variables by the homogeneous (reduced) ideal defining the variety. Every projective al... | Wikipedia - Algebraic Geometry | null | null | null |
Just as the fundamental theorem of algebra ensures that every linear transformation acting on a finite-dimensional complex vector space has a nontrivial invariant subspace, the fundamental theorem of noncommutative algebra asserts that Lat(Σ) contains nontrivial elements for certain Σ. Theorem (Burnside) Assume V is a ... | Wikipedia - Invariant vector | null | null | null |
One consequence is that every commuting family in L(V) can be simultaneously upper-triangularized. A nonempty set Σ ⊂ L(V) is said to be triangularizable if there exists a basis {e1, ..., en} of V such that span { e 1 , … , e k } ∈ Lat ( Σ ) for all k ≥ 1 . {\displaystyle \operatorname {span} \{e_{1},\ldots ,e_{k}\... | Wikipedia - Invariant vector | null | null | null |
In other words, Σ is triangularizable if there exists a basis such that every element of Σ has an upper-triangular matrix representation in that basis. It follows from Burnside's theorem that every commutative algebra Σ in L(V) is triangularizable. Hence every commuting family in L(V) can be simultaneously upper-triang... | Wikipedia - Invariant vector | null | null | null |
Just as there are many different types of representations for Kac–Moody algebras and their universal enveloping algebras, so there are many different types of representation for quantum groups. As is the case for all Hopf algebras, Uq(G) has an adjoint representation on itself as a module, with the action being given b... | Wikipedia - Quantum group | null | null | null |
Just as two (distinct) points determine a line, five points determine a conic. Formally, given any five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non-degenerate; this is true in both the Euclidean plane and its extension, the ... | Wikipedia - Focal parameter | null | null | null |
Thus knowing the center is equivalent to knowing two points on the conic for the purpose of determining the curve.Furthermore, a conic is determined by any combination of k points in general position that it passes through and 5 – k lines that are tangent to it, for 0≤k≤5.Any point in the plane is on either zero, one o... | Wikipedia - Focal parameter | null | null | null |
All the conic sections share a reflection property that can be stated as: All mirrors in the shape of a non-degenerate conic section reflect light coming from or going toward one focus toward or away from the other focus. In the case of the parabola, the second focus needs to be thought of as infinitely far away, so th... | Wikipedia - Focal parameter | null | null | null |
The theorem also holds for degenerate conics consisting of two lines, but in that case it is known as Pappus's theorem. Non-degenerate conic sections are always "smooth". This is important for many applications, such as aerodynamics, where a smooth surface is required to ensure laminar flow and to prevent turbulence. | Wikipedia - Focal parameter | null | null | null |
Just as with Bresenham's line algorithm, this algorithm can be optimized for integer-based math. Because of symmetry, if an algorithm can be found that only computes the pixels for one octant, the pixels can be reflected to get the whole circle. We start by defining the radius error as the difference between the exact ... | Wikipedia - Midpoint circle algorithm | null | null | null |
It is useful to start with the point ( r , 0 ) {\displaystyle (r,0)} on the positive X-axis. Because the radius will be a whole number of pixels, clearly the radius error will be zero: R E ( x i , y i ) = | x i 2 + 0 2 − r 2 | = 0 {\displaystyle RE(x_{i},y_{i})=\left\vert x_{i}^{2}+0^{2}-r^{2}\right\vert =0} Because it... | Wikipedia - Midpoint circle algorithm | null | null | null |
Also, because it concerns this octant only, the X values have only 2 options: to stay the same as the prior iteration, or decrease by 1. A decision variable can be created that determines if the following is true: R E ( x i − 1 , y i + 1 ) < R E ( x i , y i + 1 ) {\displaystyle RE(x_{i}-1,y_{i}+1) 0, the term ( 1 − 2 x... | Wikipedia - Midpoint circle algorithm | null | null | null |
If 2 ( R E + Y Change ) + X Change ≤ 0 {\displaystyle 2(RE+Y_{\text{Change}})+X_{\text{Change}}\leq 0} , then keep the same x value. Again, by reflecting these points in all the octants, a full circle results. We may reduce computation by only calculating the delta between the values of this decision formula from its v... | Wikipedia - Midpoint circle algorithm | null | null | null |
Just as with classical stochastic calculus, the appropriate product rule can be derived for Itô and Stratonovich integration, respectively:: 156, 159 ( I ) d ( a b ) = a d b + b d a + d a d b , {\displaystyle (\mathbf {I} )\,\mathrm {d} (ab)=a\,\mathrm {d} b+b\,\mathrm {d} a+\mathrm {d} a\,\mathrm {d} b\,,} ( S ) d ( a... | Wikipedia - Quantum stochastic calculus | null | null | null |
Just as with the Dirac equation on flat spacetime, we make use of the Clifford algebra, a set of four gamma matrices { γ μ } {\displaystyle \{\gamma ^{\mu }\}} satisfying { γ μ , γ ν } = 2 η μ ν {\displaystyle \{\gamma ^{\mu },\gamma ^{\nu }\}=2\eta ^{\mu \nu }} where { ⋅ , ⋅ } {\displaystyle \{\cdot ,\cdot \}} is the ... | Wikipedia - Dirac equation in curved spacetime | null | null | null |
They in fact form a representation of Spin ( 1 , 3 ) . {\displaystyle {\text{Spin}}(1,3).} | Wikipedia - Dirac equation in curved spacetime | null | null | null |
However, it is a standard abuse of terminology to any representations of the Lorentz algebra as representations of the Lorentz group, even if they do not arise as representations of the Lorentz group. The representation space is isomorphic to C 4 {\displaystyle \mathbb {C} ^{4}} as a vector space. In the classification... | Wikipedia - Dirac equation in curved spacetime | null | null | null |
The abuse of terminology extends to forming this representation at the group level. We can write a finite Lorentz transformation on R 1 , 3 {\displaystyle \mathbb {R} ^{1,3}} as Λ σ ρ = exp ( i 2 α μ ν M μ ν ) σ ρ {\displaystyle \Lambda _{\sigma }^{\rho }=\exp \left({\frac {i}{2}}\alpha _{\mu \nu }M^{\mu \nu }\right)... | Wikipedia - Dirac equation in curved spacetime | null | null | null |
If another representation ρ {\displaystyle \rho } has generators T μ ν = ρ ( M μ ν ) , {\displaystyle T^{\mu \nu }=\rho (M^{\mu \nu }),} then we write ρ ( Λ ) j i = exp ( i 2 α μ ν T μ ν ) j i {\displaystyle \rho (\Lambda )_{j}^{i}=\exp \left({\frac {i}{2}}\alpha _{\mu \nu }T^{\mu \nu }\right){}_{j}^{i}} where i , j ... | Wikipedia - Dirac equation in curved spacetime | null | null | null |
Just as with the closely related signature algorithms DSA, ECDSA, and ElGamal, reusing the secret nonce value k {\displaystyle k} on two Schnorr signatures of different messages will allow observers to recover the private key. In the case of Schnorr signatures, this simply requires subtracting s {\displaystyle s} value... | Wikipedia - Schnorr signature | null | null | null |
Just like decimal engineering notation can be viewed as a base-1000 scientific notation (103 = 1000), binary engineering notation relates to a base-1024 scientific notation (210 = 1024), where the exponent of two must be divisible by ten. This is closely related to the base-2 floating-point representation (B notation) ... | Wikipedia - Variable scientific notation | null | null | null |
Just like natural forests, the carbon sequestered in a shade‐grown coffee farm's shade trees will be stored in the tree trunks, limbs, leaves, and roots of the foliage as opposed to being in the atmosphere and adding to global warming. Soil also acts as a sink; soil in shade-grown coffee holds carbon from the organic m... | Wikipedia - Shade-grown coffee | null | null | null |
Just like other technologies, AR application development kits are available for a rapid development process in the form of Software development kits (SDKs) including: CloudRidAR, Vuforia, AR ToolKit, Catchoom CraftAR, Mobinett AR, Wikitude, Blippar, Layar, Meta, and ARLab. | Wikipedia - Commercial augmented reality | null | null | null |
Just like the general concept of energy, free energy has a few definitions suitable for different conditions. In physics, chemistry, and biology, these conditions are thermodynamic parameters (temperature T {\displaystyle T} , volume V {\displaystyle V} , pressure p {\displaystyle p} , etc.). Scientists have come up wi... | Wikipedia - Thermodynamic free energy | null | null | null |
For example, if a researcher wanted to perform a combustion reaction in a bomb calorimeter, the volume is kept constant throughout the course of a reaction. Therefore, the heat of the reaction is a direct measure of the free energy change, q = Δ U {\displaystyle q=\Delta U} . In solution chemistry, on the other hand, m... | Wikipedia - Thermodynamic free energy | null | null | null |
Under this condition, the heat q {\displaystyle q} of the reaction is equal to the enthalpy change Δ H {\displaystyle \Delta H} of the system. Under constant pressure and temperature, the free energy in a reaction is known as Gibbs free energy G {\displaystyle G} . G = H − T S {\displaystyle G=H-TS} These functions hav... | Wikipedia - Thermodynamic free energy | null | null | null |
In addition, they also have theoretical importance in deriving Maxwell relations. Work other than p dV may be added, e.g., for electrochemical cells, or f dx work in elastic materials and in muscle contraction. Other forms of work which must sometimes be considered are stress-strain, magnetic, as in adiabatic demagneti... | Wikipedia - Thermodynamic free energy | null | null | null |
These are described by tensors. In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. | Wikipedia - Thermodynamic free energy | null | null | null |
Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy. N i {\displaystyle N_{i}} is the number of molecules (alternatively, moles) of type i {\displaystyle i} in the sy... | Wikipedia - Thermodynamic free energy | null | null | null |
The differentials for processes at uniform pressure and temperature are (assuming only p V {\displaystyle pV} work): d A = − p d V − S d T + ∑ i μ i d N i {\displaystyle \mathrm {d} A=-p\,\mathrm {d} V-S\,\mathrm {d} T+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,} d G = V d p − S d T + ∑ i μ i d N i {\displaystyle \mathrm {d... | Wikipedia - Thermodynamic free energy | null | null | null |
Just three weeks earlier she had launched the Women's Engineering Society (WES) in collaboration with her daughter Rachel, and five other women of influence, Eleanor Shelley-Rolls; Janetta Mary Ornsby; Margaret D Rowbotham; Margaret, Lady Moir & Laura Annie Willson in order to protect women's position in the field, and... | Wikipedia - Katharine Parsons | null | null | null |
Just-in-time compilation is supported in PHP 8.PHP 8's JIT compiler can provide substantial performance improvements for some use cases, while PHP developer Nikita Popov stated that the performance improvements for most websites will be less substantial than the upgrade from PHP 5 to PHP 7. Substantial improvements are... | Wikipedia - PHP | null | null | null |
Justin Lessler and others from Johns Hopkins University reported a rise in the usage of the ambiguous term "hotspot" in research and policy documents in late 2010s. Hotspots have been variously described as areas of elevated incidence or prevalence, higher transmission efficiency or risk, or higher probability of disea... | Wikipedia - Hyperendemic | null | null | null |
Justus von Liebig was the first to understand the importance of ammonia as fertilizer, and promoted the importance of inorganic minerals to plant nutrition. In England, he attempted to implement his theories commercially through a fertilizer created by treating phosphate of lime in bone meal with sulfuric acid. Another... | Wikipedia - Technological Revolution | null | null | null |
Jutlandic also exhibits a strong tendency towards apocope, i.e. skipping the e often found in unstressed syllables, which is itself a weakening of an original North Germanic -i, -a or -u, which causes many words to be distinguished based purely on vowel length or the presence of the stød. Most unstressed syllables are... | Wikipedia - Jutlandic dialect | null | null | null |
It is pronounced in the majority of Jutland as but in South Jutlandic and North Western Jutlandic as . The difference goes back to different forms in Proto-Norse, namely ek and eka, both found in early Runic inscriptions. The latter form has a regular breaking of e to ja before an a in the following syllable. | Wikipedia - Jutlandic dialect | null | null | null |
The short form, without breaking, is also found in Norwegian, Faroese and Icelandic. In Northern Jutlandic v is a labiovelar approximant before back vowels (in the northernmost dialects also before front vowels), whereas it is a Labiodental approximant in Standard Danish, e.g. vaske 'wash' = Standard Danish . The same... | Wikipedia - Jutlandic dialect | null | null | null |
Juvenile avian song learning is one of the best animal models used to study generation and recognition of rhythm. The ability for birds to process a tutor song and then generate a perfect replica of that song, underlies our ability to learn rhythm. Two very famous computational neuroscientists Kenji Doya and Terrence J... | Wikipedia - Neuroscience of rhythm | null | null | null |
The young Zebra Finch is exposed to a "tutor song" from the adult, during a critical period. This is defined as the time of life that learning can take place, in other words when the brain has the most plasticity. After this period, the bird is able to produce an adult song, which is said to be crystallized at this poi... | Wikipedia - Neuroscience of rhythm | null | null | null |
Doya and Sejnowski evaluated three possible ways that this leaning could happen, an immediate, one shot perfection of the tutor song, error learning, and reinforcement learning. They settled on the third scheme. Reinforcement learning consists of a "critic" in the brain capable of evaluating the difference between the ... | Wikipedia - Neuroscience of rhythm | null | null | null |
Assuming the two are closer than the last trial, this "critic" then sends a signal activating NMDA receptors on the articulator of the song. In the case of the Zebra Finch, this articulator is the robust nucleus of archistriatum or RA. The NMDA receptors allow the RA to be more likely to produce this template of the tu... | Wikipedia - Neuroscience of rhythm | null | null | null |
Sam Sober explains the process of tutor song recognition and generation using error learning. This refers to a signal generated by the avian brain that corresponds to the error between the tutor song and the auditory feedback the bird gets. The signal is simply optimized in order to be as small of a difference as possi... | Wikipedia - Neuroscience of rhythm | null | null | null |
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