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Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition...

the ΛCDM model, or is the universe inhomogeneous or anisotropic? More unsolved problems in physics An inhomogeneous cosmology is a physical cosmological...

In mathematics, a homogeneous space is, very informally, a space that looks the same everywhere as one moves through it, with movement given by the action...

In statistics, a sequence of random variables is homoscedastic (/ˌhoʊmoʊskəˈdæstɪk/) if all its random variables have the same finite variance; this is...

Poisson point process. In the second case, the point process is called an inhomogeneous or nonhomogeneous Poisson point process, and the average density of...

on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homogeneous, as exemplified by Lf = g, with g a fixed function...

the "trivial solution" y = 0 {\displaystyle y=0} . Nonhomogeneous (or inhomogeneous) A linear differential equation is nonhomogeneous if r ( x ) ≠ 0 {\displaystyle...

In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example...

radiation, is the bending of sound propagation trajectories (rays) in inhomogeneous elastic media (gases, liquids, and solids) in which the wave velocity...

narrow Lorentzian that is significantly broadened is a Gaussian. If inhomogeneous broadening dominates homogeneous, Spectral hole burning may be used...

integral is an exact solution to the paraxial Helmholtz equation. The inhomogeneous Helmholtz equation is the equation ∇ 2 A ( x ) + k 2 A ( x ) = − f (...

\over \partial r}={1 \over ir}{\partial f \over \partial \theta }.} The inhomogeneous Cauchy–Riemann equations consist of the two equations for a pair of...

In electromagnetism and applications, an inhomogeneous electromagnetic wave equation, or nonhomogeneous electromagnetic wave equation, is one of a set...

The Stern–Gerlach experiment involves sending silver atoms through an inhomogeneous magnetic field and observing their deflection. Silver atoms were evaporated...

Duhamel's principle is a general method for obtaining solutions to inhomogeneous linear evolution equations like the heat equation, wave equation, and...

The grand potential or Landau potential or Landau free energy is a quantity used in statistical mechanics, especially for irreversible processes in open...

In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale...

vector representation of it; it is sometimes dubbed, informally, as the inhomogeneous Lorentz group. In turn, it can also be obtained as a group contraction...

homogeneous medium, an approximation in an inhomogeneous medium. A matrix representation for an inhomogeneous medium was presented using a pair of matrix...

potential. ( Δ E ∼ 1 / r 6 ) {\displaystyle (\Delta E\sim 1/r^{6})} Inhomogeneous broadening is a general term for broadening because some emitting particles...

the inhomogeneous dephasing can be removed by applying a 180° inversion pulse that inverts the magnetisation vectors. Examples of inhomogeneous effects...

Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial...

observed in solid solutions and liquid sols that involves the change of an inhomogeneous structure over time, in that small crystals or sol particles first dissolve...

thresholding. They are particularly adapted to cases where images have inhomogeneous lighting, such as in the sudoku image on the right. In those cases,...

Time-inhomogeneous hidden Bernoulli model (TI-HBM) is an alternative to hidden Markov model (HMM) for automatic speech recognition. Contrary to HMM, the...

In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied...

constants, is a general method to solve inhomogeneous linear ordinary differential equations. For first-order inhomogeneous linear differential equations it...

in spacetime, is an inhomogeneous Lorentz transformation, an element of the Poincaré group, which is also called the inhomogeneous Lorentz group. A "stationary"...

uniform inhomogeneous statement whenever 1 , α , β {\displaystyle 1,\alpha ,\beta } span a totally real cubic number field. Strong inhomogeneous results...

scatter within the paint layer. Later he generalized the theory to inhomogeneous layers (see below). The Kubelka–Munk theory is also used in the paper...

time. Her dissertation was titled, The Study of Light Propagation in Inhomogeneous Universes Using the Gravitational Lensing Method. Richard Matzner was...

that may occur in media that are both anisotropic and inhomogeneous, such as an inhomogeneous anisotropic birefringent waveplate. Q-plates are also currently...

with spatial rotations and translations in space and time form the inhomogeneous Galilean group (assumed throughout below). Without the translations...

electromagnetic radiation emitted when a charged particle passes through inhomogeneous media, such as a boundary between two different media. This is in contrast...

sources to the wave equations makes the partial differential equations inhomogeneous. The general solution to the electromagnetic wave equation is a linear...

averaged Lagrangian description of slowly varying nonlinear wave trains in inhomogeneous media: ∂ ∂ t A + ∇ ⋅ B = 0 , {\displaystyle {\frac {\partial }{\partial...

{1}{2c}}\int _{x-ct}^{x+ct}h(\xi )\,d\xi .} The general form of an inhomogeneous canonical hyperbolic type differential equation takes the form of: u...

University. Chew's chief contributions are in the areas of waves in inhomogeneous media for various geophysical subsurface sensing and non-destructive...

ovoid in the 3-dimensional projective space over K (represented in inhomogeneous coordinates). Only when m = 1 is the ovoid O {\displaystyle {\mathcal...

constructed so that π is a steady-state distribution. Even with time-inhomogeneous Markov chains, where multiple transition matrices are used, if each...

r_{2}r_{3}-p_{1}p_{2}r_{1}r_{2}r_{3}=0} Inhomogeneous martini-B (3–5) lattice, bond percolation Inhomogeneous martini lattice with outside enclosing triangle...

X {\displaystyle X} be an inhomogeneous Markov process with values in R d {\displaystyle \mathbb {R} ^{d}} , inhomogeneous transition probabilities (...

(A) No disturbing force (B) With an electric field, E (C) With an independent force, F (e.g. gravity) (D) In an inhomogeneous magnetic field, grad H...

and between homogeneous differential equations and inhomogeneous ones, defined above. Inhomogeneous first-order linear constant-coefficient ordinary differential...

the operator K(x,y) are thus seen to be decreasing towards zero. The inhomogeneous Fredholm integral equation f ( x ) = − ω φ ( x ) + ∫ K ( x , y ) φ (...

Stranski-Krastanov growth mode, inhomogeneous line broadening is inherently present that is caused by quantum dot size-dispersion. Inhomogeneous line broadening adversely...

Sainte-Barbe. Duhamel's principle, a method of obtaining solutions to inhomogeneous linear evolution equations, is named after him. He was primarily a mathematician...

mono-monostatic. However, it is inhomogeneous; its material density varies across its body. Another example of an inhomogeneous mono-monostatic body is the...

field of a heterogeneous planet such as Earth is deformed due to the inhomogeneous spatial distribution of materials with different densities. Actual horizontal...

both homogeneous (all ions exhibit the same broadened spectrum) and inhomogeneous (different ions in different glass locations exhibit different spectra)...

simplest example of such devices is inhomogeneous anisotropic birefringent waveplate that performs transversally inhomogeneous polarization transformations of...

result in a correctly represented sample. In either the homogeneous or inhomogeneous case, the bias is defined in terms of a prior distribution of distances...

price of $5,321,850 (or about $10.92 million today). The response of inhomogeneous plates undergoing explosive welding was analytically modeled in 2011...

plasticity. There are two kinds of structural rejuvenation: homogeneous and inhomogeneous. Dmowski, W.; Yokoyama, Y.; Chuang, A.; Ren, Y.; Umemoto, M.; Tsuchiya...

In inhomogeneous systems the pressure depends on the position and orientation of the surface on which the pressure acts. Therefore, in inhomogeneous systems...

from a collection of identical chromophores in a matrix is said to be inhomogeneously broadened because each chromophore is surrounded by a somewhat different...

transverse relaxation time, is related to homogeneous and inhomogeneous broadening. An inhomogeneous broadening results from the fact that the different spins...

doi:10.1111/j.1468-4004.2010.51331.x. Browning, Philippa K. (1984). Inhomogeneous magnetic fields in the solar atmosphere. st-andrews.ac.uk (PhD thesis)...

approximation (DDA). Most of the software applies to arbitrary-shaped inhomogeneous nonmagnetic particles and particle systems in free space or homogeneous...

as standard dark energy. Some alternatives to dark energy, such as inhomogeneous cosmology, aim to explain the observational data by a more refined use...

potential that propagates at the speed of light and is the solution to an inhomogeneous wave equation: ∇ 2 V − 1 c 2 ∂ 2 V ∂ t 2 = − ρ ε 0 {\displaystyle \nabla...

{r}})=-{\boldsymbol {\mu }}\cdot \mathbf {B} (\mathbf {r} )} in an inhomogeneous magnetic field B ( r ) {\displaystyle \mathbf {B} (\mathbf {r} )} produces...

{\displaystyle \lim _{(x,t)\to (x^{0},0)}u_{t}(x,t)=h(x^{0})} Consider the inhomogeneous wave equation in 1 + D {\displaystyle 1+D} dimensions ( ∂ t t − c 2...

materials exhibit as they undergo plastic deformation, specifically inhomogeneous deformation. This effect has been long associated with dynamic strain...

imperfections in the microstructure of solids, such as impurities, inhomogeneous strain and crystallographic defects such as dislocations, perfect single...

nonlocal effects in a system of gravitating particles, leads to the inhomogeneous Dirichlet boundary problem for the Poisson equation Δ Φ ( x ) = A N...

electrically neutral silver atom beams through Stern–Gerlach experiment's inhomogeneous magnetic field splits into two, each of which corresponds to one possible...

contributions to the fields of defect mechanics and micromechanics of inhomogeneous solids for fifty years, including important aspects of the controlling...

emerges before the singularity, effectively covering it. By allowing an inhomogeneous initial density profile, one can demonstrate a significant alteration...

matter physics, and his main interest has been the optical properties of inhomogeneous systems. His recent work has focused on colloidal systems. Born in Mexico...

magnetic field strength of 0.55 ±0.03 Megagauss. The magnetism can lead to inhomogeneous brightness distribution and the TESS light curve shows that the white...

H_{Z}} which in turn focus the electron. Note that the magnetic field is inhomogeneous, particles close to the center are less strongly deflected than those...

path followed by light and the refractive index of the medium. For inhomogeneous optical media, the product above is generalized as a path integral as...

discovered by James Dunlop on May 28, 1826. Its stellar population is inhomogeneous, varying with distance from the core. The effective temperature of the...

(corresponding to negligible stress) general Cauchy momentum equation becomes an inhomogeneous Burgers' equation (here we make explicit the material derivative): Burgers'...

transducers. Forward propagation can be used to predict the influence of inhomogeneous, nonlinear media on acoustic transducer performance. Wave field synthesis...

Optics has been translated to Chinese and Persian and his monograph on Inhomogeneous Optical Waveguides (coauthored with Professor Sodha) has been translated...

y(t)=e^{At}y_{0}.} The matrix exponential can also be used to solve the inhomogeneous equation d d t y ( t ) = A y ( t ) + z ( t ) , y ( 0 ) = y 0 . {\displaystyle...

random topographies (landscapes), or composition variations of an inhomogeneous material. This list is currently incomplete. See also Category:Stochastic...

to depend on both x {\displaystyle x} and t {\displaystyle t} . The inhomogeneous heat equation models thermal problems in which a heat source modeled...

Richardson-Gaudin model, physical models of the Riemann Zeros, quantum Hall states, inhomogeneous spin chains, infinite matrix product states, The Prime State, quantum...

ellipse smoothly together, one gets a non-conic oval. If one takes the inhomogeneous representation of a conic oval as a parabola plus a point at infinity...

Mathematical Sciences in 1967 for the dissertation “Electromagnetic fields in inhomogeneous media” and was awarded the title of professor in 1969. From 1960 to...

the atmosphere and the Rytov approximation for wave propagation in inhomogeneous media bear his name. Sergei Mikhailovich Rytov was born in Kharkov,...

projective space. Let (a, L) be an element of the Poincaré group (the inhomogeneous Lorentz group). Thus, a is a real Lorentz four-vector representing the...

reaching a more accurate model than if those constraints are ignored. In inhomogeneous cosmology, in which structure formation is taken into account in a...

is a special case of a Sturm–Liouville equation. Consider a general inhomogeneous second-order linear differential equation P ( x ) y ″ + Q ( x ) y ′...

sufficiently near equilibrium state, so that they have defined entropy. Some inhomogeneous systems out of thermodynamic equilibrium still satisfy the hypothesis...

Implementations of filtering operations for all but the simplest flows are inhomogeneous filter operations. This means that the flow either has non-periodic...

10.24 billion years old. The stellar population of this cluster is inhomogeneous, varying with distance from the core. The effective temperature of the...

transverse wave with phase velocity approaching zero. In the case of an inhomogeneous fluids (that is, a fluid where at least one of the background quantities...

Js band. The team found that the variability is likely driven by an inhomogeneous cloud cover. Later the rotational velocity helped to constrain the inclination...

media originating from the coupling of electron spin to microscopically inhomogeneous magnetic field of magnetic background. In 1966, after the Institute...

Method of solution for inhomogeneous ODEs...

half light radius, or experienced a stronger UV background due to the inhomogeneous nature of reionization. Li 李, Jiaxuan 嘉轩; Greene, Jenny E.; Carlsten...

surface wave or Sommerfeld-Zenneck surface wave is a longitudinal, inhomogeneous or non-uniform electromagnetic plane wave incident at the complex Brewster's...

(in dimensionless units, for simplicity). (Equivalently, consider the inhomogeneous Helmholtz equation.) If the function V ( x ) {\displaystyle V(\mathbf...

(demographics) Jack Cuzick and Robert Edwards (1990). "Spatial clustering for inhomogeneous populations". Journal of the Royal Statistical Society, Series B. 52...

Hilbert space is a space of irreducible unitary representations of the inhomogeneous Lorentz group (the Poincaré group); the S-matrix is the evolution operator...

solutions to the Einstein field equation. These are a widely used family of inhomogeneous cosmological models. Kantowski received his Ph.D. in 1966 from the University...

an inhomogeneous magnetic field, and being deflected up or down depending on their spin; (1) furnace, (2) beam of silver atoms, (3) inhomogeneous magnetic...

relativity and theoretical cosmology. His graduate work included studies on inhomogeneous cosmologies, wormholes, exact solutions in general relativity of compact...

to find that the rigidity in homogeneous spaces has an echo in the inhomogeneous world of moduli space." Mirzakhani was awarded the Fields Medal in 2014...

semiconductor optoelectronics, wave propagation and mode coupling in inhomogeneous media, magnetospheric physics, plasma astrophysics, gamma- and radio-astronomy...

with homogenous magnetic fields or for an idealized, Coulomb-like, inhomogeneous magnetic field. For the case of where the magnetic field is constant...

; Driebe, T.; Millour, F.; et al. (2009). "Spatially resolving the inhomogeneous structure of the dynamical atmosphere of Betelgeuse with VLTI/AMBER"...

transformation v of Lindblad operators and constants, and also under the inhomogeneous transformation where ai are complex numbers and b is a real number....

greater) than that of the air, so that the wave is travelling in an inhomogeneous medium. In consequence CPW will not support a true TEM wave; at non-zero...

aberration. In refractive corneas, the lens tissue is corrected with inhomogeneous lens material (see Luneburg lens), or with an aspheric shape. Flattening...

R(z;A)=(A-zI)^{-1}~.} Among other uses, the resolvent may be used to solve the inhomogeneous Fredholm integral equations; a commonly used approach is a series solution...

therefore solutions to a special class of linear difference equation: inhomogeneous first order linear recurrences with constant coefficients. The elements...

While electrically neutral, its spin magnetic moments interact with an inhomogeneous magnetic field; some atoms will be attracted to a magnetic minimum,...

CT-scan of vascular malformations in the liver in a patient with hereditary hemorrhagic telangiectasia causing an inhomogeneous perfusion pattern....

terms with n positive converge for |z| <1 to a function satisfying an inhomogeneous linear equation with singularities at z = 0 and z=1, so can be continued...

the Volterra integral equation which has variable integral limits. An inhomogeneous Fredholm equation of the first kind is written as g ( t ) = ∫ a b K...

wave equation resp. one-way wave operator is also valid in inhomogeneous media. For inhomogeneous media with location-dependent elasticity module E ( x )...

vector potential. Another approach involves a general solution of the inhomogeneous wave equation for the vector potential in the case of constant currents...

some complex diffusion processes, for instance, diffusion process in inhomogeneous or heterogeneous medium, e.g. porous media. Fractional diffusion equations...

experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous magnetic fields in a Stern–Gerlach experiment, or by measuring the magnetic...

}{\partial t}}+\mu _{0}\mathbf {J} \end{aligned}}} and reduce to the inhomogeneous Maxwell equation: ∂ α F β α = − μ 0 J β , {\displaystyle \partial _{\alpha...

One example is spreading resistance profiling, where the material is inhomogeneous (different resistivity in different places), and the exact paths of...

(by which is meant the variation in structure of an inhomogeneous structure such as an inhomogeneous coronal loop) and heating has been demonstrated by...

radiated from infinity into ... the field." Mathematically, consider the inhomogeneous Helmholtz equation ( ∇ 2 + k 2 ) u = − f  in  R n {\displaystyle (\nabla...

Kingdom in 2003. Later, the inverse Doppler effect was observed in some inhomogeneous materials, and predicted inside a Vavilov–Cherenkov cone. Bistatic Doppler...

dimension n of the space, and is commonly denoted E(n) or ISO(n), for inhomogeneous special orthogonal group. The Euclidean group E(n) comprises all translations...

justified by the observations that, while the universe is "weakly" inhomogeneous and anisotropic (see the large-scale structure of the cosmos), it is...

produce a magnetic moment. These magnetic moments can interact with an inhomogeneous magnetic field; some of the antihydrogen atoms can be attracted to a...

Fried, D. L. (October 1966). "Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures". Journal of the Optical...

Also the strain states in the body and the inclusion are potentially inhomogeneous and complicated. Eshelby found that the resulting elastic field can...

magnetic-susceptibility-induced line broadening is attenuated which reduces inhomogeneous broadening of the spectral lines for samples in heterogeneous environments...

gold Sakiewicz P., Nowosielski R., Babilas R. Production aspects of inhomogeneous hot deformation in as-cast CuNi25 alloy, Indian Journal of Engineering...

Stern-Gerlach device, a charged spin 1/2 particle enters into an inhomogeneous magnetic field. Only two possible outcomes are possible, the particle is...

Extraction of a net momentum "from nothing" has been postulated in an inhomogeneous vacuum, but this remains highly controversial as it will violate Lorentz...

applies to homogeneous thermodynamic systems. It does not apply to inhomogeneous systems such as small thermodynamic systems, systems subject to long-range...

The Lommel differential equation, named after Eugen von Lommel, is an inhomogeneous form of the Bessel differential equation: z 2 d 2 y d z 2 + z d y d...

Quaoar and also beyond its Roche limit. The outer ring appears to be inhomogeneous, containing a thin, dense section as well as a broader, more diffuse...

molecular gas, and the dynamics of blast waves in both homogeneous and inhomogeneous media. In collaboration with Jeremiah Ostriker (Columbia University)...

ƒ represents the attenuation data of a tomographic scan through an inhomogeneous medium whose density is represented by the function ƒ. Inversion of...

sequence of single-time propositions at different times. These are called inhomogeneous history propositions. An example is the proposition α {\displaystyle...

Contributions to the theory and modelling of seismic waves in anisotropic inhomogeneous media with applications to subduction-zones. queensu.ca (PhD thesis)...

New York: Academic. Mandelstam, L.I. (1926). "Light Scattering by Inhomogeneous Media". Zh. Russ. Fiz-Khim. Ova. 58: 381. Fuller, Michael P.; Griffiths...

Fried, D. L. (October 1966). "Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures". Journal of the Optical...

gravitational fields, which have some formal similarities to the real, inhomogeneous gravitational fields of curved spacetime in general relativity. In the...

(1 February 2005). "On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation". Inventiones Mathematicae....

Kirchhoff–Helmholtz integral theorem and related identities for waves in an inhomogeneous moving fluid", Journal of the Acoustical Society of America, 99 (4):...

magnetized when brought into the strong magnetic field and create additional inhomogeneous fields. The process of correcting for these inhomogeneities is called...

Calculator (With Graph Generation ) General method, including locally inhomogeneous case and Fortran 77 software An explanation from the Atlas of the Universe...

2 January 2014. Demory, Brice-Olivier; et al. (2013). "Inference of Inhomogeneous Clouds in an Exoplanet Atmosphere". The Astrophysical Journal Letters...

magnetic susceptibility is the Gouy balance. In this technique there is an inhomogeneous magnetic field in the central region between two (flat) poles of a magnet...

represented mathematical operations. This machine was capable of solving inhomogeneous differential equations. The first versions of Lukyanov's integrators...

have adverse effects on different environmental matrices. They are an inhomogeneous group of anthroprogenic chemical compounds that is discharged by human...

the time derivatives are straightforward and we obtain the following inhomogeneous wave equation ∇ 2 E r a d + μ 0 ω 2 ( ϵ 0 + i σ / ω ) E r a d = − i...

ISBN 978-1-83953-613-7. Aki, K., & Richards, P. G. (2002). Quantitative Seismology. Chew, W. C. (1995). Waves and Fields in Inhomogeneous Media. IEEE Press. v t e...

materials, ε and μ are constant throughout the material, while for inhomogeneous materials they depend on location within the material (and perhaps time)...

advisor was Michael Turner and his thesis was titled Particle Creation in Inhomogeneous Spacetimes. After completing his PhD, Frieman held a postdoc position...

(September 2000), "Enhanced Room-Temperature Geometric Magnetoresistance In Inhomogeneous Narrow-Gap Semiconductors" (PDF), Science, 289 (5484): 1530–2, Bibcode:2000Sci...

delta function δ(x), a fundamental solution F is a solution of the inhomogeneous equation LF = δ(x). Here F is a priori only assumed to be a distribution...

Project Timescape, education center at the Wittenham Clumps, England Inhomogeneous cosmology § Timescape cosmology, a cosmological model This disambiguation...

that moves separately from the ovary. In around 60% of cases, it is an inhomogeneous or a noncystic adnexal mass, sometimes known as the "blob sign". It...

operators. The name comes from the Green's functions used to solve inhomogeneous differential equations, to which they are loosely related. (Specifically...

in a cold, sparse gas is most clearly visible due to the absence of inhomogeneous broadening of the individual transitions. Vibronic transitions are drawn...

single-use envelopes of mixed powders; and solid boluses of homogeneous or inhomogeneous mixture called bath bombs. Bath fizzies are a form of bath salts in...

the incident field and with each other. DDA can handle targets with inhomogeneous composition and anisotropic material properties, as well as periodic...

from the semirelativistic Thomas term. This might be a macroscopically inhomogeneous field of ferromagnets that is already used for operating Electric dipole...

(as opposed to the cosmological constant, which remains a constant). Inhomogeneous cosmology. One of the fundamental assumptions of Lambda-CDM is that...

result of two states within the same defect. [citation needed] The inhomogeneous linewidth for this feature reduces in isotopically pure silicon-28....

J.; Lednický, F.; Luňák, S. (1978-04-01). "Are cured epoxy resins inhomogeneous?". Polymer. 19 (4): 393–397. doi:10.1016/0032-3861(78)90243-4. ISSN 0032-3861...

taenite. Gamma (fcc) Fe-Ni alloys with low-Ni (about 25% Ni) are probably inhomogeneous on a nanometer scale. Antitaenite and taenite have the same crystal...

light beam can acquire OAM by crossing a spiral phase plate, with an inhomogeneous thickness (see figure). A more convenient approach for generating OAM...

Green's matrix helps to determine a particular solution to a first-order inhomogeneous linear system of ODEs. The concept is named after George Green. For...

considerably by the mass distribution, either if they are homogeneous or inhomogeneous - see Torque, moment of inertia, wobble, imbalance and stability. Bouguer...

SAFE AIR (Simulation of Air pollution From Emissions Above Inhomogeneous Regions) is an advanced atmospheric pollution dispersion model for calculating...

It can also be used to solve for the quark-photon vertex from the inhomogeneous Bethe-Salpeter equation, for the elastic form factors of pseudoscalar...

result is an incoherent spectrum containing absolute band shapes through inhomogeneous broadening. Spectrum simulation is one of the most fundamental tasks...

terms of infinite series. In case of more complex geometries and for inhomogeneous particles the original Maxwell's equations are discretized and solved...

Reiche wrote about the deflection of beams of polar molecules in an inhomogeneous electric field, with the ultimate aim of measuring their dipole moments...

(NSE). The compressible NSE are rearranged into various forms of the inhomogeneous acoustic wave equation. Within these equations, source terms describe...

in the number of cloud drops. A contrasting model of entrainment is inhomogeneous mixing. This model assumes that the time it takes to evaporate cloud...

At the constituent level, the values of the materials vary and are inhomogeneous. Precise calculation of the many constituent values is nearly impossible...

force-free magnetic fields, stability of jets and cylinders and stability of inhomogeneous plasmas. His work on the mathematical treatment of gaseous polytropes...

uniform polarization and/or magnetization. After their application to any inhomogeneous region, they predict the existence of even parts in functions of the...

Research and Engineering for nearly 18 years, leading the Interfaces and Inhomogeneous Materials Group and Complex Fluids Area. He then became a Professor...

time-independent Klein–Gordon equation. In the inhomogeneous case, the screened Poisson equation is very similar to the inhomogeneous Helmholtz equation, the only difference...

PMID 16578292. E. Wigner (1937). "On Unitary Representations Of The Inhomogeneous Lorentz Group" (PDF). Annals of Mathematics. 40 (1): 149–204. Bibcode:1939AnMat...

by a liquid in a container Mercury beating heart — a consequence of inhomogeneous surface tension Sessile drop technique Spinning drop method Stalagmometric...

rotating stick (with moment of inertia I {\displaystyle I} ) in an inhomogeneous "gravitation like" field that is periodically switched on in short pulses...

tensor Metric tensor (general relativity) Relativistic angular momentum inhomogeneous cosmology Tolman, Richard C. (1934). "Effect of Inhomogeneity on Cosmological...

Olivier; Paricaud, Patrice (2017-09-12). "Long Range Corrections for Inhomogeneous Simulations of Mie n – m Potential". Journal of Chemical Theory and...

Inhomogeneities in the masses of the hydrometeors along the cloud-base may cause inhomogeneous descent along the base. Frictional drag and associated eddy-like structures...

vertices. In terms of the Laplacian, the positive solutions to the inhomogeneous equation: Δ ϕ = ϕ − 2. {\displaystyle \Delta \phi =\phi -2.} The resulting...

least squares to some cases, in which a combination of certain types of inhomogeneous random sources of errors gives these a 'systematic' character, T. N...

Of course, since the above equations are simply the solution to an inhomogeneous differential equation, any solution to the homogeneous equation can...

to one million base-pairs (1 Mbp) long. GENSCAN utilizes a general inhomogeneous, three periodic, fifth order Markov model of DNA coding regions. Additionally...

service representative. B0 inhomogeneity leads to mismapping of tissues. Inhomogeneous external magnetic field causes either spatial, intensity, or both distortions...

one scalar homogeneous first-order linear ODE in each coordinate. An inhomogeneous equation y ( n ) + c n − 1 y ( n − 1 ) + ⋯ + c 1 y ( 1 ) + c 0 y = f...

number of particles (molecules in this case), or to generalize to an inhomogeneous system the local form holds: P = n k B T , {\displaystyle P=nk_{\text{B}}T...

is, roughly, a classification of all unitary representations of the inhomogeneous Lorentz group amounts to a classification of all possible relativistic...

"Class of fast methods for processing Irregularly sampled or otherwise inhomogeneous one-dimensional data". Physical Review Letters. 74 (7): 1060–1063....

J. N. (Sep 2006). "Can Electric Charges and Currents Survive in an Inhomogeneous Universe?". arXiv:astro-ph/0609031. Bibcode:2006astro.ph..9031S. {{cite...

sensitivity, but have the disadvantage of producing an inhomogeneous excitation field. This inhomogeneous field causes spatial variations in spin flip angles...

on a torus), mechanics (brachistochrone) and optics (light beam in inhomogeneous medium). Totally geodesic submanifold Archived 2015-08-10 at the Wayback...

also in terms of kinetic energy and potential energies of parts of the inhomogeneous system with respect to each other and with respect to long-range external...

such as serum amyloid P component, resulting in complex, and sometimes inhomogeneous structures. Recently this definition has come into question as some...

period of rotation of the star. It is thought that they are caused by an inhomogeneous distribution of chemical elements in the atmospheres of these stars...

Drummond, Peter D (1990). "Electromagnetic quantization in dispersive inhomogeneous nonlinear dielectrics" (PDF). Physical Review A. 42 (11): 6845–6857...

problems beyond classical general relativity. Fractal cosmology – Models inhomogeneous universe structure on large scales. Gravitational-wave astronomy – study...

the University of Minnesota for graduate research, where she studied inhomogeneous materials and tissues. Her thesis proposed nanoindentation as a means...

slow long-distance charge separation in dielectric spectroscopy on inhomogeneous soft matter Polarization (electrochemistry), a change in the equilibrium...

charge conservation. The Klein–Gordon equation can be elevated to the inhomogeneous Klein–Gordon equation through the introduction of a source term J (...

the value V(t) satisfies the inhomogeneous first-order ODE L V = f {\displaystyle {\mathcal {L}}V=f} ("inhomogeneous" is because one has f rather than...

function of t {\displaystyle t} , the resulting process is called an inhomogeneous or nonhomogeneous Poisson process, where the average density of points...

Y.V.; Krylov, V.V.; Plessky, V.P. (1995). Surface Acoustic Waves in Inhomogeneous Media. Springer. ISBN 978-3-540-58460-5. "Jeffrey Collins Obituary Herald...

{\displaystyle \eta (\mathbf {q} |\Gamma )} satisfies the resulting inhomogeneous equation: − ℏ 2 2 m ∇ 2 η + ( u ~ 1 − E ) η + i ℏ 2 2 m [ 2 τ 12 ∇ +...

the Kerch Strait. Therefore, the plankton species are distributed inhomogeneously in the Sea of Azov. Although many additional species are brought in...

years, he worked on fluctuation-dissipative theorem for the case of an inhomogeneous plasma. In 2018 V. Belyi published an article in Scientific Reports...

and the prototype. This has been ascribed to non-radial pulsations, inhomogeneous rotating discs, or the rotation of the star itself. These stars are...

enabled coherent control of the exciton population in the presence of inhomogeneous broadening. In interfacial quantum dots MDCS revealed induced inter-dot...

uniform stellar population, but the interstellar medium in it may be inhomogeneous. Its mass is estimated to be about 2×108 times the mass of the Sun,...

explicit space and time dependence could also occur if the material is inhomogeneous or changing with time. In some solids, thermal conduction is anisotropic...

identically, we obtain Laplace's equation. Poisson's equation is linear inhomogeneous partial differential equation, and invariant under rotations or translations...

proposed a method for the production of population inversion using inhomogeneous electric and magnetic fields. Their results were first presented at...

{1}{\varepsilon _{0}}}\rho .} These are simpler and more symmetric forms of the inhomogeneous Maxwell's equations. Here c = 1 ε 0 μ 0 {\displaystyle c={\frac {1}{\sqrt...

than a solar radius from the photosphere and looks very complex and inhomogeneous in the X-rays images taken by satellites (see the figure on the right...

inequalities governing the probabilities p of coincidences. Working from the inhomogeneous version of the inequality, we can write: − 1 ≤ p j k ( a , b ) − p j...

rule Leibniz's linear differential equation, a first-order, linear, inhomogeneous differential equation Leibniz's notation, a notation in calculus Leibniz...

has a magnetic moment and the antiparallel state does not. A strong inhomogeneous magnetic field will separate atoms in the higher energy state from a...

luminosity) with periods of a few days. The stellar magnetic field creates an inhomogeneous pattern of dark star spots and bright faculae across the surface, which...

calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres". www.scopus.com. Retrieved 7 June 2018...

and was applied to homogeneous spheres, spherical shells, radially inhomogeneous spheres and infinite cylinders. Peter Debye has contributed to the theory...

geometric transformation represented by a diagonalizable matrix is an inhomogeneous dilation (or anisotropic scaling). That is, it can scale the space by...

mixture can be thought of as the distribution of a certain quantity in an inhomogeneous population consisting of many different normal distributed subpopulations...

X-ray spectroscopy showed inhomogeneous distributions of some cations. Neither impurity peaks nor evidence of inhomogeneous cation distribution was found...

equations, which govern the flow of a compressible viscous fluid, into an inhomogeneous wave equation, thereby making a connection between fluid mechanics and...

equation In phase Inertial wave Infragravity wave Infrared gas analyzer Inhomogeneous electromagnetic wave equation Interference (wave propagation) Interferometry...

current accepted idea of dark energy, inhomogeneous-cosmology models propose that the universe is much more inhomogeneous than currently assumed — for example...

possible to make x t {\displaystyle x_{t}} evolve according to the simple inhomogeneous first-order linear difference equation x t + 1 = ( d − η c η c + a )...

results of Planck data analysis confirming those of WMAP, including the inhomogeneous sky distribution of those structures. In a 2018 paper authors Daniel...

on electromagnetic ground wave propagation 1966 Illumination of an inhomogeneous spherical earth by an LF plane electromagnetic wave 1972 Effect of edge...

nonzero solution, then its solution space is finite-dimensional, and the inhomogeneous equation is solvable only for those f {\displaystyle f} satisfying finitely...

of an initial outward explosion of matter. Milne's model assumes an inhomogeneous density function which is Lorentz Invariant (around the event t=x=y=z=0)...

ISBN 0-521-55001-7 Wigner, E. P. (1939). "On unitary representations of the inhomogeneous Lorentz group". Annals of Mathematics. 40 (1): 149–204. Bibcode:1939AnMat...

is an age-dependent branching process driven by immigration from an inhomogeneous Poisson process. The process, named after Alan G. Hawkes, is also called...

original on 25 September 2005. Cornille, P. (1990). "On the propagation of inhomogeneous waves". Journal of Physics D: Applied Physics. 23 (2): 129–135. Bibcode:1990JPhD...

polynomials Bernoulli map Bernoulli operator Hidden Bernoulli model Time-inhomogeneous hidden Bernoulli model Bernoulli sampling Bernoulli distribution Continuous...

)=\lambda ^{n}+a_{1}\lambda ^{n-1}+\dotsb +a_{n-1}\lambda +a_{n}\,} The inhomogeneous case can be easily solved if the input function r is also of the form...

ISBN 978-0-387-87867-6. Wigner, E. P. (1939), "On unitary representations of the inhomogeneous Lorentz group", Annals of Mathematics, 40 (1): 149–204, Bibcode:1939AnMat...

characteristics in the outcome. These few identifications are known as inhomogeneous (i.e. differing eye and hair colours as well as divergent eyebrows in...

of Waves and Materials. Bouzdine contributed into the theory of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase in the superconducting state...

the signal processing method to compensate for the nonspherical and inhomogeneous nature of cell nuclei. This early system required up to 40 minutes to...

transition). However, it was realised that this procedure would create a very inhomogeneous Universe on the large scales, contrary to what we observe. The theory...

Stern-Gerlach experiment reported quantized results for silver atoms in an inhomogeneous magnetic field. The confirmation would turn out to be premature: more...

surrounding the nucleus violate cubic symmetry and therefore generate an inhomogeneous electric field at the position of the nucleus. EFGs are highly sensitive...

research on axially symmetric jet flows and propagation of fluids in inhomogeneous porous media. More recently, he has studied the mathematical theory...

or using the averaged Lagrangian approach for wave propagation in inhomogeneous media. Luke's Lagrangian formulation can also be recast into a Hamiltonian...

of stresses may be due to geometric constraints in the electrode or inhomogeneous plating of the ion. This phenomenon is very concerning as it may lead...

1103/PhysRevA.45.101. PMID 9906704. Hohenberg, P.; Kohn, W. (1964). "Inhomogeneous Electron Gas". Physical Review. 136 (3B): B864. Bibcode:1964PhRv..136...

relativistic red-shift effects. This makes the Unruh temperature spatially inhomogeneous across the uniformly accelerated frame. In special relativity, an observer...

including the current version of the ΛCDM model, or is the universe inhomogeneous or anisotropic? Is the CMB dipole purely kinematic, or does it signal...

Figure 2. Oblique interaction of KdV solitons in a weakly inhomogeneous medium. The evolution of transverse perturbations of finite length and amplitude...

the schlieren (shadows) or slight variations in optical properties in inhomogeneous solutions. This method combined with the theoretical and experimental...

are possible. The fuel mixes with the ambient air in a way that an inhomogeneous mixture reaches the flame, e.g., the blobs of fuel-and-air that reach...

"Using Aumann-Shapley Values to Allocate Insurance Risk: The Case of Inhomogeneous Losses," North American Actuarial Journal, 11, 3, 113-127. See http://www...

strings. New Journal of Physics (2008) H. Alnes, M. Amarzguioui, An inhomogeneous alternative to dark energy? Phys. Rev. D 73 083519 (2006) Ø. Grøn and...

transitions in the Shpolskii systems exhibit narrow lines instead of the inhomogeneously broadened features normally associated with spectra of chromophores...

proposed a method for the production of population inversion using inhomogeneous electric and magnetic fields. Their results were presented at a national...

R. (1981-01-01). "Variational principles for dynamic problems for inhomogeneous elastic media". Wave Motion. 3 (1): 1–11. doi:10.1016/0165-2125(81)90008-1...

dynamics and V-states for 2D flows; vortex projectiles for accelerated inhomogeneous flows; and visiometrics for reduced modeling.” 1986: Potts Medal of...

of this type govern the physics of inhomogeneous or heterogeneous materials. Of course, all matter is inhomogeneous at some scale, but frequently it is...

of atherosclerotic plaques in a part of the arterial endothelium is inhomogeneous. The multiple and focal development of atherosclerotic changes is similar...

and semiconductors and experiments probing the excitation spectra of inhomogeneously magnetized systems, particularly magnetic vortices." "Paul Crowell"...

instability, Contemp. Math. 255 (2000), 189-198, with J. Shatah. An inhomogeneous boundary value problem for nonlinear Schrodinger equations, J. Diff...

propagates at an angle to the direction of the wavefront in air. In an inhomogeneous medium with a variable index of refraction, different parts of the wavefront...

Inge Schmitz-Feuerhake Inglis–Teller equation Ingrid Daubechies Inhomogeneous Inhomogeneous electromagnetic wave equation Initial mass function Initial singularity...

results in nonuniform solar illumination across the line of sight and inhomogeneous irradiance of the atmosphere at once. Thick clouds determine a perfect...

1985) or isolated mid-shelf bars (La Fon 1981). Mainly due to the inhomogeneous nature of shoreline deposits, lateral variation is intense throughout...

(help). Wigner, Eugene P. (1939), "On unitary representations of the inhomogeneous Lorentz group", Annals of Mathematics, 40 (1): 149–204, Bibcode:1939AnMat...

entropy of inhomogeneous systems is the sum of the entropies of the various subsystems. The laws of thermodynamics hold rigorously for inhomogeneous systems...

counteract the slowing process. The required form of the spatially inhomogeneous magnetic field as we showed above has the form B ( z ) = B 0 + B a 1...

1981 with J. D. Louck: Biedenharn, L. C.; Louck, J. D. (Feb 1990). "Inhomogeneous basis set of symmetric polynomials defined by tableaux". Proc Natl Acad...

Don; Wu, Chai Wah (2008-12-01). "Conditions for weak ergodicity of inhomogeneous Markov chains". Statistics & Probability Letters. 78 (17): 3082–3085...

to solve. Cramer's rule is used to derive the general solution to an inhomogeneous linear differential equation by the method of variation of parameters...

Mukhamedov, Farrukh (2024). "Nonlinear Stochastic Operators and Associated Inhomogeneous Entangled Quantum Markov Chains". Journal of Nonlinear Mathematical...

most important are: Combination of the current density and spatially inhomogeneous resistance Ionization of species within the dielectric to form heterocharge...

polymer segments under mechanical stress. Crazing involves a localized or inhomogeneous plastic strain of the material. However, while plastic deformation essentially...

heat flows from the hotter body to the colder. If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence,...

the theory of partial differential equations, the theory of strongly inhomogeneous elastic media, and the mathematical theory of boundary layers. She was...

setup contains 3 parts: an inhomogeneous magnetic field in front, the rotating field at the middle, and another inhomogeneous magnetic field at the end...

problem, SoC architectures are usually heterogeneous, creating spatially inhomogeneous heat fluxes, which cannot be effectively mitigated by uniform passive...

the defining integral and integrating by parts gives the first-order inhomogeneous differential equation G ′ ( z ) + 2 z G ( z ) = π − 1 z . {\displaystyle...

Academic, New York. Mandelstam, L.I. (1926). "Light Scattering by Inhomogeneous Media". Zh. Russ. Fiz-Khim. Ova. 58: 381. van de Hulst, H.C. (1981)...

a lower surface tension than water. If alcohol is mixed with water inhomogeneously, a region with a lower concentration of alcohol will pull on the surrounding...

k q z {\displaystyle q=q_{w}+iq_{x}+jq_{y}+kq_{z}} is given by the inhomogeneous expression: R = [ 1 − 2 ( q y 2 + q z 2 ) 2 ( q x q y − q w q z ) 2...

solution of the inhomogeneous equation is the sum of the solution of the homogeneous equation with a particular solution of the inhomogeneous equation | ψ...

1441M. Mikeyev, S.P; Smirnov, A.Yu (1987). "Neutrino Oscillations in an Inhomogeneous Medium: Adiabatic Regime". Zh. Eksp. Teor. Fiz. 92: 404. Bibcode:1987ZhETF...

applies to the more general class of synchronous automata networks (inhomogeneous networks of automata over directed graphs, allowing external inputs...

"waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g., a photonic crystal), whether or not the waves are confined...

is the kernel of α, because the difference of two solutions of the inhomogeneous equation α(x) = c lies in the kernel. An analogous construction applies...

the observations using sliding or Kelvin probe force microscope of inhomogeneous charge variations between nominally identical materials. The details...

T>0} , and giving off heat, Q < 0 {\displaystyle Q<0} . Others are inhomogeneous systems that do not meet the strict definition of thermodynamic equilibrium...

do not in general coincide with each other, the wave is said to be inhomogeneous. The refracted wave is exponentially attenuated, with exponent proportional...

processes should be taken into account during the investigation of inhomogeneous materials like suspensions or colloids, biological materials, phase...

dy}{z-\zeta }}.} One may use this representation formula to solve the inhomogeneous Cauchy–Riemann equations in ⁠ D {\displaystyle D} ⁠. Indeed, if φ {\displaystyle...

R. (1981-01-01). "Variational principles for dynamic problems for inhomogeneous elastic media". Wave Motion. 3 (1): 1–11. Bibcode:1981WaMot...3....1W...

to study the Lagrangian dynamics of slowly-varying wave trains in an inhomogeneous (moving) medium. The method is applicable to both linear and non-linear...

homogeneous powder layers" though "equation systems for combination of inhomogeneous layers cannot be solved for the scattering and absorbing properties...

{dc(x)}{dx}}-v(x)c(x)=-\int _{x}R(x')dx'} Where D is not zero, this is an inhomogeneous first-order linear differential equation with variable coefficients...

few hundred meters. Compared to typical igneous rocks they are rather inhomogeneous and may show zones with different mineral assemblages. Crystal size...

force is a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field. It causes the particle to move towards...

completing her Ph.D. in 2005. Her dissertation, Magnetoresistance of inhomogeneous semiconductors, and, ultracold atomic Fermi gases, was supervised by...

planets difficult, and the stars are frequently active with flares and inhomogeneous stellar surfaces (faculae and starspots), which can produce erroneous...

either the Bochner–Martinelli–Koppelman formula or the solution of the inhomogeneous Cauchy–Riemann equations with compact support. The latter approach is...

\end{aligned}}} The Taylor scraping flow is similar to this problem but driven inhomogeneous boundary condition. The solution is obtained by the eigenfunction expansion...

(density-functional perturbation theory). Hohenberg, P.; Kohn, W. (1964). "Inhomogeneous Electron Gas". Physical Review. 136 (3B): B864. Bibcode:1964PhRv..136...

definite. It is needed to make the right-hand side operator elliptic. For inhomogeneous anisotropic media these two forms of the diffusion equation should be...

Lagrangian optics and Hamiltonian optics. The wave equation for an inhomogeneous medium is u t t = c 2 ∇ ⋅ ∇ u , {\displaystyle u_{tt}=c^{2}\nabla \cdot...

constants of the material with rough sample surface or presence of inhomogeneous media. New methodological approaches allow the use of reflection ellipsometry...

ice-wedges producing thawing; erosion from fluvial channels causing inhomogeneous sediments. Before complete drainage, lake edges recede through retrogressive...

Gulyaev YV, Krylov VV, Plessky VP (1995). Surface Acoustic Waves in Inhomogeneous Media. Heidelberg: Springer. ISBN 978-3-540-58460-5. Crocker MJ, ed...

consider an ensemble of spins in a magnetic field that is sufficiently inhomogeneous to completely dephase the spins in the interval between the pulses....

may differ from that of D (or B). Even in isotropic media, so-called inhomogeneous waves can be launched into a medium whose refractive index has a significant...

along the cross-section of vertical reinforced concrete elements is inhomogeneous. The reinforcement in an RC structure, such as a steel bar, has to undergo...

an inhomogeneous magnetic field, and being deflected up or down depending on their spin; (1) furnace, (2) beam of silver atoms, (3) inhomogeneous magnetic...

9734. Conduit, G. J.; Green, A. G.; Simons, B. D. (9 November 2009). "Inhomogeneous Phase Formation on the Border of Itinerant Ferromagnetism". Physical...

20, 2009. Holdren, John Paul (1970). Collisionless Stability of an Inhomogeneous, Confined, Planar Plasma (PhD thesis). Stanford University. OCLC 25848776...

By modifying the scattering matrix S {\displaystyle {\textbf {S}}} inhomogeneous and lossy materials can be modelled. By adjusting the connection equations...

ultrasound technique for detection of weak and local changes in complex inhomogeneous media. Sound waves that travel through a medium are scattered multiple...

reduction to binary tasks. It is a type of kernel machine that uses an inhomogeneous polynomial kernel. Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome...

distribution of gas holdup in the fully developed flow regime. The inhomogeneous MUSIG model gives a little better result than other models in the prediction...

include dynamic fragmentation; shear dominated intersonic rupture of inhomogeneous materials and composites, rupture mechanics of crustal earthquakes,...

different metals and their junction region. The junction region is an inhomogeneous body, assumed to be stable, not suffering amalgamation by diffusion...

two-particle irreducible Green functions, which is nowadays referred to as the inhomogeneous Bethe–Salpeter equation. Given a polynomially bounded functional F {\displaystyle...

members per household is 2.71. The population in this village is very inhomogeneous and the last three censuses registered a decline in the population....

Ming-Chung; Hung, Yao-Chen; Jiang, I-Min (2004). "Phase synchronization in inhomogeneous globally coupled map lattices" (PDF). Physics Letters A. 324 (5–6)....

or building. By means of a thermographic camera thermal bridges and inhomogeneous insulation parts can be identified. However, it does not produce any...

In practice there may also be broadening of the line shape due to inhomogeneous broadening, most notably due to the Doppler effect resulting from the...

Scanner LA-UR-93-1637, Tomographic gamma scanning (TGS) to measure inhomogeneous nuclear material matrices from future fuel cycles, LANL, 1993 "H100...

Retrieved 2018-09-21. Mandelstam, L.I. (1926). "Light Scattering by Inhomogeneous Media". Zh. Russ. Fiz-Khim. Ova. 58: 381. Archibald, P.S. and Bennett...

in size, but with the density varying in different places (i.e. an inhomogeneous universe). Thus some regions will be over-dense (Ω > 1) and some under-dense...

distribution. In contrast, real networks are often scale-free networks inhomogeneous in degree, having hubs and a scale-free degree distribution. Such networks...

no disk can be spun up rigidly) — at least, not without sustaining inhomogeneous stresses. The easiest way to see this is to observe that in Newtonian...

{\displaystyle \lambda \varphi (x)-\int _{a}^{b}K(x,y)\varphi (y)\,dy=0} and the inhomogeneous equation λ φ ( x ) − ∫ a b K ( x , y ) φ ( y ) d y = f ( x ) . {\displaystyle...

cross-sectional problems are solved for materials with anisotropic and inhomogeneous properties. VABS, a novel finite-element-based code, for the beam cross-sectional...

characterized commercially available solid silicon monoxide materials as an inhomogeneous mixture of amorphous SiO2 and amorphous Si with some chemical bonding...

pointed out the possibility of type-II superconductors that should form inhomogeneous state in strong magnetic fields. However, at that time, all known superconductors...

and drastically improves personalized medicine. Vascular tissues are inhomogeneous with a strongly non linear behaviour. Generally this study involves...

induced by light (e.g. A→B, bright to dark). The sample is illuminated inhomogeneously with the illumination intensity at one position being very small (zero...

cosmology, but is not related to the Standard Model of particle physics. Inhomogeneous cosmology Deruelle, Nathalie; Uzan, Jean-Philippe (2018-08-30). de Forcrand-Millard...

the kiln are often amplified during the sintering process, yielding inhomogeneous densification. Some pores and other structural defects associated with...

dissertation was entitled "Electromagnetic Scattering from Certain Radially Inhomogeneous Dielectrics." Nicolaos Alexopoulos's late brother, Aristides Georgiou...

well-defined mass, with variable sizes, usually single, solid consistency with inhomogeneous structure. Rarely the central scar can be distinguished. Spectral Doppler...

Soper, A. K.; Teixeira, J; Head-Gordon, T (2010). "Is ambient water inhomogeneous on the nanometer-length scale?". Proceedings of the National Academy...

scattered in space with random jet orientations will look like a very inhomogeneous population on Earth. The few objects where θ is small will have one...

t^{2}}}\mathbf {P} ^{\text{NL}}.} The nonlinear wave equation is an inhomogeneous differential equation. The general solution comes from the study of...

Barahona M, Buzsáki G, Koch C (February 2010). "The effect of spatially inhomogeneous extracellular electric fields on neurons". J. Neurosci. 30 (5): 1925–36...

Vol. 158, No. 2, pp. 462–475 (1967). APS P. Hohenberg, and W. Kohn, "Inhomogeneous Electron Gas," Physical Review, Vol. 136, No. 3B, pp. B864–B871 (1964)...

2017. Her dissertation, Scalar Fields in Numerical General Relativity: Inhomogeneous Inflation and Asymmetric Bubble Collapse, was supervised by Eugene A...

Y. (2006). "A recursion formula for the correlation functions of an inhomogeneous XXX model". St. Petersburg Mathematical Journal. 17: 85–117. arXiv:hep-th/0405044...

Chen, The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations, Boundary Elements Communications. 5...

did extensive work in the study of optical propagation in a randomly inhomogeneous atmosphere and the consequent effects on optical system performance...

Inhomogeneous structures on stellar surfaces, i.e. temperature differences, chemical composition or magnetic fields, create characteristic distortions...

result is called the total Hamiltonian. The uk must solve a set of inhomogeneous linear equations of the form { ϕ j , H } P B + ∑ k u k { ϕ j , ϕ k }...

simplest semilinear reaction-diffusion equations, the one which has the inhomogeneous term f ( u , x , t ) = r u ( 1 − u ) , {\displaystyle f(u,x,t)=ru(1-u)...

ferroelectricity is also caused by inhomogeneous magnetoelectric interaction. This effect appears due to the coupling between inhomogeneous order parameters. It was...

alkaloids content in plants is usually within a few percent and is inhomogeneous over the plant tissues. Depending on the type of plants, the maximum...

Tang; Van To, Tan (2006). "Using generating functions to solve linear inhomogeneous recurrence equations" (PDF). Proc. Int. Conf. Simulation, Modelling...

isomeric state: the shorter the lifetime, the more broadened the line. Inhomogeneous broadening comprises all mechanisms by which the homogeneously broadened...

dispersion medium, and possibly colloid stabilizer constitute initially an inhomogeneous system resulting in particles of colloidal dimensions containing the...

different speeds, the material has a local electric charge, inducing an inhomogeneous electric field which can be calculated with Gauss's law: ∂ E ∂ x = ρ...

doi:10.1086/143448. Israelian, G.; Chentsov, E.; Musaev, F. (1997). "The inhomogeneous circumstellar envelope of Rigel (β Orionis A)". Monthly Notices of the...

points x k {\displaystyle x_{k}} are the abscissas. Applying this to the inhomogeneous Fredholm equation of the second kind f ( x ) = λ u ( x ) − ∫ a b K (...

buffers and solvents and also because of the scattering exhibited by inhomogeneous samples in this region. Several other advantages are associated with...

equivalent way of expressing this is that x* is a particular solution to the inhomogeneous equation, while all solutions are in the form x h + x ∗   , {\displaystyle...

2 January 2014. Demory, Brice-Olivier; et al. (2013). "Inference of Inhomogeneous Clouds in an Exoplanet Atmosphere". The Astrophysical Journal Letters...

engineering Institutions Academia Sinica Thesis Reflection of electromagnetic waves from inhomogeneous plasma (1965) Doctoral advisor Lewis B. Wetzel...

radicals, furthermore, control oxidative stress in biological media under inhomogeneous electromagnetic radiation. The magnetic nanotherapy is remotely controlled...

model, or is the universe inhomogeneous or anisotropic? More unsolved problems in physics Although the universe is inhomogeneous at smaller scales, according...

compounds such as tungsten carbide were used in small quantities of inhomogeneous and discarded sabot round, but that element was in short supply in most...

first matter condensed, the radiation traveled away, leaving a slightly inhomogeneous dark matter subject to gravitational interaction. The interaction eventually...

& Jay Baltisberger, "METHOD AND INSTALLATION FOR MULTI-DIMENSIONAL INHOMOGENEOUS-FIELD MAGNETIC RESONANCE IMAGING", issued 14 October 2004  US Patent...

University "Correlation between nanostructures and transport properties in inhomogeneous condensed systems." 2025 Takamasa Sakai (酒井 崇匡) University of Tokyo...

theoretical physics, of finding the averaged Green's function of an inhomogeneous (or disordered) system. The Green's function obtained via the CPA then...

generally produced a very hard steel, but also a composite steel that was inhomogeneous, consisting of a very high-carbon steel (formerly the pig-iron) and...

Oceanus Procellarum. Procellarum may have also been formed by spatially inhomogeneous heating during the Moon's formation. The GRAIL mission, which mapped...

definition of the homogeneous Poisson process extend to the case of the inhomogeneous (or non-homogeneous) Poisson process, which is a non-stationary stochastic...

average momentum and q the charge of the electrons. This, which is an inhomogeneous differential equation, may be solved to obtain the general solution...

expected for desert conditions where infrequent rain tends to produce inhomogeneous concentration of salts near the surface. While on average only 0.2 to...

Tsuji, Hiroshi; Niwa, Kimio (2007). "High resolution imaging in the inhomogeneous crust with cosmic-ray muon radiography: The density structure below...

non-linearity can be modeled by a convex function. Krylov (1982). "Boundedly inhomogeneous elliptic and parabolic equations". Izvestiya Akad. Nauk SSSR, Ser. Mat...

Jonathan P.; Bowden, Charles M. (1 July 1992). "Atomic emission rates in inhomogeneous media with applications to photonic band structures". Physical Review...

ISSN 0072-5285 Wigner, E. P. (1939), "On unitary representations of the inhomogeneous Lorentz group", Annals of Mathematics, 40 (1): 149–204, Bibcode:1939AnMat...

discontinuities. The AMR/ART method is well suited to model the increasingly inhomogeneous distribution of matter that evolves as the simulation proceeds. “Once...

Stokes drift may occur in all instances of oscillatory flow which are inhomogeneous in space. For instance in water waves, tides and atmospheric waves....

Červený, V. (July 2002). "Fermat's Variational Principle for Anisotropic Inhomogeneous Media". Studia Geophysica et Geodaetica. 46 (3): 567. Bibcode:2002StGG...

"Programmable Quantum Matter: Heralding Large Cluster States in Driven Inhomogeneous Spin Ensembles | PRX Quantum". Archived from the original on 2026-07-28...

the scalar multiplication operator on a vector space or affine space Inhomogeneous dilation, where scale factors may differ in different directions Dilation...

Chamard; O. Thomas (2007). "Inversion of the diffraction pattern from an inhomogeneously strained crystal using an iterative algorithm". Phys. Rev. B. 76 (10)...

zero everywhere then the linear PDE is homogeneous, otherwise it is inhomogeneous. (This is separate from asymptotic homogenization, which studies the...

Pannullo, L.; Lenz, J.; Wagner, M.; Wellegehausen, B.; Wipf, A. (2020). "Inhomogeneous phases in the 1+1 dimensional Gross-Neveu model at finite number of...

Raderschall, N. (July 2008). "Inhomogeneous precipitation distribution and snow transport in steep terrain: SNOW DRIFT AND INHOMOGENEOUS PRECIPITATION". Water...

(2007) describe it as a chemically peculiar He-variable star, having inhomogeneous distributions of chemical elements across its surface. It has a variable...

flows and dynamics of moving contact lines, statistical mechanics of inhomogeneous liquids, and coarse graining of complex multiscale systems." 2010–2016...

molten metal, the thermal fluid dynamics of the system often produces inhomogeneous compositions or unintended porosity which can cumulatively affect the...

cosmological perturbation theory is subtle. In particular, when describing an inhomogeneous spacetime, there are often no preferred coordinate choices. There are...

Emilsson, K., & Oppo, G.-L. Dynamics of spiral waves in a spatially inhomogeneous Hopf bifurcation. Physical Review A, 45(2), R567-R470 (1992). https://doi...

Schematic of the plate theory. Mid-blue: lithosphere; light-blue/green: inhomogeneous upper mantle; yellow: lower mantle; orange/red: core-mantle boundary...

continuous medium has smoothly varying density, such as in the case of an inhomogeneous colloidal suspension. In general isopycnic surfaces will occur in fluids...

processes used to mix LiF sintering aid into a powder leave fairly inhomogeneous distribution of Lif that must be homogenized by extended heat treatment...

αn are linearly dependent over the rationals. Baker (1967b) gave an inhomogeneous version of the theorem, showing that β 0 + β 1 log ⁡ α 1 + ⋯ + β n log...

{R} ^{n}} , consider the problem of solving Poisson's equation with inhomogeneous Dirichlet boundary conditions: − Δ u = f in  Ω , u = g on  ∂ Ω {\displaystyle...

along with Gian Luigi Forti, also found the solutions to the following inhomogeneous Cauchy functional equation in a Banach space E {\displaystyle E} : f...

value due to a low current efficiency and non-electrolytic consumption. Inhomogeneous anode quality due to the variation in raw materials and production parameters...

a thermodynamic system. We consider systems which, in general, are inhomogeneous. Heat and mass are transferred across the boundaries (nonadiabatic,...

are strictly ordered and called the temporal support of the history. Inhomogeneous histories are multiple-time propositions which cannot be represented...

an inhomogeneous superconducting state, most probably the FFLO state. Casalbuoni, Roberto; Nardulli, Giuseppe (26 February 2004). "Inhomogeneous superconductivity...

structure formation in the Okiep Copper District, South Africa: bulk inhomogeneous shortening of a high-grade metamorphic granite-gneiss sequence". Journal...

Genealogy Project Holdren, John Paul (1970). Collisionless Stability of an Inhomogeneous, Confied, Planar Plasma (PhD thesis). Stanford University. ProQuest 302557782...

ISBN 978-0-19-852957-6. Modern introduction to cosmology covering the homogeneous and inhomogeneous universe as well as inflation and the CMB. Dodelson, Scott (2003). Modern...

Illinois Urbana-Champaign Thesis Propagation of low-coherence fields in inhomogeneous media (2002) Doctoral advisor Aristide Dogariu Other academic advisors...

(the inverse conductivity problem). Because the human head is highly inhomogeneous and composed of multiple layers with different conductivities, the inverse...

interest is in acoustic and ultrasonic wave propagation and scattering in inhomogeneous materials, including composite materials and biological tissues. There...

whether a meaningful local helicity density can be defined in weakly inhomogeneous turbulence, leading to proposed gauge-invariant local measures and improved...

asymptotic evaluation of the Sommerfeld integrals used to solve the inhomogeneous wave equation for a point or line source near a plane interface separating...

^{1/2}Y_{1/2}^{l}+\cdots } . The O ( 1 ) {\displaystyle {\mathcal {O}}(1)} inhomogeneous condition on the left provides us the reason to start the expansion...

the kiln are often amplified during the sintering process, yielding inhomogeneous densification. Some pores and other structural defects associated with...

regions come in an enormous variety of sizes. They are usually clumpy and inhomogeneous on all scales from the smallest to largest. Each star within an H II...

notation for partial derivatives has been employed. The more general inhomogeneous case: y t + A ( y ) y x = s {\displaystyle y_{t}+A(y)y_{x}=s} is not...

resistance. This creep resistance is attributed to the formation of inhomogeneous precipitate Cr4.6MoNi2.1, which pins dislocations and prevents further...

1103/PhysRevLett.77.3865 Hohenberg, P.; Kohn, W. (9 November 1964). "Inhomogeneous Electron Gas". Physical Review. 136 (3B): B864–B871. Bibcode:1964PhRv...

slag (a liquid waste product). African ironworkers regularly produced inhomogeneous steel blooms, especially in the large natural-draft furnaces. The blooms...

and Merritt & Hernquist found a similar result in an N-body study of inhomogeneous prolate spheroids (Fig. 1). The discrepancy was resolved in 1994. The...

are homogeneous however it is possible to apply it to problems with inhomogeneous boundary conditions by letting u ( x ) = v ( x ) + L ( x ) {\displaystyle...

volume element (RVE). An RVE is understood to be a sub-volume of an inhomogeneous medium that is of sufficient size for providing all geometrical information...

(polarization) and other properties of radio waves propagating in an inhomogeneous, magnetized, collisional plasma. Thidé was involved in a project in...

(2013). "Causality and non-equilibrium second-order phase transitions in inhomogeneous systems". J. Phys.: Condens. Matter. 25 (40) 404210. arXiv:1302.3648...

08033. doi:10.5802/aif.3216. MR 3897974. Komatsu, Takao (1998). "On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm"...

of light) during early moments of the Big Bang. His recent work on inhomogeneous cosmological models purports to explain certain anomalous effects in...

1017/pasa.2025.10025. "The Astrophysical Journal". Evidence for a Dense, Inhomogeneous Circumstellar Medium in the Type Ia SNR 0519-69.0. Retrieved 24 May...

century. This was the "berganesque" method that produced inferior, inhomogeneous steel, while the other was a precursor to the modern Bessemer process...

Thomas–Fermi Theory". In S. Lundqvist; N. H. March (eds.). Theory of The Inhomogeneous Electron Gas. Plenum Press. ISBN 978-0-306-41207-3. Feynman, R. P.;...

1 {\displaystyle d=1} , this becomes the linear kernel. Polynomial (inhomogeneous): k ( x i , x j ) = ( x i ⋅ x j + r ) d {\displaystyle k(\mathbf {x}...

Y.V.; Krylov, V.V.; Plessky, V.P. (1995). Surface Acoustic Waves in Inhomogeneous Media. Springer. ISBN 978-3-642-57767-3. O'Connell-Rodwell, C.E.; Arnason...

{id} _{G}} ). This is an abelian group; its elements are called the (inhomogeneous) n-cochains. The coboundary homomorphisms are defined by { d n + 1 :...

This approach provides a material-specific framework for describing inhomogeneous superconductors and heterostructures directly from first principles...

Atmosphere-Dominated Hot Jupiter Kepler Phase Curves: Evidence That Inhomogeneous Atmospheric Reflection is Common", The Astronomical Journal, 150 (4):...

homogeneous distribution, pharmacologists should reckon with a very inhomogeneous distribution of catecholamines in the extracellular space, low in the...

"Deterministic spontaneous appearance of traffic jams in slightly inhomogeneous traffic flow". Physical Review E. 51 (6): 6243–6246. Bibcode:1995PhRvE...

p. 26. Bretherton, F. P.; Garrett, C. J. R. (1968). "Wavetrains in inhomogeneous moving media". Proceedings of the Royal Society of London, Series A...

samarium in soils strongly depends on its chemical state and is very inhomogeneous: in sandy soils, samarium concentration is about 200 times higher at...

J.; Hubbard, William B. (2003). "Phase separation in giant planets: inhomogeneous evolution of Saturn". Icarus. 164 (1): 228–243. arXiv:astro-ph/0305031...

the atoms were guided into a flat beam and the beam sent through an inhomogeneous magnetic field before colliding with a metallic plate. The laws of classical...

1007/s00466-012-0728-4. S2CID 95958719. Hohenberg, Pierre; Walter, Kohn (1964). "Inhomogeneous electron gas". Physical Review. 136 (3B): B864–B871. Bibcode:1964PhRv...

are satisfied and the particle can be treated as a point dipole in an inhomogeneous electromagnetic field. The force applied on a single charge in an electromagnetic...

George Francis FitzGerald.) The Lorenz gauge leads to the following inhomogeneous wave equations for the potentials: 1 c 2 ∂ 2 φ ∂ t 2 − ∇ 2 φ = ρ ε 0...

of interest both in compressible fluids and in incompressible (but inhomogeneous) fluids. Internal gravity waves as well as unstable Rayleigh–Taylor...

melting of recycled oceanic crust with pyroxenite lithologies within an inhomogeneous plume head, and pooling and eruption of the melts as large basaltic...

Khimicheva. Methods and devices for measuring the Peltier coefficient of an inhomogeneous electric circuit. Measurement Techniques July 1997, Volume 40, Issue...

to the basic method to allow some of these other cases to be solved: inhomogeneous aquifer: matching conditions at boundaries between properties anisotropic...

California, supervised by Burton D. Fried, titled Resonant Absorption In An Inhomogeneous, Unmagnetized Plasma. In 2007 she became a Fellow of the American Physical...

models at that time were able to explain). Latham's hypothesis of “inhomogeneous mixing” involved discrete segments of dry air being transported into...

with r. And in the source itself, or as soon as one enters a region of inhomogeneous materials, the multipole expansion is no longer valid and the full solution...

Weeks, Eric R.; Gisler, T.; et al. (2000). "Two-Point Microrheology of Inhomogeneous Soft Materials". Physical Review Letters. 85 (4): 888–891. Bibcode:2000PhRvL...

The reason is that newly-formed fraternities are understood to be inhomogeneous; they first must debate and decide to re-join the Blaues Kartell internally...

in a uniform ordinary superconductor, but it becomes possible in an inhomogeneous system, for example, if a vortex is placed on a boundary between two...

{c_{p}\,c_{g}}},} the mild slope equation can be cast in the form of an inhomogeneous Helmholtz equation: Δ ψ + k c 2 ψ = 0 with k c 2 = k 2 − Δ ( c p c g...

salinity (30‰). The depth distribution of water temperature is very inhomogeneous across the sea. For example, at the exit from Dvina Bay, water temperature...

system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some intensive variables. For example, a relatively...

these buildings collapsed because their foundations were resting on inhomogeneous ground, made of rocks and earth filling. The earth filling slipped with...

electric fields, and particularly the pseudo potential derived from the inhomogeneous electric fields resulting from rf of appropriate frequency applied to...

{\displaystyle K_{\mathrm {OvrlSld} }} is the "Overall" bulk modulus of the inhomogeneous, anisotropic solid, a quantity which depends on its microgeometry as...

field; liquid crystals; Lifshitz points; composites constructed from inhomogeneous distributions of ingredients; and calculating the elasticity of composite...

as conglomerates and laminates) are based upon approximation of an inhomogeneous material by a homogeneous effective medium (valid for excitations with...

{\displaystyle f} . Poisson hidden Markov model Doubly stochastic model Inhomogeneous Poisson process, where λ(t) is restricted to a deterministic function...

publications include the books The Theory of the Optical Properties of Inhomogeneous Materials. London: E. and F.N. Spon Ltd, (1963) and The Principles of...

2021.113813. S2CID 224818337. Lumley, J.L. (1967). The Structure of Inhomogeneous Turbulence," In: A. M. Yaglom and V. I. Tatarski, Eds., Atmospheric...

from scattering data or spectral function. Inverse problems for an inhomogeneous Schrödinger equation are studied for the first time, a non-over-determined...

generalization of the former case); a prism; and a Dove prism Examples of inhomogeneous METATOYs include the moiré magnifier, which is based on deliberately...

lines with the set of circles to form a set of blocks results in an inhomogeneous incidence structure: three distinct points determine one block, but...

from an aeroacoustic source or the propagation of sound waves in an inhomogeneous flow field. Such numerical methods can be far field integration methods...

A linear differential equation that fails this condition is called inhomogeneous. A linear differential equation can be represented as a linear operator...

1093/imamat/1.1.1 Bretherton, F. P.; Garrett, C. J. R. (1968), "Wavetrains in inhomogeneous moving media", Proceedings of the Royal Society of London, Series A...

is therefore insensitive to the Stark shift that could result from inhomogeneous electric fields within the diamond lattice. This property, together...

position to do so. The dopaminergic ensemble is thus also on this point inhomogeneous. This is another major difference with the pallidonigral ensemble. The...

worked for many decades on anisotropic cosmologies (Bianchi models) and inhomogeneous universes, and on the philosophy of cosmology. He is currently writing...

D (2006). "Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media". Physical Review Letters. 96 (16) 163905. arXiv:0712...

not an engineering strain since distribution of the deformation is inhomogeneous within the reference length. Fracture strain is nevertheless a rough...

can prove this by recognizing a symmetry of the graph y = xn under inhomogeneous dilation (by d in the x direction and dn in the y direction, algebraicizing...

published as Wärmeleitung in inhomogenen Körpern ('Thermal Conduction in Inhomogeneous Bodies') on 22 February 1906. Paul Ehrenfest asked her to investigate...

163.207. Wollan, David (1976). "Dynamic nuclear polarization with an inhomogeneously broadened ESR line. I. Theory". Physical Review B. 13 (9): 3671–3685...

c_{3}(t)\end{bmatrix}}} The above deformation becomes non-affine or inhomogeneous if F = F(X,t) or c = c(X,t). A rigid body motion is a special affine...

exponentially decaying waves. This viewpoint allows PMLs to be derived for inhomogeneous media such as waveguides, as well as for other coordinate systems and...

It also brought further possibilities of using the method, e.g., for inhomogeneous materials, coatings, etc. The measurement and evaluation procedure is...

have been unsuccessful. A few white dwarfs have been observed to have inhomogeneous atmosphere with one side dominated by hydrogen and the other side dominated...

(1974) A direct method of computation of transmission function of an inhomogeneous gaseous medium: description of the method and influence of various factors...

describe a system in which the monomer distribution and concentration are inhomogeneous, and is restricted to a small volume. Parameters determined using the...

(via the Pratt hypothesis) that the upper mantle in this region is inhomogeneous, with significant lateral variations in density. The formation of ice...

which trigonometric functions and geometric angles are avoided; the inhomogeneous waves launched into the second medium cannot be described using a single...

while Robert Remak had solved it for three variables) on the product of inhomogeneous linear forms and achieved significant progress. The complete solution...

"Application of the nonlinear Schrödinger equation with a logarithmic inhomogeneous term to nuclear physics". Physical Review A. 32 (2): 1201–1204. Bibcode:1985PhRvA...

indirectly from the subiculum). Thalamic regions may be functionally inhomogeneous. The elements of the lateral region have been frequently separated into...

carcinosarcoma heterogeneity, redox state and growth modulated by an inhomogeneous stationary magnetic field". Journal of Magnetism and Magnetic Materials...