Статті в журналах: "Green's formula"

1

Zhang, Haicheng. "Toën's formula and Green's formula." Journal of Algebra 527 (June 2019): 196–203. http://dx.doi.org/10.1016/j.jalgebra.2019.02.033.

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2

BEVERIDGE, ANDREW. "A Hitting Time Formula for the Discrete Green's Function." Combinatorics, Probability and Computing 25, no. 3 (June 29, 2015): 362–79. http://dx.doi.org/10.1017/s0963548315000152.

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The discrete Green's function (without boundary)$\mathbb{G}$is a pseudo-inverse of the combinatorial Laplace operator of a graphG= (V, E). We reveal the intimate connection between Green's function and the theory of exact stopping rules for random walks on graphs. We give an elementary formula for Green's function in terms of state-to-state hitting times of the underlying graph. Namely,$\mathbb{G}(i,j) = \pi_j \bigl( H(\pi,j) - H(i,j) \bigr),$where πiis the stationary distribution at vertexi,H(i, j) is the expected hitting time for a random walk starting from vertexito first reach vertexj, andH(π,j) = ∑k∈VπkH(k, j). This formula also holds for the digraph Laplace operator.The most important characteristics of a stopping rule are its exit frequencies, which are the expected number of exits of a given vertex before the rule halts the walk. We show that Green's function is, in fact, a matrix of exit frequencies plus a rank one matrix. In the undirected case, we derive spectral formulas for Green's function and for some mixing measures arising from stopping rules. Finally, we further explore the exit frequency matrix point of view, and discuss a natural generalization of Green's function for any distribution τ defined on the vertex set of the graph.

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3

Ruan, Shiquan. "A short proof of Green's formula." Journal of Algebra 581 (September 2021): 45–49. http://dx.doi.org/10.1016/j.jalgebra.2021.04.010.

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4

Tokmagambetov, Niyaz, and Berikbol T. Torebek. "Green's formula for integro-differential operators." Journal of Mathematical Analysis and Applications 468, no. 1 (December 2018): 473–79. http://dx.doi.org/10.1016/j.jmaa.2018.08.026.

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5

Pavlovic, Miroslav. "Green's formula and the Hardy-Stein identities." Filomat 23, no. 3 (2009): 135–53. http://dx.doi.org/10.2298/fil0903135p.

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This is a collection of some known and some new facts on the holomorphic and the harmonic version of the Hardy-Stein identity as well as on their extensions to the real and the complex ball. For example, we prove that if f is holomorphic on the unit disk D, then ??f ??Hp = ?f(0)?p + ?D?f'(z)? p-2 ?f'(z)?2(1-?z?) dA(z), (?) where Hp is the p-Hardy space, which improves a result of Yamashita [Proc. Amer. Math. Soc. 75 (1979), no. 1, 69-72]. An extension of (?) to the unit ball of Cn improves results of Beatrous an Burbea [Kodai Math. J. 8 (1985), 36-51], and of Stoll [J. London Math. Soc. (2) 48 (1993), no. 1, 126-136]. We also prove the analogous result for the harmonic Hardy spaces. The proofs of known results are shorter and more elementary then the existing ones, see Zhu [Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics, vol. 226, Springer-Verlag, New York, 2005, Ch. IV]. We correct some constants in that book and in a paper of Jevtic and Pavlovic [Publ. Inst. Math. (Beograd) (N.S.) 64(78) (1998), 36-52].

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6

Casas, Eduardo, and Luis Alberto Fernández. "A Green's formula for quasilinear elliptic operators." Journal of Mathematical Analysis and Applications 142, no. 1 (August 1989): 62–73. http://dx.doi.org/10.1016/0022-247x(89)90164-9.

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7

PARK, DAESHIK. "APPROXIMATING GREEN'S FUNCTIONS ON ℙ1 POSITIVE CHARACTERISTIC". Communications in Contemporary Mathematics 12, № 04 (серпень 2010): 537–67. http://dx.doi.org/10.1142/s0219199710003919.

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Fix a finite K-symmetric set [Formula: see text] and a K-symmetric probability vector [Formula: see text]. Let 𝔇v be a finite union of balls [Formula: see text] for some ah ∈ Kv and some [Formula: see text], where the balls 𝔅(ah, rh) are disjoint from 𝔛. Put 𝔈v := 𝔇v ∩ ℙ1(Kv). Then there exists a positive integer Nv such that for each sufficiently large integer N divisible by Nv, there are a number Rv, with [Formula: see text], and an [Formula: see text]-function fv(z) ∈ Kv(z) of degree N whose zeros form a "well-distributed" sequence in 𝔈v such that [Formula: see text] is a disjoint union of balls centered at the zeros of fv(z) and for all z ∉ 𝔇v, [Formula: see text]

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8

KIGAMI, JUN, DANIEL R. SHELDON, and ROBERT S. STRICHARTZ. "GREEN'S FUNCTIONS ON FRACTALS." Fractals 08, no. 04 (December 2000): 385–402. http://dx.doi.org/10.1142/s0218348x00000421.

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For a regular harmonic structure on a post-critically finite (p.c.f.) self-similar fractal, the Dirichlet problem for the Laplacian can be solved by integrating against an explicitly given Green's function. We give a recursive formula for computing the values of the Green's function near the diagonal, and use it to give sharp estimates for the decay of the Green's function near the boundary. We present data from computer experiments searching for the absolute maximum of the Green's function for two different examples, and we formulate two radically different conjectures for where the maximum occurs. We also investigate a local Green's function that can be used to solve an initial value problem for the Laplacian, giving an explicit formula for the case of the Sierpinski gasket. The local Green's function turns out to be unbounded, and in fact not even integrable, but because of cancelation, it is still possible to form a singular integral to solve the initial value problem if the given function satisfies a Hölder condition.

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9

Surur, Agus Miftakus, Yudi Ari Adi, and Sugiyanto Sugiyanto. "Penyelesaian Persamaan Telegraph Dan Simulasinya." Jurnal Fourier 2, no. 1 (April 1, 2013): 33. http://dx.doi.org/10.14421/fourier.2013.21.33-43.

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Equation Telegraph is one of type from wave equation. Solving of the wave equation obtainable by using Green's function with the method of boundary condition problem. This research aim to to show the process obtain;get the mathematical formula from wave equation and also know the form of solution of wave equation by using Green's function. Result of analysis indicate that the process get the mathematical formula from wave equation from applicable Green's function in equation which deal with the wave equation, that is applied in equation Telegraph. Solution started with searching public form from Green's function, hereinafter look for the solving of wave equation in Green's function. Application from the wave equation used to look for the solving of equation Telegraph. Result from equation Telegraph which have been obtained will be shown in the form of picture (knowable to simulasi) so that form of the the equation Telegraph.

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10

Zharinov, V. V. "EXTRINSIC GEOMETRY OF DIFFERENTIAL EQUATIONS AND GREEN'S FORMULA." Mathematics of the USSR-Izvestiya 35, no. 1 (February 28, 1990): 37–60. http://dx.doi.org/10.1070/im1990v035n01abeh000685.

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11

Pavlović, Miroslav, and Dragan Vukotić. "The Weak Chang-Marshall Inequality via Green's Formula." Rocky Mountain Journal of Mathematics 36, no. 5 (October 2006): 1631–36. http://dx.doi.org/10.1216/rmjm/1181069387.

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12

Bohner, Martin, and Gusein Sh Guseinov. "Line integrals and Green's formula on time scales." Journal of Mathematical Analysis and Applications 326, no. 2 (February 2007): 1124–41. http://dx.doi.org/10.1016/j.jmaa.2006.03.040.

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13

JOGLEKAR, SATISH D., and A. MISRA. "A DERIVATION OF THE CORRECT TREATMENT OF ${1\over (\eta\cdot {\lc k})^{\lc p}}$ SINGULARITIES IN AXIAL GAUGES." Modern Physics Letters A 14, no. 30 (September 28, 1999): 2083–91. http://dx.doi.org/10.1142/s0217732399002145.

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We use the earlier results on the correlations of axial gauge Green's functions and the Lorentz gauge Green's functions obtained via finite field-dependent BRS transformations to study the question of the correct treatment of [Formula: see text]-type singularities in the axial gauge boson propagator. We show how the known treatment of the [Formula: see text]-type singularity in the Lorentz-type gauges can be used to write down the axial propagator via field transformation. We examine the singularity structure of the latter and find that the axial propagator so constructed has no spurious poles, but a complex structure near [Formula: see text]. We also give the form of the much simpler propagator which can effectively replace the complicated structure near the region [Formula: see text].

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14

Roman, Svetlana. "LINEAR DIFFERENTIAL EQUATION WITH ADDITIONAL CONDITIONS AND FORMULAE FOR GREEN'S FUNCTION." Mathematical Modelling and Analysis 16, no. 3 (August 24, 2011): 401–17. http://dx.doi.org/10.3846/13926292.2011.602125.

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In this paper, we investigate the m-order linear ordinary differential equation with m linearly independent additional conditions. We have found the solution to this problem and give the formula and the existence condition of Green's function. We compare two Green's functions for two such problems with different additional conditions and apply these results to the problems with nonlocal boundary conditions.

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15

Grubb, Gerd. "Exact Green's formula for the fractional Laplacian and perturbations." MATHEMATICA SCANDINAVICA 126, no. 3 (September 3, 2020): 568–92. http://dx.doi.org/10.7146/math.scand.a-120889.

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Let Ω be an open, smooth, bounded subset of $ \mathbb{R}^n $. In connection with the fractional Laplacian $(-\Delta )^a$ ($a>0$), and more generally for a $2a$-order classical pseudodifferential operator (ψdo) $P$ with even symbol, one can define the Dirichlet value $\gamma _0^{a-1}u$, resp. Neumann value $\gamma _1^{a-1}u$ of $u(x)$, as the trace, resp. normal derivative, of $u/d^{a-1}$ on $\partial \Omega $, where $d(x)$ is the distance from $x\in \Omega $ to $\partial \Omega $; they define well-posed boundary value problems for $P$. A Green's formula was shown in a preceding paper, containing a generally nonlocal term $(B\gamma _0^{a-1}u,\gamma _0^{a-1}v)_{\partial \Omega }$, where $B$ is a first-order ψdo on $\partial \Omega $. Presently, we determine $B$ from $L$ in the case $P=L^a$, where $L$ is a strongly elliptic second-order differential operator. A particular result is that $B=0$ when $L=-\Delta $, and that $B$ is multiplication by a function (is local) when $L$ equals $-\Delta $ plus a first-order term. In cases of more general $L$, $B$ can be nonlocal.

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16

Seremet, Victor, Guy Bonnet, and Tatiana Speianu. "New Poisson's Type Integral Formula for Thermoelastic Half-Space." Mathematical Problems in Engineering 2009 (2009): 1–18. http://dx.doi.org/10.1155/2009/284380.

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A new Green's function and a new Poisson's type integral formula for a boundary value problem (BVP) in thermoelasticity for a half-space with mixed boundary conditions are derived. The thermoelastic displacements are generated by a heat source, applied in the inner points of the half-space and by temperature, and prescribed on its boundary. All results are obtained in closed forms that are formulated in a special theorem. A closed form solution for a particular BVP of thermoelasticity for a half-space also is included. The main difficulties to obtain these results are in deriving of functions of influence of a unit concentrated force onto elastic volume dilatation and, also, in calculating of a volume integral of the product of function and Green's function in heat conduction. Using the proposed approach, it is possible to extend the obtained results not only for any canonical Cartesian domain, but also for any orthogonal one.

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17

Chinram, Ronnason. "REGULARITY AND GREEN'S RELATIONS OF GENERALIZED PARTIAL TRANSFORMATION SEMIGROUPS." Asian-European Journal of Mathematics 01, no. 03 (September 2008): 295–302. http://dx.doi.org/10.1142/s1793557108000266.

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Let X be any set and P(X) be the partial transformation semigroup on X. It is well-known that P(X) is regular. To generalize this, let X and Y be any sets and P(X, Y) be the set of all partial transformations from X to Y. For θ ∈ P(Y, X), let (P(X, Y), θ) be a semigroup (P(X, Y), *) where α * β = αθβ for all α, β ∈ P(X, Y). In this paper, we characterize the semigroup (P(X, Y), θ) to be regular, regular elements of the semigroup (P(X, Y), θ), [Formula: see text]-classes, [Formula: see text]-classes, [Formula: see text]-classes and [Formula: see text]-classes of the semigroup (P(X, Y), θ).

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18

McKeon, D. G. C. "Operator regularization and composite operators." Canadian Journal of Physics 68, no. 3 (March 1, 1990): 296–300. http://dx.doi.org/10.1139/p90-047.

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We demonstrate how operator regularization can be used to compute radiative corrections to Green's functions involving composite operators. No divergences are encountered and no symmetry-breaking regulating parameter need be introduced into the initial Lagrangian. We demonstrate the technique to one-loop order by considering operators of dimension four in the [Formula: see text] model and the operator [Formula: see text] in an axial model. Anomalous dimensions of these operators are determined by considering finite Green's functions. There is no need to define "oversubtracted" operators to maintain linearity, as is the case when one uses BPH subtraction, nor is there an ambiguity between the trace of [Formula: see text] and [Formula: see text], as occurs in dimensional regularization. Quantities such as γ5, εμνλσ, and εμν (which are well-defined only in an integer number of dimensions) are treated unambiguously as we never alter the dimensionality of the problem.

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19

WANG, HUAI-YU, KE-QIU CHEN, and EN-GE WANG. "THE FERMIONIC GREEN'S FUNCTION THEORY FOR CALCULATION OF MAGNETIZATION." International Journal of Modern Physics B 16, no. 25 (October 10, 2002): 3803–16. http://dx.doi.org/10.1142/s0217979202014589.

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The fermionic Green's function theory of Heisenberg-like Hamiltonian is presented in this paper. For the case that the Hamiltonian is isotropic and the higher-order Green's function is asymmetrically decoupled, the present theory is equivalent to the bosonic Green's function theory. When the Hamiltonian is anisotropic and the higher-order Green's function is symmetrically decoupled, it gives the universal formula to calculate the three components of statistical average of spin operators which one encountered when dealing with ferromagnetic or ferroelectric systems described by anisotropic Heisenberg model or pseudospin model respectively. Both cases of <Sz> ≠ 0 and <Sz> = 0 are investigated. Explicit expressions are derived for spin value S = 1/2, 1, 3/2, 2, and 5/2. General expressions for any S value are suggested.

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20

Lin, Ji, and Liangang Peng. "Modified Ringel–Hall algebras, Green's formula and derived Hall algebras." Journal of Algebra 526 (May 2019): 81–103. http://dx.doi.org/10.1016/j.jalgebra.2019.02.009.

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21

Lee, Taeyeon. "Renormalization of Composite Operators in Non-Abelian Gauge Theories." International Journal of Modern Physics A 12, no. 27 (October 30, 1997): 4881–93. http://dx.doi.org/10.1142/s0217751x97002607.

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Renormalization of composite operators (at zero momentum transfer) is discussed in non-Abelian gauge theories. Composite operators are inserted into Green's functions by differentiating Z, the generating functional for Green's functions, with respect to the parameters coupled to the composite operators. In the case of the field strength tensor with no coupling parameter, it is possible to have the form of [Formula: see text] by rescaling gauge fields as Aμa → Aμa/g. Then the renormalization of [Formula: see text] can be carried out by the differentiation [Formula: see text]. By doing this, the renormalization procedure is different from the previous work of Kluberg–Stern and Zuber. The procedure of this paper naturally leads to the proper basis of operators which makes the triangular renormalization matrix. Explicit forms for the relation between bare and renormalized composite operators are presented, with the dimensional regularization and minimal subtraction scheme.

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22

Wang, Aiping, Jerry Ridenhour, and Anton Zettl. "Construction of regular and singular Green's functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 1 (January 30, 2012): 171–98. http://dx.doi.org/10.1017/s0308210510001630.

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The Green function of singular limit-circle problems is constructed directly for the problem, not as a limit of sequences of regular Green's functions. This construction is used to obtain adjointness and self-adjointness conditions which are entirely analogous to the regular case. As an application, a new and explicit formula for the Green function of the classical Legendre problem is found.

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23

Pozdeeva, Ekaterina, and Axel Schulze-Halberg. "A trace formula for Dirac Green's functions related by Darboux transformations." Journal of Physics A: Mathematical and Theoretical 41, no. 26 (June 9, 2008): 265201. http://dx.doi.org/10.1088/1751-8113/41/26/265201.

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24

Nazarov, S. A., and B. A. Plamenevskii. "A generalized Green's formula for elliptic problems in domains with edges." Journal of Mathematical Sciences 73, no. 6 (March 1995): 674–700. http://dx.doi.org/10.1007/bf02364945.

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25

Kong, Xiang-zhi, and K. P. Shum. "GREEN ♯-RELATIONS AND NORMAL ${\cal H}^\sharp$-CRYPTOGROUPS." Asian-European Journal of Mathematics 02, no. 04 (December 2009): 637–48. http://dx.doi.org/10.1142/s1793557109000534.

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In this paper, a new set of generalized Green's relations on a semigroup S, namely the set of Green ♯-relations, are introduced. By using these new Green ♯-relations, we prove that an [Formula: see text]-abundant semigroup is a normal [Formula: see text]-cryptogroup if and only if it is a strong semilattice of completely [Formula: see text]-simple cryptogroups. Our theorem simplifies a construction theorem of normal [Formula: see text]-abundant cryptographs previously described by the authors. Some properties of the good homomorphisms between the normal [Formula: see text]-cryptogroups are also investigated.

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26

GILBERT, ROBERT P., and MIAO-JUNG OU. "A UNIQUENESS THEOREM OF THE 3-DIMENSIONAL ACOUSTIC SCATTERING PROBLEM IN A SHALLOW OCEAN WITH A FLUID-LIKE SEABED." Journal of Computational Acoustics 11, no. 04 (December 2003): 535–49. http://dx.doi.org/10.1142/s0218396x03002127.

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This paper shows that under the assumption of the out-going radiation conditions at infinity, the time-harmonic acoustic scattered field off a sound-soft solid in a shallow ocean with a fluid-like seabed is unique in [Formula: see text]. Here M1 is the water part, M2 the seabed, [Formula: see text] the waveguide and Ω the solid object. The associated modal problem is studied and a representation formula for the solution in terms of the Green's function is derived.

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27

POZDEEVA, EKATERINA, and AXEL SCHULZE-HALBERG. "TRACE FORMULA FOR GREEN'S FUNCTIONS OF EFFECTIVE MASS SCHRÖDINGER EQUATIONS AND NTH-ORDER DARBOUX TRANSFORMATIONS." International Journal of Modern Physics A 23, no. 16n17 (July 10, 2008): 2635–47. http://dx.doi.org/10.1142/s0217751x08039955.

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We derive a trace formula for Green's functions of position-dependent (effective) mass Schrödinger equations that are defined on a real, finite interval and connected by a Darboux transformation of arbitrary order. Our findings generalize former results (J. Phys. A37, 10287 (2004)) on constant mass Schrödinger equations to the effective mass case.

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28

Trimarco, Carmine. "The Green's and the Eshelby's identities in generalised continua and in dielectrics." Theoretical and Applied Mechanics, no. 30 (2003): 41–52. http://dx.doi.org/10.2298/tam0301041t.

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In 1973, A. E. Green pointed out several interesting formulae, which hold true in finite elasticity [1]. One of them (formula (2.10), p.75) is repeatedly quoted in the literature as the Green identity. This remarkable identity has been successfully employed in several contexte. We only mention here its central role in theorems on uniqueness in elastostatics [2,3]. A deeper insight to the Green identity shows in evidence an intimate link of this formula with the Eshelby tensor and with the material balance law of equilibrium [4,5]. In homogeneous hyperelastic materials, this law turns out to an identity, the Eshelby identity, and one can easily prove that the Green identity stems straightforwardly from the Eshelby identity. These identities possibly extend to generalized continua, such as continua with microstructure and elastic dielectrics. Hereafter, the validity of the Eshelby identity is discussed for these materials. Basing on the novel extended Eshelby-like identity, the corresponding extended Green-like identity can be also established, under specifie assumptions. In the case of dielectrics, two equivalent forms for the Eshelby tensor emerge from the treatment, both satisfying the Eshelby identity. One of them is more appropriate for deriving the desired Green-like identity. The second one, which is a reduced form of the first one, represents the physical Eshelby tensor in dielectrics [4-5].

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29

Takizawa, M., and S. Takeuchi. "STRUCTURE OF X(3872) WITH COUPLING TO MULTI-HADRONIC STATES." International Journal of Modern Physics E 19, no. 12 (December 2010): 2465–69. http://dx.doi.org/10.1142/s021830131001696x.

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In order to understand the structure of the X (3872), we have studied the effects of the [Formula: see text] core state coupling to the multi-hadronic states such as [Formula: see text], ρ J/ψ etc. We have calculated the transition strength S(E) using the Green's function approach with the simple solvable interactions. We have also studied the S(E) in the case of no [Formula: see text] core state, namely, the [Formula: see text] molecule. Since the calculated shapes of the transition strengths are different from each other, we shall be able to determine the degree of the mixing of the [Formula: see text] state in the X (3872) from the shape of the energy spectrum.

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30

Joachim Telega, Józef. "On unjustified criticism of Green's formula for Hencky plates with microperiodic structure." Nonlinear Analysis: Theory, Methods & Applications 49, no. 2 (April 2002): 293. http://dx.doi.org/10.1016/s0362-546x(01)00100-6.

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31

Manakov, N. L., A. Maquet, S. I. Marmo, and C. Szymanowski. "Generalized Sturmian expansions of Coulomb Green's functions and two-photon Gordon formula." Physics Letters A 237, no. 4-5 (January 1998): 234–39. http://dx.doi.org/10.1016/s0375-9601(97)00893-1.

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32

Phillips, Stephen. "A study of the path-integral quantization of Abelian gauge theories when no explicit gauge-fixing term is included in the bilinear part of the gauge-field action." Canadian Journal of Physics 63, no. 10 (October 1, 1985): 1334–36. http://dx.doi.org/10.1139/p85-220.

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The mathematical problem of inverting the operator [Formula: see text] as it arises in the path-integral quantization of an Abelian gauge theory, such as quantum electrodynamics, when no gauge-fixing Lagrangian field density is included, is studied in this article.Making use of the fact that the Schwinger source functions, which are introduced for the purpose of generating Green's functions, are free of divergence, a result that follows from the conversion of the exponentiated action into a Gaussian form, the apparently noninvertible partial differential equation, [Formula: see text], can, by the addition and subsequent subtraction of terms containing the divergence of the source function, be cast into a form that does possess a Green's function solution. The gauge-field propagator is the same as that obtained by the conventional technique, which involves gauge fixing when the gauge parameter, α, is set equal to one.Such an analysis suggests also that, provided the effect of fictitious particles that propagate only in closed loops are included for the study of Green's functions in non-Abelian gauge theories in Landau-type gauges, then, in quantizing either Abelian gauge theories or non-Abelian gauge theories in this generic kind of gauge, it is not necessary to add an explicit gauge-fixing term to the bilinear part of the gauge-field action.

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33

FERRAZ, A. "RENORMALIZATION GROUP OF A TWO-DIMENSIONAL PATCHED FERMI SURFACE." Modern Physics Letters B 17, no. 04 (February 20, 2003): 167–74. http://dx.doi.org/10.1142/s021798490300507x.

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Using the renormalization group we calculate the single particle Green's function G and the momentum occupation function [Formula: see text] for a quasiparticle in a two-dimensional Fermi Surface (FS) composed of four symmetric patches with both flat and curved arcs in [Formula: see text]-space. We show that G develops an anomalous dimension as a result of the vanishing of the quasiparticle weight at the FS. [Formula: see text] is a continuous function of [Formula: see text] with an infinite slope at FS for CU*2/(1 - CU*2) < 1. This result resembles a Luttinger liquid and indicates the breakdown of Fermi liquid theory in this regime.

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34

Fernandes, Vítor H., and Jintana Sanwong. "On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range." Algebra Colloquium 21, no. 03 (June 24, 2014): 497–510. http://dx.doi.org/10.1142/s1005386714000431.

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Let [Formula: see text] be the semigroup of all partial transformations on X, [Formula: see text] and [Formula: see text] be the subsemigroups of [Formula: see text] of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let [Formula: see text], [Formula: see text] and [Formula: see text]. In 2008, Sanwong and Sommanee described the largest regular subsemigroup and determined Green's relations of [Formula: see text]. In this paper, we present analogous results for both [Formula: see text] and [Formula: see text]. For a finite set X with |X| ≥ 3, the ranks of [Formula: see text], [Formula: see text] and [Formula: see text] are well known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of [Formula: see text], [Formula: see text] and [Formula: see text] for any proper non-empty subset Y of X.

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35

Tifrea, I., I. Grosu, and M. Crisan. "FLUCTUATION CONTRIBUTION TO THE SPECIFIC HEAT IN NON-FERMI MODELS FOR SUPERCONDUCTIVITY." International Journal of Modern Physics B 14, no. 25n27 (October 30, 2000): 2988–93. http://dx.doi.org/10.1142/s0217979200003216.

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We investigate the fluctuation contribution to the specific heat of a two-dimensional superconductor with a non-Fermi normal state described by a Anderson Green's function [Formula: see text]. The specific heat corrections contain a term proportional to [Formula: see text] and another logarithmic one. We define a coherence length as function of the non-Fermi paramter α, which shows that a crossover study between BCS and Bose-Einstein condensation is possible by varying the non-Fermi parameter α.

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36

Denecke, K., and N. Sarasit. "SEMIGROUPS OF TREE LANGUAGES." Asian-European Journal of Mathematics 01, no. 04 (December 2008): 489–507. http://dx.doi.org/10.1142/s1793557108000400.

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Sets of terms of type τ are called tree languages (see [6]). There are several possibilities to define superposition operations on sets of tree languages. On the basis of such superposition operations we define binary associative operations on tree languages and investigate the properties of the arising semigroups. We characterize idempotent and regular elements and Green's relations [Formula: see text] and [Formula: see text]. Moreover, we determine constant, left-zero and right-zero subsemigroups and rectangular bands.

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37

Aleixo, R., and E. Capelas de Oliveira. "Green's function for the lossy wave equation." Revista Brasileira de Ensino de Física 30, no. 1 (2008): 1302.1–1302.5. http://dx.doi.org/10.1590/s1806-11172008000100003.

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Using an integral representation for the first kind Hankel (Hankel-Bessel Integral Representation) function we obtain the so-called Basset formula, an integral representation for the second kind modified Bessel function. Using the Sonine-Bessel integral representation we obtain the Fourier cosine integral transform of the zero order Bessel function. As an application we present the calculation of the Green's function associated with a second-order partial differential equation, particularly a wave equation for a lossy two-dimensional medium. This application is associated with the transient electromagnetic field radiated by a pulsed source in the presence of dispersive media, which is of great importance in the theory of geophysical prospecting, lightning studies and development of pulsed antenna systems.

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38

Guo, Xiaojiang, and K. P. Shum. "On an Open Problem of Hereditary Property of Green's $\mathcal{H}$-Relation on Compact Semigroups." Algebra Colloquium 20, no. 02 (April 3, 2013): 319–26. http://dx.doi.org/10.1142/s100538671300028x.

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We give a negative answer to an open problem concerning the hereditary property of Green's [Formula: see text]-relation on a compact semigroup proposed by Carruth and Clark in 1972. In addition, we give a positive answer to this open problem by adding some suitable conditions on the compact semigroup.

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39

PANTIĆ, M. R. "LONGITUDINAL DYNAMICAL SPIN SUSCEPTIBILITY IN HEISENBERG FERROMAGNETS." International Journal of Modern Physics B 16, no. 31 (December 10, 2002): 4743–54. http://dx.doi.org/10.1142/s0217979202014838.

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We study the longitudinal dynamical spin susceptibility [Formula: see text] within the framework of Heisenberg model in the ferromagnetic phase, where no external field exists. On the basis of memory function formalism within the framework of the irreducible Green's functions we obtained the self-consistent equations for [Formula: see text] in mode coupling approximation. The expression for the longitudinal spin susceptibility is valid in the whole range of system frequencies. Its validity in the range of low and high frequencies was discussed in particular for the magnetic systems in ferromagnetic phase.

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40

Ghoumaid, Ali, Farid Benamira, and Larbi Guechi. "Bound and scattering state solutions of a hyperbolic-type potential." Canadian Journal of Physics 91, no. 2 (February 2013): 120–25. http://dx.doi.org/10.1139/cjp-2012-0295.

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A hyperbolic-type potential with a centrifugal term is solved approximately using the path integral approach. The radial Green's function is expressed in closed form, from which the energy spectrum and the suitably normalized wave functions of bound and scattering states are extracted for (1/2) − [Formula: see text] < σ < (1/2) + [Formula: see text]. Besides, the phase shift and the scattering function Sl for each angular momentum l are deduced. The particular cases corresponding to the s-waves (l = 0) and the barrier potential (σ = 1) are also analyzed.

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41

Schulze-Halberg, Axel. "A New Formula to Obtain Exact Green's Functions of Time-Dependent Schrödinger Equation." Communications in Theoretical Physics 41, no. 5 (May 15, 2004): 723–25. http://dx.doi.org/10.1088/0253-6102/41/5/723.

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42

Şeremet, Victor. "New Explicit Green's Function and Poisson's Integral Formula for a Thermoelastic Quarter-Space." Journal of Thermal Stresses 33, no. 4 (March 31, 2010): 356–86. http://dx.doi.org/10.1080/01495731003658838.

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43

Bachar, Imed, Habib Maâgli, and Noureddine Zeddini. "Estimates on the Green Function and Existence of Positive Solutions of Nonlinear Singular Elliptic Equations." Communications in Contemporary Mathematics 05, no. 03 (June 2003): 401–34. http://dx.doi.org/10.1142/s0219199703001038.

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We establish a 3G-Theorem for the Green's function for an unbounded regular domain D in ℝn(n ≥ 3), with compact boundary. We exploit this result to introduce a new class of potentials K(D) that properly contains the classical Kato class [Formula: see text]. Next, we study the existence and the uniqueness of a positive continuous solution u in [Formula: see text] of the following nonlinear singular elliptic problem [Formula: see text] where φ is a nonnegative Borel measurable function in D × (0, ∞), that belongs to a convex cone which contains, in particular, all functions φ(x, t) = q(x)t-σ, σ ≥ 0 with q ∈ K(D). We give also some estimates on the solution u.

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44

MAKI, KAZUMI. "SINGLE PARTICLE GREEN'S FUNCTION AND QUANTUM MAGNETIC OSCILLATION IN VORTEX STATE OF UNCONVENTIONAL SUPERCONDUCTORS." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 82–86. http://dx.doi.org/10.1142/s0217979293000202.

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Within weak-coupling model we construct the superconducting order parameter in the vortex states of the axial and hybrid wave function. In terms of these order parameters the quasi-particle Green's function in the vortex state in the vicinity of upper critical field is constructed. In general the most important modification on the quantum oscillation in the vortex state is increase of the damping constant (or the Dingle temperature). However, since this extra term is proportional to the average of | f |2 over the electron orbit at the belly or neck of the Fermi surface, we find that this exrtra term vanishes for the hybrid state for both [Formula: see text] and [Formula: see text], while it vanishes in the axial state only for [Formula: see text]. This should provide a unique probe to the nature of the superconducting wave functions.

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45

SHENG, L., and C. S. TING. "INTRINSIC SPIN HALL EFFECT IN MESOSCOPIC SYSTEMS." International Journal of Modern Physics B 20, no. 17 (July 10, 2006): 2339–58. http://dx.doi.org/10.1142/s0217979206034613.

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The intrinsic spin Hall effect has been attracting increasing theoretical and experimental interest since its discovery about two years ago. In this article, we review the main achievements in the theoretical aspect of both dissipative and nondissipative spin Hall effects in mesoscopic systems. The Landauer–Büttiker formula and Green's function approach based numerical method for the spin Hall effect is also introduced.

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46

Petrich, Mario. "Embedding Regular Semigroups into Idempotent Generated Ones." Algebra Colloquium 17, no. 02 (June 2010): 229–40. http://dx.doi.org/10.1142/s1005386710000246.

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Any semigroup S can be embedded into a semigroup, denoted by ΨS, having some remarkable properties. For general semigroups there is a close relationship between local submonoids of S and of ΨS. For a number of usual semigroup properties [Formula: see text], we prove that S and ΨS simultaneously satisfy [Formula: see text] or not. For a regular semigroup S, the relationship of S and ΨS is even closer, especially regarding the natural partial order and Green's relations; in addition, every element of ΨS is a product of at most four idempotents. For completely regular semigroups S, the relationship of S and ΨS is still closer. On the lattice [Formula: see text] of varieties of completely regular semigroups [Formula: see text] regarded as algebras with multiplication and inversion, by means of ΨS, we define an operator, denoted by Ψ. We compare Ψ with some of the standard operators on [Formula: see text] and evaluate it on a small sublattice of [Formula: see text].

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47

DOLAN, P., and B. MURATORI. "GRAVITATIONAL POTENTIALS AND THE EXISTENCE OF GRAVITATIONAL GREEN'S TENSORS." Modern Physics Letters A 13, no. 29 (September 21, 1998): 2347–53. http://dx.doi.org/10.1142/s0217732398002497.

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The non-local part of the gravitational field Cabcd can be generated by the 16-component Lanczos tensor potential Labc. When six gauge conditions are imposed, Labe;e=0, its ten degrees of freedom match those of the Weyl tensor. The Penrose wave equation for Cabcd can be independently derived from that for Labc. The consistency between Labc and Cabcd is also shown by the compatibility of their algebraic classifications. An unexpected insight into the relationship of Labc and Cabcd is found in "Euclidean gravity" which in turn leads to the introduction of a gravitational Green's tensor [Formula: see text] corresponding to the potential Labc.

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48

Sun, Jianguo, and Dirk Gajewski. "True‐amplitude common‐shot migration revisited." GEOPHYSICS 62, no. 4 (July 1997): 1250–59. http://dx.doi.org/10.1190/1.1444226.

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In Kirchhoff‐type migration, two dynamic ray‐tracing computations are usually needed for computing the complex weighting (Green's) functions necessary for recovering the source pulse with true amplitude. One computation is from the source point to the image point, the other is from the receiver point to the image point. Since it is a time‐consuming procedure, dynamic ray tracing is a main factor slowing down the performance speed of weighted diffraction stack migration. Here, the known weighting function for a common‐shot configuration is revisited and a new, alternative formula is developed. Because only the takeoff angles of rays are involved in this alternative formula, the module of the complex weighting function can be computed solely by kinematic ray tracing. Further, it is shown that the phase (caustic) correction is not essential for the stack process. As a consequence, the weighted diffraction stack migration can be implemented without using dynamic ray tracing at all. In other words, the subsurface structure can be imaged without using any Green's function. Therefore, using the new formula may accelerate the performance of the Kirchhoff‐type migration, especially in 3-D cases. In addition, the new formula may affect the model smoothing process necessary for using some traveltime computing methods based on ray tracing. As is known, kinematic quantities associated with a given ray are less sensitive to the velocity distribution than the dynamic ones. Thus, the new formula allows one to use a model less smoothed than that demanded for using dynamic ray tracing. As a result, less smoothing operation is needed by building a velocity model without interfaces. The latter points are vital for the accuracy and efficiency of the ray tracers for computing the traveltime of point‐diffracted rays.

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49

Afsar, Mohammed Z., Adrian Sescu, and Stewart J. Leib. "Modelling and prediction of the peak-radiated sound in subsonic axisymmetric air jets using acoustic analogy-based asymptotic analysis." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2159 (October 14, 2019): 20190073. http://dx.doi.org/10.1098/rsta.2019.0073.

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This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein 2003 JFM 488 , 315–333. ( doi:10.1017/S0022112003004890 )) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (Ma). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low-frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation. We then address the predictive capability of the solution to this partial differential equation when used in the analogy through first-of-its-kind numerical calculations when an experimentally verified model of the turbulence source structure is used together with Reynolds-averaged Navier–Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at Ma = 0.9, for Strouhal numbers up to about 0.6, and at Ma = 0.5 using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.

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50

CHADLI, R., A. KHATER, and R. TIGRINE. "SURFACE PHONONS IN THE ORDERED c(2 × 2) PHASE OF Pd ON Au(100)." Surface Review and Letters 20, no. 02 (April 2013): 1350019. http://dx.doi.org/10.1142/s0218625x13500194.

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The vibrational properties of the Au(100)-c(2 × 2)-Pd ordered phase, which is a stable system in the temperature range of 500 K to 600 K, are presented. This surface alloy is formed by depositing Pd atoms onto the Au(100) surface, and annealing at higher temperatures. The equilibrium structural characteristics, phonon dispersions as well as the local density of phonon states are calculated using the matching theory associated with Green's function formalism evaluated in the harmonic approximation. New surface modes have been found on the ordered metallic surface alloy along the three directions of high symmetry [Formula: see text], [Formula: see text], and [Formula: see text], in comparison with the clean surface Au(100) . Three of them are observed above the bulk bands spectrum.

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