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Conditions for the convolution of two Wigner distributions to be itself a Wigner distribution (1988)

Narcowich, Francis J.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 2036-2041

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: The convolution of two Wigner distribution functions (WDF's) is always non-negative, but not always a WDF, as Jagannathan et al. [Phys. Lett. A 120, 161 (1987)] have shown. In this paper conditions are given that are sufficient, and probably necessary, for such a convolution to be a WDF, and a new characterization of Gaussian WDF's is obtained as a by-product.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.527861

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2

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On the representation of Slater-type densities by Gaussian densities (1988)

Braunss, G. ; Teubner, E.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1758-1760

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: It is proved that for arbitrary m, n∈N0 and α〉0, β〉0, there exists an integral representation ||x||m ||y||n exp(−α||x||−β||y||) =∫R+×RKmn(s,t)exp[−(s +it)||x||2−(s−it)||y||2]d(s,t), x,y∈R3, where Kmn(s,t) is a singular distribution in D' (R)⊗Z'(R).

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.527874

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3

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Nonperturbative solutions of nonlinear differential equations using continued fractions (1988)

Ditto, William L. ; Pickett, Thomas J.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1761-1770

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: A new approach to the solution of nonlinear differential equations of mathematical physics is presented. Continued fractions are exploited to convert a power series of a solution into a closed form expression that yields an excellent approximation to the exact solution. These solutions contain the appropriate number of arbitrary constants to accommodate boundary conditions. The method is also shown to be capable of generating certain exact solutions. Evidence is provided for the conjecture that the known exact solutions are members of families of exact solutions.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.527875

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4

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Solutions of reaction-diffusion integral equations describing explosive evolution of densities for localized structures (1988)

Wilhelmsson, Hans

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1776-1779

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: Reaction-diffusion integral equations are studied with special regard to explosive-type solutions. Certain localized structures can grow explosively in time without change in spatial structure. The characteristic shapes can be described in terms of elliptic functions.

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URL: http://dx.doi.org/10.1063/1.527877

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5

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Solutions of the wave equations with boundary conditions on the hyperplane z−ct=0 (1988)

Hillion, P.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1771-1775

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: The boundary value problem for the wave equation is discussed with data cursive-phi(r) on the hyperplane z−ct=0. We give the general form of the solution when cursive-phi(r) is an entire function of r2 of order 1 and type 0〈τ〈∞. As a particular case the focus wave mode solutions of the wave equation are obtained.

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URL: http://dx.doi.org/10.1063/1.527876

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6

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Introducing division by an "a'' number and a new "b'' number in particle physics (1988)

Quan Xiang-Lin ; Wang Lian-Ji ; Song He-Shan

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1780-1785

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: In this paper a new "b'' number (b=a1a2⋅⋅⋅an, where n is even and each a is an anticommutative number or Grassmann number) is introduced, and the specialities of this "b'' number are also expounded. Moreover, division by an "a'' number is defined. At the same time a derivative concept of the functional containing an "a'' number is also given in the traditional approach, and a new formula for the derivative of this functional is advanced. The new formula not only encompasses Berezin's formula but also solves the problems that cannot be solved by Berezin's formula. For "b'' numbers, a unique infinitesimal calculus will be proposed.

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URL: http://dx.doi.org/10.1063/1.527878

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7

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Global anomalies and algebraic topology (1988)

Lundell, Albert T. ; Tosa, Yasunari

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1795-1806

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: The algebraic topology aspect of the global pure gauge anomaly calculation is investigated. In particular, the use of a cohomology sequence clarifies the method initiated by Witten [Nucl. Phys. 223, 422, 433 (1983)] and Elitzur and Nair [Nucl. Phys. B 243, 205 (1984)]. Examples in SU(N), Sp(N), and SO(N) are discussed.

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URL: http://dx.doi.org/10.1063/1.527881

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8

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The existence of regular partially future asymptotically predictable space-times (1988)

Królak, Andrzej

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1786-1788

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: A new definition of asymptotically flat space-times is proposed. It is shown that singularities in these new space-times arise from regular initial data. This leads to a simplification of the assumptions of the cosmic censorship theorem recently proved by the author [Class. Quantum Gravit. 3, 267 (1986)]. It is also shown that in the new asymptotically flat space-times a stronger censorship theorem than that proved so far by the author holds.

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URL: http://dx.doi.org/10.1063/1.527879

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9

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Cohomology of the structure sheaf of real and complex supermanifolds (1988)

Bartocci, Claudio ; Bruzzo, Ugo

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1789-1794

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: The cohomology of the structure sheaf of real and complex supermanifolds is studied. It is found to be nontrivial (also in the real case), unless the supermanifold is De Witt, i.e., it is a fiber bundle on an ordinary manifold with a vector fiber. As a consequence, the Dolbeault theorem can be extended only to complex De Witt supermanifolds. The relevance of the nontrivial cohomology of the structure sheaf to the classification of complex line superbundles is discussed. The relationship between the Picard group of a complex De Witt supermanifold and the Picard group of its body is shown.

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URL: http://dx.doi.org/10.1063/1.527880

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10

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Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra (1988)

Leach, P. G. L. ; Mahomed, F. M.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 29 (1988), S. 1807-1813

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: Conventionally the symmetries of a dynamical system are used to determine the first integrals associated with the system. In this paper the reverse procedure is adopted for one-dimensional systems possessing SL(3,R) symmetry. The equivalence of such systems enables the free particle equation to be used as a vehicle. It is observed that for three particular first integrals, each gives rise to a triplet of generators having isomorphic algebras. It is then shown how the knowledge of a first integral and its associated triplet enables one to obtain the remaining integrals and triplets.

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URL: http://dx.doi.org/10.1063/1.527882

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