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991.
S. L. Woronowicz 《Letters in Mathematical Physics》1991,21(1):35-39
A simpler set of axioms of the theory of compact matrix quantum groups (pseudogroups) is found.Supported by Japan Society for Promoting Science. On leave from the Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoa 74, 00-682 Warsaw, Poland. 相似文献
992.
Branislav Jurčo 《Letters in Mathematical Physics》1991,21(1):51-58
The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU
q
(2) and the discrete series of representations of SU
q
(1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed. 相似文献
993.
George D. Raikov 《Letters in Mathematical Physics》1991,21(1):41-49
We consider the Schrödinger operator with electric potential V, which decays at infinity, and magnetic potential A. We study the asymptotic behaviour for large values of the electric field coupling constant of the eigenvalues situated under the essential-spectrum lower bound. We concentrate on the cases of rapidly decaying V (e.g. V L
m/2(
m
) for m 3) and arbitrary A, or slowly decaying V (i.e. V(x |x|–
, (0,2), as |x| ) and magnetic potentials A corresponding to constant magnetic fields B = curl A.Partially supported by the Ministry of Culture, Science and Education under Grant No. 52. 相似文献
994.
A. D. Groza V. L. Strizhevskii 《Applied Physics A: Materials Science & Processing》1991,52(3):180-183
We have obtained the solution of the stationary problem for P-polarized nonlinear surface polaritons (NLSP) near the interface of two media, one of which is optically linear and the other having an optical nonlinearity with saturation and a dielectric function of the form: =xx=zz=0+a|E|2/(1+b|E|2), where E is the amplitude of the electric field. On this basis the NLSP energy and propagation properties, the polarization structure and the localization depth of the NLSP field as well as the physically allowed region in the parameter space have been investigated for the case in which the parameter 0 is positive, b is non-negative, and a and 1 are negative (1 is the dielectric function of the linear medium); 0>|1|. 相似文献
995.
Tao Tang 《Numerische Mathematik》1992,61(1):373-382
Summary We discuss the application of a class of spline collocation methods to first-order Volterra integro-differential equations (VIDEs) which contain a weakly singular kernel (t–s)– with 0<<1. It will be shown that superconvergence properties may be obtained by using appropriate collocation parameters and graded meshes. The grading exponents of graded meshes used are not greater thanm (the polynomial degree) which is independent of . This is in contrast to the theories of spline collocation methods for Volterra (or Fredholm) integral equation of the second kind. Numerical examples are given to illustrate the theoretical results. 相似文献
996.
A second order nonlinear differential equation
相似文献
997.
Summary Forf ( C
n() and 0 t x letJ
n
(f, t, x) = (–1)n
f(–x)f
(n)(t) +f(x)f
(n)
(–t). We prove that the only real-analytic functions satisfyingJ
n
(f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e
x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ
0
(f, x, x) 0 and
0
x
(x – t)n – 1Jn(f, t, x)dt 0 (n 1). 相似文献
998.
Summary Letf be a map from a groupG into an abelian groupH satisfyingf(xy) + f(xy
–1) = 2f(x), f(e) = 0, wherex, y G ande is the identity inG. A set of necessary and sufficient conditions forS(G, H) = Hom(G, H) is given whenG is abelian, whereS(G, H) denotes all the solutions of the functional equation. The case whenG is non-abelian is also discussed. 相似文献
999.
Walter Benz 《Aequationes Mathematicae》1992,43(2-3):177-182
Summary The following theorem holds true.
Theorem.
Let X be a normed real vector space of dimension 3 and let k > 0 be a fixed real number. Suppose that f: X X and g: X × X are functions satisfying x – y = k f(x) – f(y) = g(x, y)(x – y) for all x, y X. Then there exist elements and t X such that f(x) = x + t for all x X and such that g(x, y) = for all x, y X with x – y = k. 相似文献
1000.
Janusz Matkowski 《Aequationes Mathematicae》1992,43(2-3):219-224
Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned. 相似文献
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