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991.
Ordinary differential equations with impulse action are considered at fixed moments of time when finite limits points are admitted to the set of moments of the shocks. The topological structure of this set is clarified: it must be resolvable, in particular nowhere dense in R.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 378–383, March, 1990. 相似文献
992.
Yu. I. Volkov 《Ukrainian Mathematical Journal》1990,42(7):785-796
The concept of the deformation of positive linear operators of type B is introduced, in particular, that of a linear deformation of operators. These concepts are applied to the solving of operator equations of type B. One solves completely the problems of the determination of all positive linear operators of type B for which the covariance of the operators is 1) a polynomial of degrees 3; 2) any power function; 3) an exponential function. In addition, one finds; two families of positive linear operators of type B for which the covariance is a polynomial of degree four.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 888–900, July, 1990. 相似文献
993.
For eachd1 there is a constantc
d>0 such that any finite setXR
d contains a subsetYX, |Y|[1/4d(d+3)]+1 having the following property: ifEY is an ellipsoid, then |E X|c
d |X|.On leave from the Mathematical Institute of the Hungarian Academy of Sciences, 1364 Budapest, P.O. Box 127, Hungary. Supported by a research fellowship from the Science and Engineering Research Council, U.K., and by Hungarian National Foundation for Scientific Research Grant No. 1812. 相似文献
994.
V. I. Inozemtsev 《Journal of statistical physics》1990,59(5-6):1143-1155
Extra integrals of motion and the Lax representation are found for interacting spin systems with the HamiltonianH = (J/2)
j, k=1,j k
N
P(j – k)
j
k
, where one of the periods of the WeierstrassP function is equal toN. The Heisenberg and Haldane-Shastry chains appear as limiting cases of these systems at some values of the second period. The simplest eigenvectors and eigenvalues ofH corresponding to the scattering of two spin waves are presented explicitly for these finite-dimensional systems and for their infinite-dimensional version. 相似文献
995.
The behavior of effective charges i(t) corresponding to the parameters of nonminimal coupling of scalar and gravitational fields in E6 Grand Unification Theory (GUT) in curve spacetimes is studied. It is shown that in a strong gravitational field ¦i(t)¦ grows indefinitely.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 74–11, September, 1990. 相似文献
996.
The class of dynamical systems is considered, which are described by several mutually noncommuting Hamiltonian currents, in particular, relativistic bi-Hamiltonian systems, the evolution of which is described by a pair of 4-momenta p and p The examination is conducted in classical and quantum realizations. The evolution equations are derived of relativistic bi-Hamiltonian systems in the Heisenberg and Schrödinger pictures. It is shown that the quantum theory of relativistic bi-Hamiltonian systems is not compatible with the unitary condition and is nonunitary. A physical interpretation is given of nonunitary quantum theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 5–12, October, 1990. 相似文献
997.
An ultrabroadband (up to 35 nm FWHM) generation by a pulsed dye laser is reported. The principle of laser operation is based on a recently proposed cavity configuration, which we have termed spatially-dispersive resonator. By means of a prism pair this spreads the various spectral components into different spatial areas in the active medium and thus reduces the competition between them. A generation of a spectrum containing a number of equally spaced lines is also demonstrated. 相似文献
998.
A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels
In this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the space X+ = {c∈L1: ∫ (1 + x)∣c(x)∣dx < ∞} whenever the kernels satisfy certain growth properties and the non-negative initial data belong to X+. The proof is based on weak L1 compactness methods applied to suitably chosen approximating equations. 相似文献
999.
I. Palásti 《Periodica Mathematica Hungarica》1989,20(3):231-235
Here we establish a set of eight points in general position in the plane, i.e. no three on a line, no four on a circle, and they determine 7 distinct distances, so that, thei-th distance occursi times,i = 1, 2, , 7. The points are embedded in a triangular net, and the distances are not ordered by size or in any other way. We shall show that some known and unknown examples forn < 8 with the above properties may also be lattice points of a similar net.Research (partially) supported by the Hungarian National Foundation for Scientific Research (OTKA) grant, no. 1808. 相似文献
1000.
G. I. Ol'shanskii 《Journal of Mathematical Sciences》1989,47(2):2466-2473
Starting from the universal enveloping algebras u(gl(n)), n=1,2,... we construct an algebra A, which gives a realization of the Yangian Y(gl(m)) and is a proper way to define the universal enveloping algebra for infinite-dimensional classical Lie algebras.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 142–150, 1987. 相似文献