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1.
Let A be a symmetric matrix of size n×n with entries in some (commutative) field K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T∈Matn(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base field. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Matn(K) there exist symmetric, absolutely indecomposable matrices iff n is congruent to 0, 1 or −1 modulo 2s. 相似文献
2.
In this paper we relate the operators in the operator representations of a generalized Nevanlinna function N(z) and of the function −N(z)−1 under the assumption that z=∞ is the only (generalized) pole of nonpositive type. The results are applied to the Q-function for S and H and the Q-function for S and H∞, where H is a self-adjoint operator in a Pontryagin space with a cyclic element w, H∞ is the self-adjoint relation obtained from H and w via a rank one perturbation at infinite coupling, and S is the symmetric operator given by S=H∩H∞. 相似文献
3.
L.-Q. Han S.-Y. Zhao Y.-D. Zhou P.-L. Zhang 《Applied physics. B, Lasers and optics》1997,65(3):399-402
Received: 18 June 1996/Revised version: 3 January 1997 相似文献
4.
Jin Hu Gang Liu Jixiu Zhang Lingchao Kong Weidong Fei 《Applied Surface Science》2006,253(5):2792-2795
The microstructure of a laser treated Al18B4O33w/2024Al composite has been investigated using transmission electron microscope (TEM), low-angle (glancing angle) X-ray diffraction (XRD) techniques. Various surface microstructures were observed in the laser treated composite. The Al18B4O33 whisker on the surface of the composite was decomposed during laser surface melting, various decomposition products were studied in the laser treated composite. Eutectic phases and the precipitation in the matrix of the composite with laser-treated were observed. The main phases detected in the molten zone were aluminum and decomposition products Al2O3. The effect of laser treatment on the hardness of the composite was also examined. A surface hardness of 400 Hv was noted. 相似文献
5.
Hirofumi Tsumura 《Journal of Number Theory》2004,106(1):155-168
In this paper, we define the multiple Euler numbers and consider some multiple harmonic series of Mordell-Tornheim's type, which is a partial sum of the Mordell-Tornheim zeta series defined by Matsumoto. Indeed, we prove a certain reducibility of these series as well as the multiple zeta values. 相似文献
6.
In this paper the neo-classical economic Solow-Swan model (1956) has been improved replacing its Malthusian manpower law with
the Verhulst (logistic) one. The relevant ordinary differential equation for the ratio capital/work has been then integrated
in closed form via the Hypergeometric function2
F
1. The logistic growth injection for the manpower is detected to induce a more slow dynamics onto the Solow-Swan system, which
keeps its stability. Increasing developments are displayed as the technologic progress rises. Further sceneries are tested
and the congruence of the new solution with the classical one is shown switching to zero the selflimitation coefficent in
the logistic law.
Research supported by MURST grant:Metodi matematici in economia 相似文献
7.
We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with
a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular
behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the
error is of order k
2 + h
2, where k and h are the parameters for the time and space meshes, respectively. 相似文献
8.
Various types of LU-factorizations for nonsingular matrices, where L is a lower triangular matrix and U is an upper triangular matrix, are defined and characterized. These types of LU-factorizations are extended to the general m × n case. The more general conditions are considered in the light of the structures of [C.R. Johnson, D.D. Olesky, P. Van den Driessche, Inherited matrix entries: LU factorizations, SIAM J. Matrix Anal. Appl. 10 (1989) 99-104]. Applications to graphs and adjacency matrices are investigated. Conditions for the product of a lower and an upper triangular matrix to be the zero matrix are also obtained. 相似文献
9.
This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R0-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically. 相似文献
10.
V. S. Antonov V. S. Letokhov A. N. Shibanov 《Applied Physics A: Materials Science & Processing》1981,25(1):71-76
The paper presents the results of studies into ion desorption from the surface of adenine and anthracene molecular crystals
and anthracene molecules adsorbed on a metal as the surface is irradiated by an uv laser at λ=249, 308, and 337 nm. A sharp
increase in molecular ion yield has been revealed with a decrease in radiation wavelength down to 249 nm. At this wavelength
the effect of molecular ion desorption is observed at the radiation intensity of 20∶50 kW/cm2 and pulse duration of 20 ns, it cannot be explained by thermal mechanisms. The initial velocity distribution of photoions
is nonthermal by character, with maximum velocity of 2·105 cm/s in case of adenine. The mechanisms responsible for the effect observed are discussed. 相似文献