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51.
Edmund I. Zverovich 《Complex Analysis and Operator Theory》2008,2(4):709-732
In this paper, we present a general solution of the scalar Riemann problem on a closed Riemann surface in the case of a compound
contour in the class of piecewise meromorphic functions multiple of a given divisor. All the results are known and belong
to the author [15–17], except for the existence theorems and properties of basic functionals and also properties of a θ-function.
The solution of the problem in a ‘special case’ has been announced by the author but not published [15]. Similar problems
and some applications are considered in [1, 2, 12].
The main results of the paper were obtained by the author during his collaboration with Professor G. S. Litvinchuk, and this
paper is devoted to his cherished memory.
Received: April 13, 2007. Accepted: June 13, 2008. 相似文献
52.
We compute the largest dimension of the Abelian Lie subalgebras contained in the Lie algebra
of n×n strictly upper triangular matrices, where n ∈ ℕ \ {1}. We do this by proving a conjecture, which we previously advanced,
about this dimension. We introduce an algorithm and use it first to study the two simplest particular cases and then to study
the general case.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 419–429, September, 2007. 相似文献
53.
Two methods for symmetrizing Markov processes are discussed. Letu
a(x, y) be the potential density of a Lévy process on a compact Abelian groupG. A general condition is given that guarantees thatv(x, y)=ua(x, y)+ua(y, x) is the potential density of a symmetric Lévy process onG. The second method arises by considering the linear space of one-potentialsU
1
f, withf inL
2, endowed with the inner product (U
1
f,U
1
g)=fU
1
g+gU
1
f. If the semigroup ofX(t) is normal, then the completionH of this space is the Dirichlet space of a symmetric processY(t). A set that is semipolar forX(t) is polar forY(t). 相似文献
54.
Vieri Benci Donato Fortunato 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4402-4421
In this paper we consider an Abelian Gauge Theory in R4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein–Gordon–Maxwell equations, which provide models for the interaction between the electromagnetic field and matter. A three-dimensional vortex is a finite energy solution of these equations in which the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of vortex solutions. 相似文献
55.
The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous
to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our
earlier work (Levine and Peres, Indiana Univ Math J 57(1):431–450, 2008). For the shape consisting of sites, where ω
d
is the volume of the unit ball in , we show that the inradius of the set of occupied sites is at least r − O(logr), while the outradius is at most r + O(r
α
) for any α > 1 − 1/d. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total
mass. For the classical abelian sandpile model in two dimensions, with n = πr
2 particles, we show that the inradius is at least , and the outradius is at most . This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions, improving on bounds of Fey and
Redig.
Yuval Peres is partially supported by NSF grant DMS-0605166. 相似文献
56.
David S. Lyubshin 《Discrete Mathematics》2009,309(13):4343-4348
In this paper we give a criterion for the adjacency matrix of a Cayley digraph to be normal in terms of the Cayley subset S. It is shown with the use of this result that the adjacency matrix of every Cayley digraph on a finite group G is normal iff G is either abelian or has the form for some non-negative integer n, where Q8 is the quaternion group and is the abelian group of order 2n and exponent 2. 相似文献
57.
Lubomir Gavrilov Iliya D. Iliev 《Journal of Mathematical Analysis and Applications》2009,357(1):69-1669
We study the stratum in the set of all quadratic differential systems , with a center, known as the codimension-four case Q4. It has a center and a node and a rational first integral. The limit cycles under small quadratic perturbations in the system are determined by the zeros of the first Poincaré-Pontryagin-Melnikov integral I. We show that the orbits of the unperturbed system are elliptic curves, and I is a complete elliptic integral. Then using Picard-Fuchs equations and the Petrov's method (based on the argument principle), we set an upper bound of eight for the number of limit cycles produced from the period annulus around the center. 相似文献
58.
The finite generators of Abelian integral are obtained, where Γh is a family of closed ovals defined by H(x,y)=x2+y2+ax4+bx2y2+cy4=h, h∈Σ, ac(4ac−b2)≠0, Σ=(0,h1) is the open interval on which Γh is defined, f(x,y), g(x,y) are real polynomials in x and y with degree 2n+1 (n?2). And an upper bound of the number of zeros of Abelian integral I(h) is given by its algebraic structure for a special case a>0, b=0, c=1. 相似文献
59.
Katerina Saneva 《Journal of Mathematical Analysis and Applications》2010,370(2):543-554
We develop a distribution wavelet expansion theory for the space of highly time-frequency localized test functions over the real line S0(R)⊂S(R) and its dual space , namely, the quotient of the space of tempered distributions modulo polynomials. We prove that the wavelet expansions of tempered distributions converge in . A characterization of boundedness and convergence in is obtained in terms of wavelet coefficients. Our results are then applied to study local and non-local asymptotic properties of Schwartz distributions via wavelet expansions. We provide Abelian and Tauberian type results relating the asymptotic behavior of tempered distributions with the asymptotics of wavelet coefficients. 相似文献
60.
Degree conditions for group connectivity 总被引:1,自引:0,他引:1
Let G be a 2-edge-connected simple graph on n≥13 vertices and A an (additive) abelian group with |A|≥4. In this paper, we prove that if for every uv∉E(G), max{d(u),d(v)}≥n/4, then either G is A-connected or G can be reduced to one of K2,3,C4 and C5 by repeatedly contracting proper A-connected subgraphs, where Ck is a cycle of length k. We also show that the bound n≥13 is the best possible. 相似文献