共查询到20条相似文献,搜索用时 31 毫秒
1.
Rasul Ganikhodzhaev 《Linear algebra and its applications》2010,432(1):24-35
In the present we introduce a concept of doubly stochastic quadratic operator. We study necessary and sufficient conditions for doubly stochasticity of operator. Moreover, we study analogue of Birkhoff’s theorem for the class of doubly stochastic operators. 相似文献
2.
We introduce the concept of conditional cubic stochastic operator in this study. We show that any conditional cubic stochastic operator has a unique fixed point and such an operator has the property of being regular. 相似文献
3.
A. M. Sinev 《Theoretical and Mathematical Physics》2009,158(3):377-390
We consider a solvable problem describing the dynamics of a quantum oscillator interacting with an electromagnetic field,
a classical force, and a heat bath. We propose a general method for solving Markovian master equations, the method of quantum
trajectories. We construct the stochastic evolution operator involving the stochastic analogue of the Baker-Hausdorff formula
and calculate the system density matrix for an arbitrary initial state. As a physical application, we evaluate the influence
of the environment at a finite temperature on the accuracy of measuring a weak classical force by the interference method.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 444–459, March, 2009. 相似文献
4.
V. A. Yurko 《Siberian Mathematical Journal》2009,50(2):373-378
We study inverse nodal problems for the second order differential operators on a star-type graph satisfying the standard matching
conditions at the interior vertex. We prove uniqueness theorems and obtain a constructive solution to the inverse problems
of this class.
Original Russian Text Copyright ? 2009 Yurko V. A.
The author was supported by the Russian Foundation for Basic Research (Grant 07-01-00003) and the National Science Council
of Taiwan (Grant 07-01-92000-NSC-a).
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Saratov. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 469–475, March–April, 2009. 相似文献
5.
本文研究了双随机循环矩阵中素元的分类问题.由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式,从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程.应用此原理,本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题,并给出了n阶双随机循环矩阵中一类具有位数4的素元. 相似文献
6.
Ping WANG Jiong Sheng LI 《数学学报(英文版)》2005,21(5):1087-1092
Let G be a finite simple graph with adjacency matrix A, and let P(A) be the convex closure of the set of all permutation matrices commuting with A. G is said to be compact if every doubly stochastic matrix which commutes with A is in P(A). In this paper, we characterize 3-regular compact graphs and prove that if G is a connected regular compact graph, G - v is also compact, and give a family of almost regular compact connected graphs. 相似文献
7.
We study the
boundedness of generalized multilinear fractional integrals. An O’Neil type inequality for a k-linear integral operator is proved. Using an O’Neil type inequality for a k-linear integral operator, we obtain a pointwise rearrangement estimate of generalized multilinear fractional integrals. By
way of application we prove a Sobolev type theorem for these integrals.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 3, pp. 577–585, May–June, 2007. 相似文献
8.
J. Hilgert 《Semigroup Forum》2008,77(1):64-85
In this paper we relate Mayer’s transfer operator for the geodesic flow of the modular surface to the representation theory
of the semigroup of invertible 2×2-matrices with non-negative entries. It turns out that similarly to the case of the Kac-Baker
model (see Hilgert et al., Convex Cones, and Semigroups, Oxford University Press, London, 1989 and Hilgert and Mayer, Commun. Math. Phys. 232:19–58, 2002) from statistical mechanics which is related to Howe’s oscillator semigroup one has to introduce an additional multiplication
operator to obtain a self-adjoint Hilbert space operator of trace class with the correct spectrum from the natural operators
provided by the representation theory. In the present case the representations naturally live on weighted Bergman spaces,
but can also be realized on weighted L
2-spaces. Using the representation theory of Ol’shanskiĭ semigroups the semigroup representations can be analytically extended
to the simply connected covering of SL(2,ℝ) where they can be identified as holomorphic discrete series representations.
To Karl Heinrich Hofmann on the occasion of his 75th birthday. 相似文献
9.
Sriram Balasubramanian 《Integral Equations and Operator Theory》2010,68(4):529-550
We prove a Carathéodory–Fejér type interpolation theorem for certain matrix convex sets in
\mathbbCd{\mathbb{C}^d} using the Blecher–Ruan–Sinclair characterization of abstract operator algebras. Our results generalize the work of Dmitry
S. Kalyuzhnyĭ-Verbovetzkiĭ for the d-dimensional non-commutative polydisc. 相似文献
10.
Helmut Abels 《Journal of Evolution Equations》2002,2(4):439-457
In this article we prove the existence of bounded purely imaginary powers of the Stokes operator , which is defined on the space of solenoidal vector fields < q < , where is an infinite layer. It is a consequence of a special representation of the resolvent of the Stokes operator in terms of
the Stokes operator on , a composition of a trace and a Poisson operator – a singular Green operator – and a negligible part. 相似文献
11.
Lorenzo Rosasco Silvia Villa Bằng Công Vũ 《Numerical Functional Analysis & Optimization》2017,38(5):602-626
In this article, we investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the stochastic extension to monotone inclusions of a proximal method studied in the literature for saddle point problems. It consists in a forward step determined by the stochastic evaluation of the cocoercive operator, a backward step in the dual variables involving the resolvent of the monotone operator, and an additional forward step using the stochastic evaluation of the cocoercive operator introduced in the first step. We prove weak almost sure convergence of the iterates by showing that the primal-dual sequence generated by the method is stochastic quasi-Fejér-monotone with respect to the set of zeros of the considered primal and dual inclusions. Additional results on ergodic convergence in expectation are considered for the special case of saddle point models. 相似文献
12.
S. Yu. Shustikov 《Mathematical Notes》2000,67(5):665-671
There exists a deep relationship between the nonexplosion conditions for Markov evolution in classical and quantum probability
theories. Both of these conditions are equivalent to the preservation of the unit operator (total probability) by a minimal
Markov semigroup. In this work, we study the Heisenberg evolution describing an interaction between the chain ofN two-level atoms andn-mode external Bose field, which was considered recently by J. Alli and J. Sewell. The unbounded generator of the Markov evolution
of observables acts in the von Neumann algebra. For the generator of a Markov semigroup, we prove a nonexplosion condition,
which is the operator analog of a similar condition suggested by R. Z. Khas’minski and later by T. Taniguchi for classical
stochastic processes. For the operator algebra situation, this condition ensures the uniqueness and conservativity of the
quantum dynamical semigroup describing the Markov evolution of a quantum system. In the regular case, the nonexplosion condition
establishes a one-to-one relation between the formal generator and the infinitesimal operator of the Markov semigroup.
Translated fromMatematicheskie Zemetki, Vol. 67, No. 5, pp. 788–796, May, 2000. 相似文献
13.
Jun Ling ZHOU Yan Xun CHANG 《数学学报(英文版)》2006,22(1):311-318
In this paper, we first define a doubly transitive resolvable idempotent quasigroup (DTRIQ), and show that aDTRIQ of order v exists if and only ifv ≡0(mod3) and v ≠ 2(mod4). Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang (J. Combin. Designs, 4 (1996), 301-321). As an application, we obtain an LRDTS(4·3^n) for any integer n ≥ 1, which provides an infinite family of even orders. 相似文献
14.
We solve the problem of the interaction of two quasimolecular electrons at an arbitrary distance from each other, i.e., near
different atoms (nuclei). We regard the interaction as a second-order effect of the quantum electrodynamic perturbation theory
in the coordinate representation. Taking the natural condition of the symmetry of the retardation factor, the electron spins,
and the effects of retardation of the relativistic interaction of the two quasimolecular electrons located near different
nuclei into account consistently, we obtain additional terms in the interelectron interaction operator compared with the standard
Breit operator.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 391–404, March, 2009. 相似文献
15.
In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii~erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly. 相似文献
16.
Andreas Rößler 《BIT Numerical Mathematics》2007,47(3):657-680
The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main
novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due
to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with
order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly.
AMS subject classification (2000) 65C30, 65L06, 60H35, 60H10 相似文献
17.
Mohan Joshi 《Proceedings Mathematical Sciences》1980,89(2):95-100
Let (Ω,B,μ) be ameasure space andX a separable Hubert space. LetT be a random operator from Ω ×X intoX. In this paper we investigate the measurability ofT
-1. In our main theorems we show that ifT is a separable random operator withT(w) almost sure invertible and monotone and demicontinuous thenT
-1is also a random operator. As an application of this we give an existence theorem for random Hammerstein operator equation. 相似文献
18.
During the last few years the authors have studied extensively the invariant subspace problem of positive operators; see [6] for a survey of this investigation. In [4] the authors introduced the class of compact-friendly operators and proved for them a general theorem on the existence of invariant subspaces. It was then asked if every positive operator is compact-friendly. In this note, we present an example of a positive operator which is not compact-friendly but which, nevertheless, has a non-trivial closed invariant subspace.In the process of presenting this example, we also characterize the multiplication operators that commute with non-zero finite-rank operators. We show, among other things, that a multiplication operator M
commutes with a non-zero finite-rank operator if and only the multiplier function is constant on some non-empty open set. 相似文献
19.
A class of bilinear stochastic partial differential equations is investigated using a semigroup approach. Existence of a mild solution is obtained by proving a maximal inequality for stochastic convolution integrals with a stochastic evolution operator U(t,s) as integrand; moreover, we show the existence of a regular version in t. Under an additional assumption we show the existence of a continuous version of U (.,.) in the space of bounded operators on the state space. Finally, we analyse a p.d.e. model of a simply supported beam to illustrate the applicability of our results to modelling uncertainty in large flexible space structures 相似文献
20.
AbstractIn this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration. 相似文献