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991.
We derive trace formulas for a pair of self-adjoint operators and H under the assumption that is in a Schatten class. This extends the trace formulas of [8], where V alone is assumed to be in a Schatten class. Our trace formulas apply, in particular, in the setting of differential operators and are based on Taylor-like approximations of operator functions. This significantly improves non-Taylor based trace formulas of [10]. 相似文献
992.
In this paper, the structure of locally finite groups of infinite rank whose subgroups of infinite rank are permutable in a subgroup of finite index is investigated. 相似文献
993.
We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy’s Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke’s identity in the case of quivers \({\mathcal {Q}}\) of Dynkin type A. Our identity is stated in terms of the lacing diagrams of S. Abeasis–A. Del Fra, which parameterize orbits of the representation space of \({\mathcal {Q}}\) for a fixed dimension vector. 相似文献
994.
The space of real Borel measures \(\mathcal {M}(S)\) on a metric space S under the flat norm (dual bounded Lipschitz norm), ordered by the cone \(\mathcal {M}_+(S)\) of nonnegative measures, is considered from an ordered normed vector space perspective in order to apply the well-developed theory of this area. The flat norm is considered in place of the variation norm because subsets of \(\mathcal {M}_+(S)\) are compact and semiflows on \(\mathcal {M}_+(S)\) are continuous under much weaker conditions. In turn, the flat norm offers new challenges because \(\mathcal {M}(S)\) is rarely complete and \(\mathcal {M}_+(S)\) is only complete if S is complete. As illustrations serve the eigenvalue problem for bounded additive and order-preserving homogeneous maps on \(\mathcal {M}_+(S)\) and continuous semiflows. Both topics prepare for a dynamical systems theory on \(\mathcal {M}_+(S)\). 相似文献
995.
996.
Jonathan M. Borwein Scott B. Lindstrom Brailey Sims Anna Schneider Matthew P. Skerritt 《Set-Valued and Variational Analysis》2018,26(2):385-403
We expand upon previous work that examined the behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations:that of a line and an ellipse and that of a line together with a p-sphere. With computer assistance we discover a beautiful geometry that illustrates phenomena which may affect the behavior of the iterates by slowing or inhibiting convergence for feasible cases. We prove local convergence near feasible points, and—seeking a better understanding of the behavior—we employ parallelization in order to study behavior graphically. Motivated by the computer-assisted discoveries, we prove a result about behavior of the method in infeasible cases. 相似文献
997.
In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h→0.We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenterqh(t) satisfies the equation
998.
Marco D’Anna Carmelo A. Finocchiaro Marco Fontana 《Journal of Pure and Applied Algebra》2010,214(9):1633-1641
Let f:A→B be a ring homomorphism and let J be an ideal of B. In this paper, we study the amalgamation of A with B along J with respect to f (denoted by A?fJ), a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied by D’Anna and Fontana in 2007, and other classical constructions (such as the A+XB[X], the A+XB?X? and the D+M constructions). In particular, we completely describe the prime spectrum of the amalgamated duplication and we give bounds for its Krull dimension. 相似文献
999.
We formulate a fractional stochastic oscillation equation as a generalization of Bagley’s fractional differential equation. We do this in analogy with the case for Basset’s equation, which gives rise to fractional stochastic relaxation equations. We analyze solutions under some conditions of spatial regularity of the operators considered. 相似文献
1000.
Let β be a standard Brownian motion, let X be an α-stable process, and let f=[^(m)]f=\widehat \mu be the Fourier transform of a discrete measure. It is shown that weakly in C([0, + ∞ )),
$ \eta ^{\alpha /2} \int_0^t f(\eta X_s)\text{d}s \Rightarrow \sqrt{C_{f,\alpha}}\beta_t\qquad \text{as $ \eta ^{\alpha /2} \int_0^t f(\eta X_s)\text{d}s \Rightarrow \sqrt{C_{f,\alpha}}\beta_t\qquad \text{as 相似文献 |