SEMI-LINEAR SYSTEMS OF BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN $R^n$

This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.     

Solving the Simple Plant Location Problem using a Data Correcting Approach

The Data Correcting Algorithm is a branch and bound type algorithm in which the data of a given problem instance is `corrected' at each branching in such a way that the new instance will be as close as possible to a polynomially solvable instance and the result satisfies an acceptable accuracy (the difference between optimal and current solution). In this paper the data correcting algorithm is applied to determining exact and approximate optimal solutions to the simple plant location problem. Implementations of the algorithm are based on a pseudo-Boolean representation of the goal function of this problem, and a new reduction rule. We study the efficiency of the data correcting approach using two different bounds, the Khachaturov-Minoux bound and the Erlenkotter bound. We present computational results on several benchmark instances, which confirm the efficiency of the data-correcting approach.     

Problem of invariant subspaces in C*-algebras

Let A be a separable simple C*-algebra. For each a(≠0) in A, there exists a separable faithful and irreducible * representation (π, Hπ) on A such that π(a) has a non-trivial invariant subspace in Hπ.     

关于H．Yao－D．Knuth定理

本文研究一类有限连分数展开的部分商数之平均和。所得结果改进了这方面已有的最好工作。     

r-Matrix Structure for a Restricted Flow with Bargmann Constraint

This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R^2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure.     

具有平行平均曲率向量的子流形的二次表示

本文证明了具有平行平均曲率向量的子流形的二次表示不可能是零２型的，以及若具有平行平均曲率向量的ａ－子流形的二次表示是２－型的，则它的数量曲率必为常数．     

On Shioda-Inose structures of one-parameter families of K3 surfaces

We develop an algorithm to determine a one-parameter family of elliptic curves associated to a one-parameter family of K3 surfaces with generic Picard number 19 by a Shioda-Inose structure. The family of elliptic curves is determined up to an isomorphism and an isogeny. An application to a generalized congruence number problem is also discussed.     

Decomposition of Marsden–Weinstein Reductions for Representations of Quivers

We decompose the Marsden–Weinstein reductions for the moment map associated to representations of a quiver. The decomposition involves symmetric products of deformations of Kleinian singularities, as well as other terms. As a corollary we deduce that the Marsden–Weinstein reductions are irreducible varieties.     

Electron crystallization using localized representation

The character of the ground state of the electron crystal—an electron gas with periodic density and/or spin density is investigated. Calculations for non-magnetic, ferromagnetic and anti-ferromagnetic electron crystals based on the Koster-Kohn variational principle for direct calculation of Wannier functions are presented. The Wannier function is approximated by a symmetrically orthonormalized Gaussian. The orbital exponent of the Gaussian is used as a variational parameter. The effect of the positive background is suitably taken into account. The results of our calculation support Wigner’s prediction of electron crystallization.     

Local rings of countable Cohen-Macaulay type

We prove (the excellent case of) Schreyer's conjecture that a local ring with countable CM type has at most a one-dimensional singular locus. Furthermore, we prove that the localization of a Cohen-Macaulay local ring of countable CM type is again of countable CM type.