Lie-trotter product formulas for nonlinear filtering

The nonlinear filtering problem for a diffusion process whose drift and diffusion coefficients depend parametrically on a finite-state jump process involves the solution of a vector system of linear, stochastic partial differential equations. A Lie-Trotter product formula is proven to hold for this system and a recursive implementation is discussed.     

Resolvents of cone pseudodifferential operators,asymptotic expansions and applications

We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the spectral parameter tends to infinity, and use it to derive corresponding heat trace and zeta function expansions as well as an analytic index formula.      

一类平面多项式微分系统赤道环量的代数递推公式

本文研究一类形式相当一般的平面多项式系统赤道环量(Gauss球面的无穷远点奇点量)的计算,建立了系统赤道环量计算的简明的线性代数递推公式.应用递推公式计算赤道环量,只需用系统系数做四则运算,避免了通常计算赤道环量需要的复杂的积分运算和解方程,极易用计算机代数系统作符号推导并且不含舍入误差.     

第一类双变量Chebyshev多项式的最小零偏差性质研究

利用Rivlin和Shapiro提出的符号理论,证明了文献[10]中提出的第一类双变量Chebyshev多项式恰为所谓的Steiner区域上具有特殊首项的最小零偏差多项式,并由此导出了几类具有一定代数精度的数值积分公式.     

On the relaxation time of Gauss's continued-fraction map I. The Hilbert space approach (Koopmanism)

It is shown thatU ^*, the adjoint of Koopman's isometric operatorUf(x) =f(Tx) corresponding to the mapTx=x ^–1 (mod 1) of the unit interval, is isomorphic to a symmetric integral operator when restricted to a Hilbert space of holomorphic functionsf This result, also obtained by Babenko in a different setting, allows us to derive new trace formulas. Using generalized Temple's inequalities, we determine the relaxation time of the above system with great accuracy. In contrast to a widespread belief, it appears to be unrelated to the entropy of the mapT.     

Support functions and integral formulas in the Lorentzian plane

In the Lorentzian plane, the support function of a closed convex curve is not a periodic one. We redefine this concept and the envelope of a families of lines. Using these, we prove integral formulas in the Crofton's style for convex sets in the Lorentzian plane. Received 10 February 2000.     

Calabi-Yau 4-folds and toric fibrations

We present a general scheme for identifying fibrations in the framework of toric geometry and provide a large list of weights for Calabi-Yau 4-folds. We find 914 164 weights with degree d ≤ 150 whose maximal Newton polyhedra are reflexive and 525 572 weights with degree d ≤ 4000 that give rise to weighted projective spaces such that the polynomial defining a hypersurface of trivial canonical class is transversal. We compute all Hodge numbers, using Batyrev's formulas (derived by toric methods) for the first and Vafa's formulas (obtained by counting of Ramond ground states in N = 2 LG models) for the latter class, checking their consistency for the 109 308 weights in the overlap. Fibrations of k-folds, including the elliptic case, manifest themselves in the N lattice in the following simple way: The polyhedron corresponding to the fiber is a subpolyhedron of that corresponding to the k-fold, whereas the fan determining the base is a linear projection of the fan corresponding to the k-fold.     

一阶模糊谓词逻辑公式的解释模型真度理论及其应用

基于一阶模糊谓词逻辑公式的有限和可数解释真度的理论,引入了一阶模糊谓词逻辑公式的解释模型及解释模型真度的概念,并讨论了它们的一系列性质及其在近似推理中的应用.