On Rational Bases of Subspaces of F((D))~n

ＯｎＲａｔｉｏｎａｌＢａｓｅｓｏｆＳｕｂｓｐａｃｅｓｏｆＦ（（Ｄ））~ｎＷａｎＺｈｅｘｉａｎ（万哲先）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ，１０００８０ａｎｄＤｅｐａｒ?..     

K-Convergent Sequences in Topological Vector Spaces with a Basis

Ｋ┐ＣｏｎｖｅｒｇｅｎｔＳｅｑｕｅｎｃｅｓｉｎＴｏｐｏｌｏｇｉｃａｌＶｅｃｔｏｒＳｐａｃｅｓｗｉｔｈａＢａｓｉｓ＊）ＷｕＪｕｎｄｅ（武俊德）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＤａｑｉｎｇＰｅｔｒｏｌｅｕｍＩｎｓｔｉｔｕｔｅ，Ａｎｄａ，...     

On the Convergence of Iterative Difference Method with Nonuniform Meshes for Quasilinear Parabolic Systems

ＯｎｔｈｅＣｏｎｖｅｒｇｅｎｃｅｏｆＩｔｅｒａｔｉｖｅＤｉｆｆｅｒｅｎｃｅＭｅｔｈｏｄｗｉｔｈＮｏｎｕｎｉｆｏｒｍＭｅｓｈｅｓｆｏｒＱｕａｓｉｌｉｎｅａｒ　Ｐａｒａｂｏｌｉｃ　Ｓｙｓｔｅｍｓ（周毓麟）（沈隆钧）（袁光伟）ＺｈｏｕＹｕｌｉｎ；ＳｈｅｎＬ...     

On the Convergence of Iterative Difference Schemes with Nonuniform Meshes for Nonlinear Parabolic Systems

ＯｎｔｈｅＣｏｎｖｅｒｇｅｎｃｅｏｆＩｔｅｒａｔｉｖｅＤｉｆｆｅｒｅｎｃｅＳｃｈｅｍｅｓｗｉｔｈＮｏｎｕｎｉｆｏｒｍＭｅｓｈｅｓｆｏｒＮｏｎｌｉｎｅａｒＰａｒａｂｏｌｉｃＳｙｓｔｅｍｓ￥（周毓麟）（沈隆钧）（袁光伟）ＺｈｏｕＹｕｌｉｎ；ＳｈｅｎＬｏｎ...     

Bounds for Determinants of Quaternion Matrices

ＢｏｕｎｄｓｆｏｒＤｅｔｅｒｍｉｎａｎｔｓｏｆＱｕａｔｅｒｎｉｏｎＭａｔｒｉｃｅｓＨｕａｎｇＬｉｐｉｎｇ（黄礼平）（Ｄｅｐｔ．ｏｆＢａｓｉｃＳｃｉｅｎｃｅｓ，ＸｉａｎｇｔａｎＭｉｎｉｎｇＩｎｓｔｉｔｕｔｅ，Ｘｉａｎｇｔａｎ，４１１２０１）ＣａｉＹｏｎ...     

k－spaces and Products of Spaces with σ－hereditarily Closure－Preserving k－networks

ｋ－ｓｐａｃｅｓａｎｄＰｒｏｄｕｃｔｓｏｆＳｐａｃｅｓｗｉｔｈσ－ｈｅｒｅｄｉｔａｒｉｌｙＣｌｏｓｕｒｅ－Ｐｒｅｓｅｒｖｉｎｇｋ－ｎｅｔｗｏｒｋｓ￥ＤａｉＭｕｍｉｎ（戴牧民）ＬｉｕＣｈｕａｎ（戴牧民）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＧ...     

Coefficient Invariants of Conway Polynomial

ＣｏｅｆｆｉｃｉｅｎｔＩｎｖａｒｉａｎｔｓｏｆＣｏｎｗａｙＰｏｌｙｎｏｍｉａｌＷｕＨｕａａｎ（吴华安）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＣｏｕｒｓｅｓ，ＷｕｈａｎＴｒａｎｓｐｏｒｔａｔｉｏｎＵｎｉｖｅｒｓｉｔｙ）ＧｅＸｉｎｔｏｎｇ（葛新同）（Ｓｈａ...     

WELL-BEHAVED BASIS AND LR ARRAYS

ＷＥＬＬ－ＢＥＨＡＶＥＤＢＡＳＩＳＡＮＤＬＲＡＲＲＡＹＳＬＩＮＤＯＮＧＤＡＩ（林东岱）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

Necessary and Sufficient Condition for Generalized Diagonal Dominance Matrices

ＮｅｃｅｓｓａｒｙａｎｄＳｕｆｆｉｃｉｅｎｔＣｏｎｄｉｔｉｏｎｆｏｒＧｅｎｅｒａｌｉｚｅｄＤｉａｇｏｎａｌＤｏｍｉｎａｎｃｅＭａｔｒｉｃｅｓＹａｎｇＹｉｍｉｎ（杨益民）（ＡｎｈｕｉＭｅｃｈａｎｉｃａｌａｎｄＥｌｅｃｔｒｏｎｉｃＣｏｌｌｅｇｅ，Ｗｕｈｕ...     

The Spectral Pictures of Completely Irreducible Operators and Decomposition Theorem Of Hilbert Space Operators

ＴｈｅＳｐｅｃｔｒａｌＰｉｃｔｕｒｅｓｏｆＣｏｍｐｌｅｔｅｌｙＩｒｒｅｄｕｃｉｂｌｅＯｐｅｒａｔｏｒｓａｎｄＤｅｃｏｍｐｏｓｉｔｉｏｎＴｈｅｏｒｅｍｏｆＨｉｌｂｅｒｔＳｐａｃｅＯｐｅｒａｔｏｒｓ￥ＪｉａｎｇＣｈｕｎｌａｎ（蒋春澜）（Ｄｅｐａｒｔｍｅｎ...     

On reflected Dirichlet spaces

Summary Reflecting diffusion processes on smooth domains in Euclidean space are well understood. Silverstein in [22] and [23] developed two variant procedures for constructing the reflected processes for a general class of symmetric Hunt processes from a Dirichlet space point of view. A direct approach is given in this paper and these two variant procedures are shown to yield the same result. Only the techniques of martingales and ordinary Markov processes are used.     

Intrinsic ultracontractivity and small perturbation for one-dimensional generalized diffusion operators

We consider a one-dimensional generalized diffusion operator G on an open interval which is not necessarily bounded. We characterize [SP] (i.e., 1 is a small perturbation of the operator G) in terms of the classification of the boundary points from the view point of diffusion processes and give a sufficient condition for [IU] (i.e., the associated heat kernel is intrinsically ultracontractive).     

Principal eigenvalues and equilibrium states corresponding to weakly coupled parabolic systems of PDE

This paper extends the theory from [K2] to some weakly coupled parabolic systems of PDE which generate Markov processes with switching at random times between a finite number of diffusion processes. Dedicated to Professor Shmuel Agmon Partially supported by the US-Israel Binational Science Foundation.     

Exponential integrability of Itô's processes

In this note we prove the exponential integrability of super-norms of general Itô's processes under certain assumptions, and then apply it to the diffusion processes determined by stochastic differential equations. In particular, a conjecture in [Y. Hu, Exponential integrability of diffusion processes, in: Contemp. Math., vol. 234, 1999, pp. 75-84] is solved.     

Infinite-dimensional diffusion processes as gibbs measures onC[0,1]^{Z^d }

Summary An infinite lattice system of interacting diffusion processes is characterized as a Gibbs distribution on with continuous local conditional probabilities. Using estimates for the Vasserstein metric onC[0, 1], Dobrushin's contraction technique is applied in order to obtain information about macroscopic properties of the entire diffusion process.     

The stability of stochastic partial differential equations II

We prove general results on stability (in finite time intervals) of SPDEs (stochastic partial differential equations) with unbounded coefficients, with respect to the simultaneous perturbations of the driving semimartingales, of all data, and of the underlying probability space. Hence we derive support theorems for SPDEs (with unbounded coefficients). In particular, we get theorems on supports and theorems on robustness for the nonlinear filter of diffusion processes with unbounded drift and diffusion coefficients. (The above results were proved in the case of bounded coefficients in our earlier papers [4] and [5].) Finally we treat an application in a problem of kinematic dynamo     

Grandes deviations des diffusions sur les espaces de besov-orlicz et application

Dans cet article nous demontrons le principe de grandes déviations de Freidlin et Wentzeii pour les diffusions suivant la topologie de l'espace de Besov-Orlicz. Nous étendons ainsi le résultat de Ben Arous et Ledoux [3] concernant le cas höldérien et celui de Roynetie [16] tiaitant le cas du mouvement brownien en norrne de Besov Comme application on établit la loi fonctionnelle du Logarithme itéré de Strassen pour l'aire de Lévy en norme de Besov-Orlicz. Cette loi est plus fine que celle obtenue par N'zi et Eddahbi [14] avec la norme Hölderienne

In this paper, we prove a Freidlin-Wentzell large deviations principle in Besov-Orlicz space for diffusion processes. Our result is an extension of that of Ben-Arous and Ledoux [3] who have treated the Hölder norm case and that of Roynette [16] who have considered Brownian motion in Besov space. As an application, we establish a Strassen's law of the iterated logarithm for Lévy's area process. This law is more sharper than the one in Hölder norm obtained by N'zi and Eddahbi [14]     

A maximal inequality for stochastic convolution integrals on hilbert spaces and space-time regularity of linear stochastic partial differential equations

We consider optimal control problems for one-dimensional diffusion processes [ILM0001] where the control processes υ_t are increasing, positive, and adapted. Several types of expected cost structures associated with each policy υ(.) are adopted, e.g. discounted cost, long term average cost and time average cost. Our work is related to [2,6,12,14,16 and 21], where diffusions are allowed to evolve in the whole space, and to [13] and [20], where diffusions evolve only in bounded regions. We shall present some analytic results about value functions, mainly their characterizations, by simple dynamic programming arguments. Several simple examples are explicitly solved to illustrate the singular behaviour of our problems.     

A ternary phase bi-scale FE-model for diffusion-driven dendritic alloy solidification processes

It is of high interest to describe alloy solidification processes with numerical simulations. In order to predict the material behavior as precisely as possible, a ternary phase, bi-scale numerical model will be presented. This paper is based on a coupled thermo-mechanical, two-phase, two-scale finite element model developed by Moj et al. [2], where the theory of porous media (TPM) [1] has been used. Finite plasticity extended by secondary power-law creep is utilized to describe the solid phase and linear visco-elasticity with Darcy's law of permeability for the liquid phase, respectively. Here, the microscopic, temperature-driven phase transition approach is replaced by the diffusion-driven 0D model according to Wang and Beckermann [3]. The decisive material properties during solidification are captured by phenomenological formulations for dendritic growth and solute diffusion processes. A columnar as well as an equiaxial solidification example will be shown to demonstrate the principal performance of the presented model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of the drift coefficient parameter in diffusion processes

The article considers the bias and the mean-square error of the maximum likelihood estimate of the drift coefficient parameter in diffusion processes. Weaker conditions than those in [1] are derived.