in the present paper, the concepts of module (uniform) approximate amenability and contractibility of banach algebras that are modules over another banach algebra, are introduced. the general theory is developed and some hereditary properties are given. in analogy with the banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...

In this paper, a new fractional physics-informed neural networks (fPINNs) is proposed, which combines fPINNs with spectral collocation method to solve the time-fractional phase field models. Compared fPINNs, it has large representation capacity due property of method, reduces number approximate points discrete operators, improves training efficiency and higher error accuracy. Unlike traditional...

We present a product representation of belief spaces for planning under partial observability. In earlier work we investigated backward plan construction based on a combination operation for belief states. The main problem in explicit construction of belief states is their high number. To remedy this problem, we refrain from representing individual belief states explicitly, and instead represen...

Sparse approximate inverses' usefulness in a parallel environment has motivated much interest in recent years. However, the superior capability of an approximate inverse in eliminating the local error has not yet been fully exploited in multi-grid algorithms. We propose a new class of sparse approximate inverse smoothers in this paper and present their analytic smoothing factors for constant co...

One of the basic probabilistic tools used for time series modeling is the hidden Markov model (HMM). In an HMM, information about the past of the time series is conveyed through a single discrete variable|the hidden state. We present a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. Both inference and lea...

The high computational cost involved in modeling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve a new large set of linear equations every time a new lattice bond is broken. To address this problem, we propose an algorithm that combines the multiple-rank sparse Cholesky downdating algorithm with the rank-p inverse updating algori...

We investigate the use of the multistep successive preconditioning strategies (MSP) to construct a class of parallel multilevel sparse approximate inverse (SAI) preconditioners. We do not use independent set ordering, but a diagonal dominance based matrix permutation to build a multilevel structure. The purpose of introducing multilevel structure into SAI is to enhance the robustness of SAI for...

A new framework for analyzing Fejér convergent algorithms is presented. Using this framework we define a very general class of Fejér convergent algorithms and establish its convergence properties. We also introduce a new definition of approximations of resolvents which preserve some useful features of the exact resolvent, and use this concept to present an unifying view of the Forward-Backward ...