Residual Finiteness of Finitely Generated Quasi-commutative Semigroups

A semigroup S is called residually finite if for any pair of distinct elements a,b∈S, there exists a congruence P on S such that S/p is finite and (a,b) P. In1958, Malcev proved the following theorem: Any finitely generated abelian semigroupis residually finite . In this paper,we prove that a finitely generated quasi-commu-tative semigroup is residually finite. It generalizes the above theorem.     

The Vector Epsilon Algorithm – a Residual Approach

We present an alternative to the vector -algorithm based on vector continued fractions and which is applicable when the sequence to be accelerated is generated by a one-point iteration function. These fractions are constructed in the language of Clifford algebras, which allow three-term recurrence relations. The new algorithm evidently has considerably greater numerical precision than the old one. Results from numerical experiments are reported.     

On Shemetkov’s Theorem About The Complementedness of the Residual

A formation F of finite groups is called a GWP-formation if the F-residual of the group generated by two F-subnormal subgroups is the subgroup generated by their F-residuals. The main aim of the article is to find some sufficient conditions for a finite group to split over its F-residual.     

On Using Hölder Norms in the Quasi-Minimal Residual Approach

Given a process to span a basis for the underlying Krylov subspaces, the quasi-minimal residual (QMR-)approach is often used to derive iterative methods for the solution of linear systems. The QMR-approach is only reasonable if the resulting methods are based on short recurrences. The key ingredient of the QMR-approach is the efficient solution of a sequence of least-squares problems by computing the QR decomposition of an upper Hessenberg matrix by means of Givens rotations. Since (Hölder) p-norms are not unitarily invariant, a generalization of the minimization problem from the Euclidean norm to general p-norms while still leading to methods based on short recurrences appeared infeasible. Here, it is shown that this generalization is possible if the upper Hessenberg matrix reduces to a lower bidiagonal matrix.This revised version was published online in October 2005 with corrections to the Cover Date.     

A Minimum Residual Based Gradient Iterative Method for a Class of Matrix Equations

In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and err...     

The Proportional Mean Residual Life Regression Model with Cure Fraction and Auxiliary Covariate

As biological studies become more expensive to conduct, it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured. In this paper, we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate, in which the exposure variable is only assessed in a validation set, but a corresponding continuous auxiliary covariate...     

Are You Normal? The Problem of Confounded Residual Structures in Hierarchical Linear Models

We encounter hierarchical data structures in a wide range of applications. Regular linear models are extended by random effects to address correlation between observations in the same group. Inference for random effects is sensitive to distributional misspecifications of the model, making checks for (distributional) assumptions particularly important. The investigation of residual structures is complicated by the presence of different levels and corresponding dependencies. Ignoring these dependencies leads to erroneous conclusions using our familiar tools, such as Q–Q plots or normal tests. We first show the extent of the problem, then we introduce the fraction of confounding as a measure of the level of confounding in a model and finally introduce rotated random effects as a solution to assessing distributional model assumptions. This article has supplementary materials online.     

Residual saturated porous media – from oscillating water blobs to waves in ground earth

A model for wave propagation in residual saturated porous media is presented distinguishing enclosed fluid clusters with respect to their eigenfrequency and damping properties. The additional micro-structure information of cluster specific damping is preserved during the formal upscaling process and allows a stronger coupling between micro- and macro-scale than characterisation via eigenfrequencies alone. A numerical example of sandstone filled with air and liquid clusters of different eigenfrequency and damping distributions is given. If energy dissipation due to viscous damping dominates energy storage due to cluster oscillations, the damping distribution is more influential than the eigenfrequency distribution and vice versa. Spreading the damping distribution around a constant mean value supported the effect of capillary forces and spreading the eigenfrequency distribution around a constant mean value supported the effect of viscous damping in the investigated samples. For a wide distribution of the liquid clusters' damping properties, two damping mechanisms of propagating waves occur at the same time: damping due to viscous effects (for highly damped clusters) and energy storage by cluster oscillations (for underdamped clusters). (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Residual Smoothing Techniques: Do They Improve the Limiting Accuracy of Iterative Solvers?

Many iterative methods for solving linear systems, in particular the biconjugate gradient (BiCG) method and its squared version CGS (or BiCGS), produce often residuals whose norms decrease far from monotonously, but fluctuate rather strongly. Large intermediate residuals are known to reduce the ultimately attainable accuracy of the method, unless special measures are taken to counteract this effect. One measure that has been suggested is residual smoothing: by application of simple recurrences, the iterates x _n and the corresponding residuals r _n : b – Ax _n are replaced by smoothed iterates y _n and corresponding residuals s _n : b– Ay _n. We address the question whether the smoothed residuals can ultimately become markedly smaller than the primary ones. To investigate this, we present a roundoff error analysis of the smoothing algorithms. It shows that the ultimately attainable accuracy of the smoothed iterates, measured in the norm of the corresponding residuals, is, in general, not higher than that of the primary iterates. Nevertheless, smoothing can be used to produce certain residuals, most notably those of the minimum residual method, with higher attainable accuracy than by other frequently used algorithms.     

An Electrocardiogram Signal Classification Algorithm Based on Improved Deep Residual Shrinkage Networks北大核心CSCD

心电信号分类是医疗保健领域的重要研究内容.针对大多数方法不能很好地降低样本数量少的类别漏诊率,以及降低预处理操作的复杂性问题,提出了一种基于改进深度残差收缩网络(IDRSN)的心电信号分类算法(即DRSL算法).首先,使用合成少数类过采样技术(SMOTE)扩充数量少的类别样本,从而解决了类不平衡问题;其次,利用改进深度残差收缩网络提取空间特征,其残差模块可以避免网络层加深造成的过拟合,压缩激励和软阈值化子网络可以提取重要局部特征并自动去除噪声;然后,通过长短期记忆网络(LSTM)提取时间特征;最后,利用全连接网络输出分类结果.在MIT-BIH心律失常数据集上的实验结果表明,该算法的分类性能优于IDRSN、DRSN、GAN+2DCNN、CNN+LSTM_ATTENTION、SE-CNN-LSTM分类算法.     

Residual symmetry,nth Bäcklund transformation,and soliton-cnoidal wave interaction solution for the combined modified KdV–negative-order modified KdV equation

This paper is concerned with the nth Bäcklund transformation (BT) related to multiple residual symmetries and soliton-cnoidal wave interaction solution for the combined modified KdV–negative-order modified KdV (mKdV-nmKdV) equation. The residual symmetry derived from the truncated Painlevé expansion can be extended to the multiple residual symmetries, which can be localized to Lie point symmetries by prolonging the combined mKdV-nmKdV equation to a larger system. The corresponding finite symmetry transformation, ie, nth BT, is presented in determinant form. As a result, new multiple singular soliton solutions can be obtained from known ones. We prove that the combined mKdV-nmKdV equation is integrable, possessing the second-order Lax pair and consistent Riccati expansion (CRE) property. Furthermore, we derive the exact soliton and soliton-cnoidal wave interaction solutions by applying the nonauto-BT obtained from the CRE method.