As a generalization of -skew McCoy rings, we introduce the concept of -skew -McCoy rings, and we study the relationships with another two new generalizations, -skew -McCoy rings and -skew -McCoy rings, observing the relations with -skew McCoy rings, -McCoy rings, -skew Armendariz rings, -regular rings, and other kinds of rings. Also, we investigate conditions such that -skew -McCoy rings imply -skew -McCoy rings and -skew -McCoy rings. We show that in the case where is a nonreduced ring, if is 2-primal, then is an -skew -McCoy ring. And, let be a weak ()-compatible ring; if is an -skew -McCoy ring, then is -skew -McCoy.
{"title":"-Skew -McCoy Rings","authors":"Areej M. Abduldaim, Sheng Chen","doi":"10.1155/2013/309392","DOIUrl":"https://doi.org/10.1155/2013/309392","url":null,"abstract":"As a generalization of -skew McCoy rings, we introduce the concept of -skew -McCoy rings, and we study the relationships with another two new generalizations, -skew -McCoy rings and -skew -McCoy rings, observing the relations with -skew McCoy rings, -McCoy rings, -skew Armendariz rings, -regular rings, and other kinds of rings. Also, we investigate conditions such that -skew -McCoy rings imply -skew -McCoy rings and -skew -McCoy rings. We show that in the case where is a nonreduced ring, if is 2-primal, then is an -skew -McCoy ring. And, let be a weak ()-compatible ring; if is an -skew -McCoy ring, then is -skew -McCoy.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/309392","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64404892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hang Joon Jo, Stephen J Gotts, Richard C Reynolds, Peter A Bandettini, Alex Martin, Robert W Cox, Ziad S Saad
Artifactual sources of resting-state (RS) FMRI can originate from head motion, physiology, and hardware. Of these sources, motion has received considerable attention and was found to induce corrupting effects by differentially biasing correlations between regions depending on their distance. Numerous corrective approaches have relied on the identification and censoring of high-motion time points and the use of the brain-wide average time series as a nuisance regressor to which the data are orthogonalized (Global Signal Regression, GSReg). We first replicate the previously reported head-motion bias on correlation coefficients using data generously contributed by Power et al. (2012). We then show that while motion can be the source of artifact in correlations, the distance-dependent bias-taken to be a manifestation of the motion effect on correlation-is exacerbated by the use of GSReg. Put differently, correlation estimates obtained after GSReg are more susceptible to the presence of motion and by extension to the levels of censoring. More generally, the effect of motion on correlation estimates depends on the preprocessing steps leading to the correlation estimate, with certain approaches performing markedly worse than others. For this purpose, we consider various models for RS FMRI preprocessing and show that WMeLOCAL, as subset of the ANATICOR discussed by Jo et al. (2010), denoising approach results in minimal sensitivity to motion and reduces by extension the dependence of correlation results on censoring.
{"title":"Effective Preprocessing Procedures Virtually Eliminate Distance-Dependent Motion Artifacts in Resting State FMRI.","authors":"Hang Joon Jo, Stephen J Gotts, Richard C Reynolds, Peter A Bandettini, Alex Martin, Robert W Cox, Ziad S Saad","doi":"10.1155/2013/935154","DOIUrl":"https://doi.org/10.1155/2013/935154","url":null,"abstract":"<p><p>Artifactual sources of resting-state (RS) FMRI can originate from head motion, physiology, and hardware. Of these sources, motion has received considerable attention and was found to induce corrupting effects by differentially biasing correlations between regions depending on their distance. Numerous corrective approaches have relied on the identification and censoring of high-motion time points and the use of the brain-wide average time series as a nuisance regressor to which the data are orthogonalized (Global Signal Regression, GSReg). We first replicate the previously reported head-motion bias on correlation coefficients using data generously contributed by Power et al. (2012). We then show that while motion can be the source of artifact in correlations, the distance-dependent bias-taken to be a manifestation of the motion effect on correlation-is exacerbated by the use of GSReg. Put differently, correlation estimates obtained after GSReg are more susceptible to the presence of motion and by extension to the levels of censoring. More generally, the effect of motion on correlation estimates depends on the preprocessing steps leading to the correlation estimate, with certain approaches performing markedly worse than others. For this purpose, we consider various models for RS FMRI preprocessing and show that WMe<sub>LOCAL</sub>, as subset of the ANATICOR discussed by Jo et al. (2010), denoising approach results in minimal sensitivity to motion and reduces by extension the dependence of correlation results on censoring.</p>","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/935154","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32021708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a novel method named as splitting matching pursuit (SMP) is proposed to reconstruct -sparse signal in compressed sensing. The proposed method selects largest components of the correlation vector , which are divided into split sets with equal length . The searching area is thus expanded to incorporate more candidate components, which increases the probability of finding the true components at one iteration. The proposed method does not require the sparsity level to be known in prior. The Merging, Estimation and Pruning steps are carried out for each split set independently, which makes it especially suitable for parallel computation. The proposed SMP method is then extended to more practical condition, e.g. the direction of arrival (DOA) estimation problem in phased array radar system using compressed sensing. Numerical simulations show that the proposed method succeeds in identifying multiple targets in a sparse radar scene, outperforming other OMP-type methods. The proposed method also obtains more precise estimation of DOA angle using one snapshot compared with the traditional estimation methods such as Capon, APES (amplitude and phase estimation) and GLRT (generalized likelihood ratio test) based on hundreds of snapshots.
{"title":"Splitting Matching Pursuit Method for Reconstructing Sparse Signal in Compressed Sensing","authors":"L. Jing, Chong-Zhao Han, Xianghua Yao, Lian Feng","doi":"10.1155/2013/804640","DOIUrl":"https://doi.org/10.1155/2013/804640","url":null,"abstract":"In this paper, a novel method named as splitting matching pursuit (SMP) is proposed to reconstruct -sparse \u0000signal in compressed sensing. The proposed method selects largest components of the correlation \u0000vector , which are divided into split sets with equal length . The searching area is thus expanded to incorporate \u0000more candidate components, which increases the probability of finding the true components at one iteration. The \u0000proposed method does not require the sparsity level to be known in prior. The Merging, Estimation and Pruning \u0000steps are carried out for each split set independently, which makes it especially suitable for parallel computation. The \u0000proposed SMP method is then extended to more practical condition, e.g. the direction of arrival (DOA) estimation \u0000problem in phased array radar system using compressed sensing. Numerical simulations show that the proposed \u0000method succeeds in identifying multiple targets in a sparse radar scene, outperforming other OMP-type methods. \u0000The proposed method also obtains more precise estimation of DOA angle using one snapshot compared with the \u0000traditional estimation methods such as Capon, APES (amplitude and phase estimation) and GLRT (generalized \u0000likelihood ratio test) based on hundreds of snapshots.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/804640","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64260980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level-set method in some interesting inverse problems arising in elliptic PDE models.
{"title":"On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients","authors":"A. Cezaro","doi":"10.1155/2013/123643","DOIUrl":"https://doi.org/10.1155/2013/123643","url":null,"abstract":"We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level-set method in some interesting inverse problems arising in elliptic PDE models.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/123643","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64375058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a new class of mathematical structures called(m,n)-semirings(which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for(m,n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an(m,n)-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered(m,n)-semiring.
{"title":"(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems","authors":"Syed Eqbal Alam, Shrisha Rao, B. Davvaz","doi":"10.1155/2013/482391","DOIUrl":"https://doi.org/10.1155/2013/482391","url":null,"abstract":"We propose a new class of mathematical structures called(m,n)-semirings(which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for(m,n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an(m,n)-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered(m,n)-semiring.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/482391","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64426025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is devoted to metric subregularity of a kind of generalized constraint equations. In particular, in terms of coderivatives and normal cones, we provide some necessary and sufficient conditions for subsmooth generalized constraint equations to be metrically subregular and strongly metrically subregular in general Banach spaces and Asplund spaces, respectively.
{"title":"Metric Subregularity for Subsmooth Generalized Constraint Equations in Banach Spaces","authors":"Qinghai He, Ji Yang, Binbin Zhang","doi":"10.1155/2012/185249","DOIUrl":"https://doi.org/10.1155/2012/185249","url":null,"abstract":"This paper is devoted to metric subregularity of a kind of generalized constraint equations. In particular, in terms of coderivatives and normal cones, we provide some necessary and sufficient conditions for subsmooth generalized constraint equations to be metrically subregular and strongly metrically subregular in general Banach spaces and Asplund spaces, respectively.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2012/185249","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64300324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main aim of this paper is to discuss moment exponential stability for a stochastic reaction-diffusion neural network with time-varying delays and p-Laplacian. Using the Ito formula, a delay differential inequality and the characteristics of the neural network, the algebraic conditions for the moment exponential stability of the nonconstant equilibrium solution are derived. An example is also given for illustration.
{"title":"Stability of the Stochastic Reaction-Diffusion Neural Network with Time-Varying Delays and p-Laplacian","authors":"Pan Qingfei, Zhang Zi-fang, Huang Jingchang","doi":"10.1155/2012/405939","DOIUrl":"https://doi.org/10.1155/2012/405939","url":null,"abstract":"The main aim of this paper is to discuss moment exponential stability for a stochastic reaction-diffusion neural network with time-varying delays and p-Laplacian. Using the Ito formula, a delay differential inequality and the characteristics of the neural network, the algebraic conditions for the moment exponential stability of the nonconstant equilibrium solution are derived. An example is also given for illustration.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2012/405939","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64319894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A multi-degree-of-freedom dynamical system with local cubic nonlinearities subjected to super/subharmonic excitation is considered in this paper. The purpose of this paper is to approximate the nonlinear response of system at super/sub harmonic resonance. For many situations, single resonance mode is often observed to be leading as system enters into super/sub harmonic resonance. In this case, the single modal natural resonance theory can be applied to reduce the system model and a simplified model with only a single DOF is always obtained. Thus, an approximate solution and the analytical expression of frequency response relation are then derived using classical perturbation analysis. While the system is controlled by multiple modes, modal analysis for linearized system is used to decide dominant modes. The reduced model governed by these relevant modes is found and results in an approximate numerical solutions. An illustrative example of the discrete mass-spring-damper nonlinear vibration system with ten DOFs is examined. The approximation results are validated by comparing them with the calculations from direct numerical integration of the equation of motion of the original nonlinear system. Comparably good agreements are obtained.
{"title":"Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance","authors":"Yang Caijin","doi":"10.1155/2012/531480","DOIUrl":"https://doi.org/10.1155/2012/531480","url":null,"abstract":"A multi-degree-of-freedom dynamical system with local cubic nonlinearities subjected to super/subharmonic excitation is considered in this paper. The purpose of this paper is to approximate the \u0000nonlinear response of system at super/sub harmonic resonance. For many situations, single resonance mode is often observed to be leading as system enters into super/sub harmonic resonance. In this case, the single modal natural resonance theory can be applied to reduce the system model and a simplified model with only a single DOF is always obtained. Thus, an approximate solution and the analytical expression of frequency response relation are then derived using classical perturbation analysis. While the system is controlled by multiple modes, modal analysis for linearized system is used to decide dominant modes. The reduced model governed by these relevant modes is found and results in an approximate numerical solutions. An illustrative example of the discrete mass-spring-damper nonlinear vibration system with ten DOFs is examined. The approximation results are validated by comparing them with the calculations from direct numerical integration of the equation of motion of the original nonlinear system. Comparably good agreements are obtained.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2012/531480","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64330104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose and generalize a new nonlinear conjugate gradient method for unconstrained optimization. The global convergence is proved with the Wolfe line search. Numerical experiments are reported which support the theoretical analyses and show the presented methods outperforming CGDESCENT method.
{"title":"The Global Convergence of a New Mixed Conjugate Gradient Method for Unconstrained Optimization","authors":"Yang Yueting, Cao Mingyuan","doi":"10.1155/2012/932980","DOIUrl":"https://doi.org/10.1155/2012/932980","url":null,"abstract":"We propose and generalize a new nonlinear conjugate gradient method for unconstrained optimization. The global convergence is proved with the Wolfe line \u0000search. Numerical experiments are reported which support the theoretical analyses and show the presented methods outperforming CGDESCENT method.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2012/932980","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64368865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On the basis of the computer symbolic system Maple and the extended hyperbolic function method, we develop a more mathematically rigorous and systematic procedure for constructing exact solitary wave solutions and exact periodic traveling wave solutions in triangle form of various nonlinear partial differential equations that are with physical backgrounds. Compared with the existing methods, the proposed method gives new and more general solutions. More importantly, the method provides a straightforward and effective algorithm to obtain abundant explicit and exact particular solutions for large nonlinear mathematical physics equations. We apply the presented method to two variant Boussinesq equations and give a series of exact explicit traveling wave solutions that have some more general forms. So consequently, the efficiency and the generality of the proposed method are demonstrated.
{"title":"Symbolic Computation and the Extended Hyperbolic Function Method for Constructing Exact Traveling Solutions of Nonlinear PDEs","authors":"Huang Yong, Shang Yadong, Yu Wenjun","doi":"10.1155/2012/716719","DOIUrl":"https://doi.org/10.1155/2012/716719","url":null,"abstract":"On the basis of the computer symbolic system Maple and the extended hyperbolic function method, we develop a more mathematically rigorous and systematic procedure for constructing exact solitary wave solutions and exact periodic traveling wave solutions in triangle form of various nonlinear partial differential equations that are with physical backgrounds. Compared with the existing methods, the proposed method gives new and more general solutions. More importantly, the method provides a straightforward and effective algorithm to obtain abundant explicit and exact particular solutions for large nonlinear mathematical physics equations. We apply the presented method to two variant Boussinesq equations and give a series of exact explicit traveling wave solutions that have some more general forms. So consequently, the efficiency and the generality of the proposed method are demonstrated.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2012/716719","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64346128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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