Drazin invertibility for matrices over an arbitrary ring

In order to study the Drazin invertibility of a matrix with the generalized factorization over an arbitrary ring, the necessary and sufficient conditions for the existence of the Drazin inverse of a matrix are given by the properties of the generalized factorization. Let T = PAQ be a square matrix with the generalized factorization, then T has Drazin index k if and only if k is the smallest natural number such that Ak is regular and Uk（Vk） is invertible if and only if k is the smallest natural number such that Ak is regular and Uk（Vk） is invertible if and only if k is the smallest natural number such that Ak is regular and Uk（Vk） is invertible. The formulae to compute the Drazin inverse are also obtained. These results generalize recent results obtained for the Drazin inverse of a matrix with a universal factorization.

Deep Learning Enabled Autoencoder Architecture for Collaborative Filtering Recommendation in IoT Environment

The era of the Internet of things(IoT)has marked a continued exploration of applications and services that can make people’s lives more convenient than ever before.However,the exploration of IoT services also means that people face unprecedented difficulties in spontaneously selecting the most appropriate services.Thus,there is a paramount need for a recommendation system that can help improve the experience of the users of IoT services to ensure the best quality of service.Most of the existing techniques—including collaborative filtering(CF),which is most widely adopted when building recommendation systems—suffer from rating sparsity and cold-start problems,preventing them from providing high quality recommendations.Inspired by the great success of deep learning in a wide range of fields,this work introduces a deep-learning-enabled autoencoder architecture to overcome the setbacks of CF recommendations.The proposed deep learning model is designed as a hybrid architecture with three key networks,namely autoencoder(AE),multilayered perceptron(MLP),and generalized matrix factorization(GMF).The model employs two AE networks to learn deep latent feature representations of users and items respectively and in parallel.Next,MLP and GMF networks are employed to model the linear and non-linear user-item interactions respectively with the extracted latent user and item features.Finally,the rating prediction is performed based on the idea of ensemble learning by fusing the output of the GMF and MLP networks.We conducted extensive experiments on two benchmark datasets,MoiveLens100K and MovieLens1M,using four standard evaluation metrics.Ablation experiments were conducted to confirm the validity of the proposed model and the contribution of each of its components in achieving better recommendation performance.Comparative analyses were also carried out to demonstrate the potential of the proposed model in gaining better accuracy than the existing CF methods with resistance to rating sparsity and cold-start problems.

Adaptive Virtual Source Imaging Using the Sequence Intensity Factor:Simulation and Experimental Study

Virtual source(VS)imaging has been proposed to improve image resolution in medical ultrasound imaging.However,VS obtains a limited contrast due to the non-adaptive delay-and-sum(DAS)beamforming.To improve the image contrast and provide an enhanced resolution,adaptive weighting algorithms were applied in VS imaging.In this paper,we proposed an adjustable generalized coherence factor(aGCF)for the synthetic aperture sequential beamforming(SASB)ofVS imaging to improve image quality.The value of aGCF is adjusted by a sequence intensity factor(SIF)that is defined as the ratio between the effective low resolution scan lines(LRLs)intensity and total LRLs strength.The aGCF-weighted VS(aGCF-VS)images were compared with standard VS images and GCF-weighted VS(GCF-VS)images.Simulation and experimental results demonstrated that the contrast ratio(CR)and contrastto-noise ratio(CNR)of aGCF-VS are greatly improved,compared with standard VS imaging.And in comparison with GCF-VS,aGCF-VS can obtain better CNR and speckle signal-to-noise ratio(sSNR)whilemaintaining similar CR.Therefore,aGCF is suitable for VS imaging to improve contrast and preserve speckle pattern.

THE NEW CRITERIA OF ELASTIC AND FATIGUE FAILURE IN THE COMPONENT OF COMPLEX STRESS STATES

In this paper, a total criterion on elastic and fatigue failure in complex stress, that is. octahedral stress strength theory on dynamic and static states on the basis of studying modern and classic strength theories. At the same time, an analysis of an independent and fairly comprehensive theoretical system is set up. It gives generalized failure factor by 36 materials and computative theory of the 11 states of complex stresses on a point, and derives the operator equation on generalized allowable strength and a computative method for a total equation can be applied to dynamic and static states. It is illustrated that the method has a good exactness through computation of eight examples of engineering. Therefore, the author suggests applying it to engineering widely.

Latent source-specific generative factor learning for monaural speech separation using weighted-factor autoencoder

Much recent progress in monaural speech separation(MSS)has been achieved through a series of deep learning architectures based on autoencoders,which use an encoder to condense the input signal into compressed features and then feed these features into a decoder to construct a specific audio source of interest.However,these approaches can neither learn generative factors of the original input for MSS nor construct each audio source in mixed speech.In this study,we propose a novel weighted-factor autoencoder(WFAE)model for MSS,which introduces a regularization loss in the objective function to isolate one source without containing other sources.By incorporating a latent attention mechanism and a supervised source constructor in the separation layer,WFAE can learn source-specific generative factors and a set of discriminative features for each source,leading to MSS performance improvement.Experiments on benchmark datasets show that our approach outperforms the existing methods.In terms of three important metrics,WFAE has great success on a relatively challenging MSS case,i.e.,speaker-independent MSS.

Multivariate quasi-tight framelets with high balancing orders derived from any compactly supported refinable vector functions

Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and multiwavelets/multiframelets.This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders.This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms.

A direct method for solving projected generalized continuous-time Sylvester equations

This article is devoted to the numerical solution of a projected generalized Sylvester equation with relatively small size. Such an equation arises in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. The algebraic formula of the solution of the projected generalized continuous-time Sylvester equation is presented. A direct method based on the generalized Schur factorization is proposed. Moreover, its low-rank version for problems with low-rank right-hand sides is also proposed. The computational cost of the direct method is estimated. Numerical simulation show that this direct method has high accurncv

Exact expression for decoherence factor in the time-dependent generalized Cini model

The present letter finds the complete set of exact solutions of the time-dependent generalized Cini model by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation and, based on this, the general explicit expression for the decoherence factor is therefore obtained. This study provides us with a useful method to consider the geometric phase and topological properties in the time-dependent quantum decoherence process.

BEST WEIGHT PATTERN EVALUATION BASED SECURITY CONSTRAINED POWER DISPATCH ALGORITHM

This paper presents a methodology which determines the allocation of power demand among the committed generating units while minimizes number of objectives as well as meets physical and technological system constraints. The procedure considers two decoupled problems based upon the dependency of their goals on either active power or reactive power generation. Both the problems have been solved sequentially to achieve optimal allocation of active and reactive power generation while minimizes operating cost, gaseous pollutants emission objectives and active power transmission loss with consideration of system operating constraints along with generators prohibited operating zones and transmission line flow limits. The active and reactive power line flows are obtained with the help of generalized generation shift distribution factors （GGDF） and generalized Z-bus distribution factors （GZBDF）, respectively. First problem is solved in multi-objective framework in which the best weights assigned to objectives are determined while employing weighting method and in second problem, active power loss of the system is minimized subject to system constraints. The validity of the proposed method is demonstrated on 30-bus IEEE power system.