With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezo...With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezoelectric quasicrystals,an elliptical hole model under different boundary conditions is established.The analytical expressions of generalized stress intensity factors(GSIFs)are obtained,respectively,for four general cases:a Griffith crack with generalized remote uniform loading,arbitrary loading on the crack surface,concentrated loading at any position of the crack surface,and multiple collinear periodic cracks under uniform loading at infinity.Numerical examples are given,and the effects of crack length,loading position,loading condition,and crack period on GSIFs are discussed.The derived analytical solutions of cracks play a significant role in understanding the phonon-phason and electromechanical coupled behavior in quasicrystals,and they also serve as criteria for fracture analysis.展开更多
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 co...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.展开更多
This study experimentally investigated basal texture initiation and development during cold rolling,in combination with simulation using a modified visco-plastic self-consistent(VPSC)model.The results showed that the ...This study experimentally investigated basal texture initiation and development during cold rolling,in combination with simulation using a modified visco-plastic self-consistent(VPSC)model.The results showed that the orientation of extension twins exhibit a random distribution after rolling.In contrast,the matrix grains deformed by slips tend to orientate with their c-axis around the normal direction(ND).Plastic strain concentration induced by dislocation piling up at grain boundaries contributes to plastic deformation inhomogeneity,and promotes the basal-pyramidal and prismatic-prismatic binary slips.Incorporated with the interactions between the basaland pyramidal<c+a>dislocations,and between the prismaticdislocations,the VPSC model replicates the experimental results,effectively demonstrating the process of the basal texture initiation and development.The basal texture initiation is independent of twinning,and results mainly from the development of misorientation induced by the formation of dislocation sub-boundaries via the interaction between the basaland pyramidal<c+a>dislocations.展开更多
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 b...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.展开更多
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 t...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.展开更多
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....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.展开更多
Let F_q be a finite field with q = p^m, where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual...Let F_q be a finite field with q = p^m, where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length 2~ap^r over F_q, a ≥ 1.The construction of self-dual negacyclic codes of length 2~abp^r over F_q is also provided, where gcd（2, b） = gcd（b, p） = 1 and a ≥ 1.展开更多
Missingness in mixed-type variables is commonly encountered in a variety of areas.The requirement of complete observations necessitates data imputation when a moderate or large proportion of data is missing.However,in...Missingness in mixed-type variables is commonly encountered in a variety of areas.The requirement of complete observations necessitates data imputation when a moderate or large proportion of data is missing.However,inappropriate imputation would downgrade the performance of machine learning algorithms,leading to bad predictions and unreliable statistical inference.For high-dimensional large-scale mixed-type missing data,we develop a computationally efficient imputation method,missing value imputation via generalized factor models(MIG),under missing at random.The proposed MIG method allows missing variables to be of different types,including continuous,binary,and count variables,and are scalable to both data size n and variable dimension p while existing imputation methods rely on restrictive assumptions such as the same type of missing variables,the low dimensionality of variables,and a limited sample size.We explicitly show that the imputation error of the proposed MIG method diminishes to zero with the rate Op(max{n^(-1/2),p^(-1/2)})as both n and p tend to infinity.Five real datasets demonstrate the superior empirical performance of the proposed MIG method over existing methods that the average normalized absolute imputation error is reduced by 5.3%–34.1%.展开更多
As the proportion of renewable energy sources continues to increase,the local damping contributions of sources in power system decrease,posing a challenge to the power system stability.Therefore,online tracking of the...As the proportion of renewable energy sources continues to increase,the local damping contributions of sources in power system decrease,posing a challenge to the power system stability.Therefore,online tracking of the damping contributions of each source is crucial for the prevention of low-frequency oscillations.This paper proposes an online tracking method of local damping under ambient data.The proposed method is based on dissipation energy spectrum analysis(DESA)and the energy dissipation factor(EDF).First,the feasibility of using frequency-domain analysis for the dissipation energy of generator is analyzed.The frequency spectral function of dissipation energy of generator is then derived by integrating with Parseval’s theorem,and the EDF is defined.Second,the generator energy dissipation factor(GEDF)for the dominant oscillation mode frequency is established.The modal information of the dominant oscillation in the power system is obtained through DESA.The relationship between the frequency spectral function and eigenvalues is also established.Finally,an online tracking method of local damping is proposed based on DESA and GEDF.The effectiveness of the proposed method is validated through simulations on a four-machine 11-bus power system and an actual power system in Northwest China.展开更多
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...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.展开更多
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 formula...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.展开更多
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 proper...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.展开更多
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 constraint...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12272402,12102458,and 11972365)the China Agricultural University Education Foundation(No.1101-2412001).
文摘With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezoelectric quasicrystals,an elliptical hole model under different boundary conditions is established.The analytical expressions of generalized stress intensity factors(GSIFs)are obtained,respectively,for four general cases:a Griffith crack with generalized remote uniform loading,arbitrary loading on the crack surface,concentrated loading at any position of the crack surface,and multiple collinear periodic cracks under uniform loading at infinity.Numerical examples are given,and the effects of crack length,loading position,loading condition,and crack period on GSIFs are discussed.The derived analytical solutions of cracks play a significant role in understanding the phonon-phason and electromechanical coupled behavior in quasicrystals,and they also serve as criteria for fracture analysis.
基金The National Natural Science Foundation of China(Grant No.62071165)the Fundamental Research Funds for the Central Universities of China(Grant No.JZ2021HGTB0074)the China Postdoctoral Science Foundation(Grant No.2021M690853).
文摘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.
基金the financial support from the National Foundation of Natural Science(No.51371121) of China.
文摘This study experimentally investigated basal texture initiation and development during cold rolling,in combination with simulation using a modified visco-plastic self-consistent(VPSC)model.The results showed that the orientation of extension twins exhibit a random distribution after rolling.In contrast,the matrix grains deformed by slips tend to orientate with their c-axis around the normal direction(ND).Plastic strain concentration induced by dislocation piling up at grain boundaries contributes to plastic deformation inhomogeneity,and promotes the basal-pyramidal and prismatic-prismatic binary slips.Incorporated with the interactions between the basaland pyramidal<c+a>dislocations,and between the prismaticdislocations,the VPSC model replicates the experimental results,effectively demonstrating the process of the basal texture initiation and development.The basal texture initiation is independent of twinning,and results mainly from the development of misorientation induced by the formation of dislocation sub-boundaries via the interaction between the basaland pyramidal<c+a>dislocations.
基金The National Natural Science Foundation of China(No.10571026,10871051)Specialized Research Fund for the Doctoral Pro-gram of Higher Education(No.20060286006,200802860024)
文摘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.
基金supported by the deanship of Scientific Research at Prince Sattam Bin Abdulaziz University,Alkharj,Saudi Arabia through Research Proposal No.2020/01/17215。
文摘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.
文摘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.
基金Supported by Reward Fund for Outstanding Young and Middle-Aged Scientists of Shandong Province(Grant No.BS2011DX011)Qingdao Postdoctoral Fund(Grant No.861605040007)
文摘Let F_q be a finite field with q = p^m, where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length 2~ap^r over F_q, a ≥ 1.The construction of self-dual negacyclic codes of length 2~abp^r over F_q is also provided, where gcd（2, b） = gcd（b, p） = 1 and a ≥ 1.
基金supported by National Key R&D Program of China(Grant No.2022YFA1003702)National Natural Science Foundation of China(Grant Nos.11931014 and 12271441)。
文摘Missingness in mixed-type variables is commonly encountered in a variety of areas.The requirement of complete observations necessitates data imputation when a moderate or large proportion of data is missing.However,inappropriate imputation would downgrade the performance of machine learning algorithms,leading to bad predictions and unreliable statistical inference.For high-dimensional large-scale mixed-type missing data,we develop a computationally efficient imputation method,missing value imputation via generalized factor models(MIG),under missing at random.The proposed MIG method allows missing variables to be of different types,including continuous,binary,and count variables,and are scalable to both data size n and variable dimension p while existing imputation methods rely on restrictive assumptions such as the same type of missing variables,the low dimensionality of variables,and a limited sample size.We explicitly show that the imputation error of the proposed MIG method diminishes to zero with the rate Op(max{n^(-1/2),p^(-1/2)})as both n and p tend to infinity.Five real datasets demonstrate the superior empirical performance of the proposed MIG method over existing methods that the average normalized absolute imputation error is reduced by 5.3%–34.1%.
基金supported by National Key Research and Development Program of China(No.2021YFB2400800).
文摘As the proportion of renewable energy sources continues to increase,the local damping contributions of sources in power system decrease,posing a challenge to the power system stability.Therefore,online tracking of the damping contributions of each source is crucial for the prevention of low-frequency oscillations.This paper proposes an online tracking method of local damping under ambient data.The proposed method is based on dissipation energy spectrum analysis(DESA)and the energy dissipation factor(EDF).First,the feasibility of using frequency-domain analysis for the dissipation energy of generator is analyzed.The frequency spectral function of dissipation energy of generator is then derived by integrating with Parseval’s theorem,and the EDF is defined.Second,the generator energy dissipation factor(GEDF)for the dominant oscillation mode frequency is established.The modal information of the dominant oscillation in the power system is obtained through DESA.The relationship between the frequency spectral function and eigenvalues is also established.Finally,an online tracking method of local damping is proposed based on DESA and GEDF.The effectiveness of the proposed method is validated through simulations on a four-machine 11-bus power system and an actual power system in Northwest China.
基金the Key Project of the National Natural Science Foundation of China(No.U1836220)the National Natural Science Foundation of China(No.61672267)+1 种基金the Qing Lan Talent Program of Jiangsu Province,Chinathe Key Innovation Project of Undergraduate Students in Jiangsu Province,China(No.201810299045Z)。
文摘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.
基金This project is supported in part by the National Natural Science Foundation of China under the Grant No.90101024. The authors thank Xiaochun Gao for his beneficial invariant-related unitary transformation formulation.
文摘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.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)(Grant No.RGPIN-2019-04276)。
文摘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.
文摘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.
