In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously r...In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.展开更多
In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection be...In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.展开更多
In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （gener...In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.展开更多
The symbolic network adds the emotional information of the relationship,that is,the“+”and“-”information of the edge,which greatly enhances the modeling ability and has wide application in many fields.Weak unbalanc...The symbolic network adds the emotional information of the relationship,that is,the“+”and“-”information of the edge,which greatly enhances the modeling ability and has wide application in many fields.Weak unbalance is an important indicator to measure the network tension.This paper starts from the weak structural equilibrium theorem,and integrates the work of predecessors,and proposes the weak unbalanced algorithm EAWSB based on evolutionary algorithm.Experiments on the large symbolic networks Epinions,Slashdot and WikiElections show the effectiveness and efficiency of the proposed method.In EAWSB,this paper proposes a compression-based indirect representation method,which effectively reduces the size of the genotype space,thus making the algorithm search more complete and easier to get better solutions.展开更多
To improve the dynamic balancing accuracy of the micro-motor rotor,an unbalanced vibration feature extraction based on an all-phase fast Fourier transform(APFFT)method is proposed.The amplitude and phase of the signal...To improve the dynamic balancing accuracy of the micro-motor rotor,an unbalanced vibration feature extraction based on an all-phase fast Fourier transform(APFFT)method is proposed.The amplitude and phase of the signal are extracted by spectrum analysis after windowing the unbalanced signal.The mathematical model is derived to simulate the weak signal of rotor unbalance.The simulation results show that this method is accurate in extracting the weak signal of the rotor under different noise levels.The micro-motor rotor unbalanced test system is developed for experimental validations.The accuracy and stability of the vibration amplitude and phase extracted by the APFFT are better than the accuracy and stability from the hardware filtering method.The rotor unbalance is reduced by more than 80%.Furthermore,secondary balance of the rotor after the first balance is carried out.The proposed method can still extract the residual unbalance of the rotor.The results demonstrated that the proposed method can achieve a reduction rate of 90%and the accuracy is within 5mg,verifying the effectiveness of the proposed method for high-precision rotor dynamic balance.展开更多
In this paper, I introduce what are called weak gravity and magnetic anomalies and propose standards for estimating their reliability. I also introduce new techniques for processing this kind of weak anomaly. These te...In this paper, I introduce what are called weak gravity and magnetic anomalies and propose standards for estimating their reliability. I also introduce new techniques for processing this kind of weak anomaly. These techniques consist of interference elimination and weak signal extraction. Practical applications have proved their effectiveness, Weak gravity and magnetic anomalies will get more attention with the development of targeted exploration.展开更多
In his paper “On quasi-separative ‘semigroup’s’”, Krasilnikova, Yu. I. and Novikov, B. V. have studied congruences induced by certain relations on a “semigroup”. They further showed that if the “semigroup” is...In his paper “On quasi-separative ‘semigroup’s’”, Krasilnikova, Yu. I. and Novikov, B. V. have studied congruences induced by certain relations on a “semigroup”. They further showed that if the “semigroup” is quasi separative then the induced congruence is a semilattice congruence. In this paper we continue the study of these relations and the induced congruences i.e., the congruences induced by certain relations on ‘‘semigroup’s”. In this paper mainly it is observed that if S is a quasi-separative and regular “semigroup” then the necessary and sufficient condition for to be the smallest semilattice congruence η is obtained.展开更多
This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contain...This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.展开更多
Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} iso...Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} isomorphic to E° by θ：Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J（E∪ S°） satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J（S°）, called the weakly inverse hull of a weakly inverse system （S°, E, θ, φ） with I（∑） ≌ S°, E（∑） ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given.展开更多
文摘In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.
基金the Science Research Foundation of Qingdao Technological University(C2002-214)
文摘In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.
基金This work was supported by the National Natural Science Foundation of China(6177219661472136)+3 种基金the Hunan Provincial Focus Social Science Fund(2016ZDB006)Hunan Provincial Social Science Achievement Review Committee results appraisal identification project(Xiang Social Assessment 2016JD05)Key Project of Hunan Provincial Social Science Achievement Review Committee(XSP 19ZD1005)The authors gratefully acknowledge the financial support provided by the Key Laboratory of Hunan Province for New Retail Virtual Reality Technology(2017TP1026).
文摘The symbolic network adds the emotional information of the relationship,that is,the“+”and“-”information of the edge,which greatly enhances the modeling ability and has wide application in many fields.Weak unbalance is an important indicator to measure the network tension.This paper starts from the weak structural equilibrium theorem,and integrates the work of predecessors,and proposes the weak unbalanced algorithm EAWSB based on evolutionary algorithm.Experiments on the large symbolic networks Epinions,Slashdot and WikiElections show the effectiveness and efficiency of the proposed method.In EAWSB,this paper proposes a compression-based indirect representation method,which effectively reduces the size of the genotype space,thus making the algorithm search more complete and easier to get better solutions.
基金National Natural Science Foundation of China,Grant/Award Numbers:52202445,11602112。
文摘To improve the dynamic balancing accuracy of the micro-motor rotor,an unbalanced vibration feature extraction based on an all-phase fast Fourier transform(APFFT)method is proposed.The amplitude and phase of the signal are extracted by spectrum analysis after windowing the unbalanced signal.The mathematical model is derived to simulate the weak signal of rotor unbalance.The simulation results show that this method is accurate in extracting the weak signal of the rotor under different noise levels.The micro-motor rotor unbalanced test system is developed for experimental validations.The accuracy and stability of the vibration amplitude and phase extracted by the APFFT are better than the accuracy and stability from the hardware filtering method.The rotor unbalance is reduced by more than 80%.Furthermore,secondary balance of the rotor after the first balance is carried out.The proposed method can still extract the residual unbalance of the rotor.The results demonstrated that the proposed method can achieve a reduction rate of 90%and the accuracy is within 5mg,verifying the effectiveness of the proposed method for high-precision rotor dynamic balance.
基金The subject is sponsored by the National 863Project Fund (Project No.2006AA06Z201)
文摘In this paper, I introduce what are called weak gravity and magnetic anomalies and propose standards for estimating their reliability. I also introduce new techniques for processing this kind of weak anomaly. These techniques consist of interference elimination and weak signal extraction. Practical applications have proved their effectiveness, Weak gravity and magnetic anomalies will get more attention with the development of targeted exploration.
文摘In his paper “On quasi-separative ‘semigroup’s’”, Krasilnikova, Yu. I. and Novikov, B. V. have studied congruences induced by certain relations on a “semigroup”. They further showed that if the “semigroup” is quasi separative then the induced congruence is a semilattice congruence. In this paper we continue the study of these relations and the induced congruences i.e., the congruences induced by certain relations on ‘‘semigroup’s”. In this paper mainly it is observed that if S is a quasi-separative and regular “semigroup” then the necessary and sufficient condition for to be the smallest semilattice congruence η is obtained.
基金This project was supported by TRAPOYT, the Key Project of Chinese Ministry of Education(104126) the NNSF of China(10371046)
文摘This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.
文摘Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} isomorphic to E° by θ：Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J（E∪ S°） satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J（S°）, called the weakly inverse hull of a weakly inverse system （S°, E, θ, φ） with I（∑） ≌ S°, E（∑） ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given.
