Algebraic reflexivity introduced by Hadwin is related to linear interpolation.In this paper,the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolat...Algebraic reflexivity introduced by Hadwin is related to linear interpolation.In this paper,the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced.Some properties of them are obtained and some relations between them revealed展开更多
In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct pi...In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct piezoelectriccoupling and direct piezoelectric and circuit coupling. In the proposed method, implicit and explicit formulationsare used for strong and weak coupling, respectively. Three feasible partitioned algorithms are generated, namely(1) a strongly coupled algorithm that uses a fully implicit formulation for both types of coupling, (2) a weaklycoupled algorithm that uses a fully explicit formulation for both types of coupling, and (3) a partially stronglycoupled and partially weakly coupled algorithm that uses an implicit formulation and an explicit formulation forthe two types of coupling, respectively.Numerical examples using a piezoelectric energy harvester,which is a typicalstructure-piezoelectric-circuit coupling problem, demonstrate that the proposed method selects the most costeffectivealgorithm.展开更多
The presented circular current loop model reveals that charged fundamental particles such as the electron consist essentially of electric and magnetic energy. The magnetic properties have the same order of magnitude a...The presented circular current loop model reveals that charged fundamental particles such as the electron consist essentially of electric and magnetic energy. The magnetic properties have the same order of magnitude as the electric ones. The electromagnetic field energy is the origin of the inertial mass. The Higgs boson, existing or not, is not needed to “explain” particle mass. The magnetic moment of fundamental particles is not anomalous! The “anomaly” indicates the existence of a small additional amount of kinetic energy. Thus, fundamental particles are not purely field-like such as photons and not (essentially) mass-like such as atoms, they represent a special kind of matter in between. Their kinetic energy is obviously not due to any relativistic effect but is related to an independent physical law that provides, together with the magnetic energy, the angular momentum exactly to be ħ/2. Fundamental particles are (at least) two-dimensional. In the simplest case their core consists of two concentric, nearly identical current loops. Their relative design details, the “anomaly” factor, and the rotational velocity of the uniformly distributed elementary charge follow from the stability condition, i.e. electric and magnetic force balance, and do not depend on the particle’s rest mass! Fundamental particles are objects of classical physics. Their magnetic forces are the true origin of the weak and strong nuclear interactions. For their explanation bosons and gluons are not needed.展开更多
基金Supported in part by the National Natural Science Foundation of China(1 9771 0 72 ) .
文摘Algebraic reflexivity introduced by Hadwin is related to linear interpolation.In this paper,the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced.Some properties of them are obtained and some relations between them revealed
基金the Japan Society for the Promotion of Science,KAKENHI Grant Nos.20H04199 and 23H00475.
文摘In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct piezoelectriccoupling and direct piezoelectric and circuit coupling. In the proposed method, implicit and explicit formulationsare used for strong and weak coupling, respectively. Three feasible partitioned algorithms are generated, namely(1) a strongly coupled algorithm that uses a fully implicit formulation for both types of coupling, (2) a weaklycoupled algorithm that uses a fully explicit formulation for both types of coupling, and (3) a partially stronglycoupled and partially weakly coupled algorithm that uses an implicit formulation and an explicit formulation forthe two types of coupling, respectively.Numerical examples using a piezoelectric energy harvester,which is a typicalstructure-piezoelectric-circuit coupling problem, demonstrate that the proposed method selects the most costeffectivealgorithm.
文摘The presented circular current loop model reveals that charged fundamental particles such as the electron consist essentially of electric and magnetic energy. The magnetic properties have the same order of magnitude as the electric ones. The electromagnetic field energy is the origin of the inertial mass. The Higgs boson, existing or not, is not needed to “explain” particle mass. The magnetic moment of fundamental particles is not anomalous! The “anomaly” indicates the existence of a small additional amount of kinetic energy. Thus, fundamental particles are not purely field-like such as photons and not (essentially) mass-like such as atoms, they represent a special kind of matter in between. Their kinetic energy is obviously not due to any relativistic effect but is related to an independent physical law that provides, together with the magnetic energy, the angular momentum exactly to be ħ/2. Fundamental particles are (at least) two-dimensional. In the simplest case their core consists of two concentric, nearly identical current loops. Their relative design details, the “anomaly” factor, and the rotational velocity of the uniformly distributed elementary charge follow from the stability condition, i.e. electric and magnetic force balance, and do not depend on the particle’s rest mass! Fundamental particles are objects of classical physics. Their magnetic forces are the true origin of the weak and strong nuclear interactions. For their explanation bosons and gluons are not needed.