Polygonal coil systems are designed for increasing and more kinds of sensors and electromagnetic systems.This paper presents a method for calculating mutual inductance between polygonal coils including irregular polyg...Polygonal coil systems are designed for increasing and more kinds of sensors and electromagnetic systems.This paper presents a method for calculating mutual inductance between polygonal coils including irregular polygons.Based on the Biot-Savart law,the method calculates mutual inductance by dividing a polygonal coil into finite wires,and expresses the magnetic induction intensity generated by the excitation coil as a function of the spatial position of each vertex of the coil.The calculation method of the feasible region of the objective function is updated and the calculation process is simplified,so the calculation accuracy is improved.For octagon coils arbitrarily positioned in space,the accuracy of the algorithm is verified by the simulation and experiment.展开更多
Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are ...Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.展开更多
In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonli...In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonlinearity p(·)and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.展开更多
文摘Polygonal coil systems are designed for increasing and more kinds of sensors and electromagnetic systems.This paper presents a method for calculating mutual inductance between polygonal coils including irregular polygons.Based on the Biot-Savart law,the method calculates mutual inductance by dividing a polygonal coil into finite wires,and expresses the magnetic induction intensity generated by the excitation coil as a function of the spatial position of each vertex of the coil.The calculation method of the feasible region of the objective function is updated and the calculation process is simplified,so the calculation accuracy is improved.For octagon coils arbitrarily positioned in space,the accuracy of the algorithm is verified by the simulation and experiment.
基金partially supported by Grant No.DFNI I-02/9 of the Bulgarian Science Fund
文摘Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.
基金Birzeit UniversitySharjah University for their supportsponsored by MASEP Research Group in the Research Institute of Sciences and Engineering at University of Sharjah.Grant No.2002144089,2019-2020。
文摘In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonlinearity p(·)and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.
