The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function b...The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus.展开更多
The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. T...The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.展开更多
The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
The rate of uniform strong approzimation of Marcinkiewicz type for multivariable continuous functions is obtained in this paper as follows：‖1/k＋1 ^k∑j=0 ｜Sj（f）-f｜^q‖≤C/k＋1^k∑j=0 Ej^q（f）,where Sj（f） den...The rate of uniform strong approzimation of Marcinkiewicz type for multivariable continuous functions is obtained in this paper as follows：‖1/k＋1 ^k∑j=0 ｜Sj（f）-f｜^q‖≤C/k＋1^k∑j=0 Ej^q（f）,where Sj（f） denotes the square partial Fourier sum off and Ej（f） denotes the square best approximation of f by trigonometric polynomials of degree（j,j,…,j）,j=0,1,2.…展开更多
Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fo...Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2 T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1) the better result cannot be found by using the same method.展开更多
The non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, became the most significant effects in the nano-scale beam. In the present study, a generalized solution for the g...The non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, became the most significant effects in the nano-scale beam. In the present study, a generalized solution for the generalized thermoelastic vibration of a bounded nano-beam resonator induced by ramp type of heating is developed and the solutions take into account the above two effects. The Laplace transforms and direct method are used to determine the lateral vibration, the temperature, the displacement, the stress and the energy of the beam. The effects of the relaxation time and the ramping time parameters have been studied with some comparisons.展开更多
基金supported by the Ningbo Youth Foundation(0 2 J0 1 0 2 - 2 1 )
文摘The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus.
文摘The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.
文摘The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
基金Supported by NSF of China, under the Grant 10471010.
文摘The rate of uniform strong approzimation of Marcinkiewicz type for multivariable continuous functions is obtained in this paper as follows：‖1/k＋1 ^k∑j=0 ｜Sj（f）-f｜^q‖≤C/k＋1^k∑j=0 Ej^q（f）,where Sj（f） denotes the square partial Fourier sum off and Ej（f） denotes the square best approximation of f by trigonometric polynomials of degree（j,j,…,j）,j=0,1,2.…
文摘Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2 T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1) the better result cannot be found by using the same method.
文摘The non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, became the most significant effects in the nano-scale beam. In the present study, a generalized solution for the generalized thermoelastic vibration of a bounded nano-beam resonator induced by ramp type of heating is developed and the solutions take into account the above two effects. The Laplace transforms and direct method are used to determine the lateral vibration, the temperature, the displacement, the stress and the energy of the beam. The effects of the relaxation time and the ramping time parameters have been studied with some comparisons.
