Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（...Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986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
We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that weak value amplification （WVA） experiment can also be implemented by a second-order co...We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that weak value amplification （WVA） experiment can also be implemented by a second-order correlated system. We then build two-dimensional second-order correlated function patterns for achieving higher amplification factor and discuss the signal-to-noise ratio influence. Several advantages can be obtained by our proposal. For instance, detectors with high resolution are not necessary. Moreover, detectors with low saturation intensity are available in WVA setup. Finally, type-one technical noise can be effectively suppressed.展开更多
By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturb...By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.展开更多
The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the ...The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).展开更多
The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpola...The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang's main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm.展开更多
In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduc...In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.展开更多
A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations...A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the boundary condition. The solution of the problem is first obtained in the Laplace transform domain. Furthermore, a complex inversion formula of the transform based on a Fourier expansion is used to get the numerical solutions of the field equations which are represented graphically.展开更多
文摘Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986
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Project supported by the Union Research Centre of Advanced Spaceflight Technology(Grant No.USCAST2013-05)the National Natural Science Foundation of China(Grant Nos.61170228,61332019,and 61471239)the High-Tech Research and Development Program of China(Grant No.2013AA122901)
文摘We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that weak value amplification （WVA） experiment can also be implemented by a second-order correlated system. We then build two-dimensional second-order correlated function patterns for achieving higher amplification factor and discuss the signal-to-noise ratio influence. Several advantages can be obtained by our proposal. For instance, detectors with high resolution are not necessary. Moreover, detectors with low saturation intensity are available in WVA setup. Finally, type-one technical noise can be effectively suppressed.
基金Supported by the Innovation Talents of Science and Technology of Henan University(2009-HASTIT-007)Supported by the Natural Science Program of Department of Education(2011A110006)
文摘By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.
文摘The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).
文摘The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang's main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm.
文摘In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.
文摘A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the boundary condition. The solution of the problem is first obtained in the Laplace transform domain. Furthermore, a complex inversion formula of the transform based on a Fourier expansion is used to get the numerical solutions of the field equations which are represented graphically.
