The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This fu...The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.展开更多
The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-fun...The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.展开更多
By introducing the thermal entangled state representation, we investigate the time evolution of distribution functions in the dissipative channels by bridging the relation between the initial distribution function and...By introducing the thermal entangled state representation, we investigate the time evolution of distribution functions in the dissipative channels by bridging the relation between the initial distribution function and the any time distribution function. We find that most of them are expressed as such integrations over the Laguerre Gaussian function. Furthermore, as applications, we derive the time evolution of photon-counting distribution by bridging the relation between the initial distribution function and the any time photon-counting distribution, and the time evolution of Rfunction characteristic of nonclassicality depth.展开更多
文摘The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.
基金NBHM Department of Atomic Energy,Government of India,Mumbai for the finanicai assistance under PDF sanction no.2/40(37)/2014/R&D-II/14131
文摘The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11047133 and 60967002)the Key Programs Foundation of Ministry of Education of China (Grant No.210115)+1 种基金the Research Foundation of the Education Department of Jiangxi Province of China (Grant Nos.GJJ10097 and GJJ10404)the Natural Science Foundation of Jiangxi Province of China (Grant No.2010GQW0027)
文摘By introducing the thermal entangled state representation, we investigate the time evolution of distribution functions in the dissipative channels by bridging the relation between the initial distribution function and the any time distribution function. We find that most of them are expressed as such integrations over the Laguerre Gaussian function. Furthermore, as applications, we derive the time evolution of photon-counting distribution by bridging the relation between the initial distribution function and the any time photon-counting distribution, and the time evolution of Rfunction characteristic of nonclassicality depth.
