We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient p...We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient power, namely to the third power of the Fermat quotient. Using this result and the Gessel identity (2005) combined with our past work (2021), we are able to relate residues of some truncated convolutions of Bernoulli numbers with some Ernvall-Metsänkyla residues to residues of some full convolutions of the same kind. We also establish some congruences concerning other related weighted sums of powers of integers when these sums are weighted by some analogs of the Teichmüller characters.展开更多
We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by 176 and show that there is a unique surface with 176 conics, all irreducib...We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by 176 and show that there is a unique surface with 176 conics, all irreducible: it admits a faithful action of one of the Mukai groups. Therefore, we also discuss conics and lines on Mukai surfaces: we discover a double plane(ramified at a smooth sextic curve) that contains 8,910 smooth conics.展开更多
An attempt has been made to study the heat and mass transfcr effects in a boundary layer flow through porous medtium of an electrically conducting viscoelastic fluid subject to transverse magnetic field in the presenc...An attempt has been made to study the heat and mass transfcr effects in a boundary layer flow through porous medtium of an electrically conducting viscoelastic fluid subject to transverse magnetic field in the presence of heat sourcelsink and chemical reaction.It has been considered the effects of radliation,viscous and Joule dissipations and intemal heat generation/absorption.Closed form solutions for the boundary layer equations of viscoelastic,second-grxle and Walters'B’fluid models are obtained.The method of solution involves similarity transformation.The ransfommed equations of thermal and mass transport are solved by applying Kummer's function.The solutions of temperature field for both prescribed surface temperature(PST)as well as prescribed surface heat flux(PHF)are obtained.It is important to remark that the interaction of magnetic field is found to be counterproductive in enhancing velocity and concentration distibution whereas the presence of chemical reaction as well as porous matrix with moderate values of magnetic parameter reduces the temperature and concentration fields at all points of flow domain.展开更多
We discuss the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We here study the solution of that differential Equation with an inhomogeneous term, a...We discuss the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We here study the solution of that differential Equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation.展开更多
Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust ...Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.展开更多
We discuss the solution of Laplace’s differential equation and a fractional differential equation of that type, by using analytic continuations of Riemann-Liouville fractional derivative and of Laplace transform. We ...We discuss the solution of Laplace’s differential equation and a fractional differential equation of that type, by using analytic continuations of Riemann-Liouville fractional derivative and of Laplace transform. We show that the solutions, which are obtained by using operational calculus in the framework of distribution theory in our preceding papers, are obtained also by the present method.展开更多
In this article, using Fontaine＇s ФГ-module theory, we give a new proof of Coleman＇s explicit reciprocity law, which generalizes that of Artin-Hasse, Iwasawa and Wiles, by giving a complete formula for the norm re...In this article, using Fontaine＇s ФГ-module theory, we give a new proof of Coleman＇s explicit reciprocity law, which generalizes that of Artin-Hasse, Iwasawa and Wiles, by giving a complete formula for the norm residue symbol on Lubin-Tate groups. The method used here is different from the classical ones and can be used to study the Iwasawa theory of crystalline representations.展开更多
In this paper, we develop an algebraic independence method originated from a work of Mordoukhay-Boltovskoy, which allows us to establish the algebraic independence of certain numbers connected with Liouville numbers. ...In this paper, we develop an algebraic independence method originated from a work of Mordoukhay-Boltovskoy, which allows us to establish the algebraic independence of certain numbers connected with Liouville numbers. This method depends either on elementary results of the Kummer theory or on transcendence measures for certain classes of numbers.展开更多
In this paper, a hybrid algorithm for accelerating the double series of Floquet vector modes arising in the analysis of frequency selective surfaces （FSS） is presented. The asymptotic terms with slow convergence in ...In this paper, a hybrid algorithm for accelerating the double series of Floquet vector modes arising in the analysis of frequency selective surfaces （FSS） is presented. The asymptotic terms with slow convergence in the double series are first accelerated by Poisson transformation and Ewald method, and then the remained series is accelerated by Shank transformation. It results in significant savings in memory and computing time. Numerical examples verify the validity of the hybrid acceleration algorithm.展开更多
In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation wi...In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation. We there considered derivatives of a function on , when is locally integrable on , and the integral converges. We now discard the last condition that should converge, and discuss the same problem. In Appendices, polynomial form of particular solutions are given for the differential equations studied and Hermite’s differential equation with special inhomogeneous terms.展开更多
This paper deals with the study of the composite Humbert matrix function with matrix arguments . The convergence and integral form this function is established. An operational relation between a Humbert matrix functio...This paper deals with the study of the composite Humbert matrix function with matrix arguments . The convergence and integral form this function is established. An operational relation between a Humbert matrix function and Kummer matrix function is studied. Also, integral expressions of this relation are deduced. Finally, we define and study of the composite Humbert Kummer matrix functions.展开更多
Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some genera...Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.展开更多
First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise excitations is stud...First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise excitations is studied. First, by using the stochastic averaging method based on the generalized harmonic functions, the averaged It stochastic differential equation for the amplitudes of the nonlinear oscillators can be derived. Then the associated backward Kolmogorov equation of the conditional reliability function is established, and the conditional reliability is approximately expressed as a series expansion in terms of Kummer functions with time-dependent coefficients. By using the Galerkin method, the time dependent coefficients of the associated conditional reliability function can be solved by a set of differential equations. Finally, the proposed procedure is applied to Duffing-Van der Pol systems under external and/or parametric excitations of Gaussian white noises. The results are also verified by those obtained from Monte Carlo simulation of the original system. The effects of system parameters on first-passage failure are discussed briefly.展开更多
With the deployment of small cells and device to device communications in future heterogeneous networks,in many situations we would encounter mobile radio channels with partly blocked line of sight component,which are...With the deployment of small cells and device to device communications in future heterogeneous networks,in many situations we would encounter mobile radio channels with partly blocked line of sight component,which are well modeled by the Rician shadowed(RS) fading channel.In this paper,by the usage of Kummer transformation,a simplified representation of the RS fading channel with integral fading parameter is given.It is a finite series representation involving only exponential function and low order polynomials.This allows engineers not only the closed-form expressions for exact performance analysis over RS fading channel,but also the insights on the system design tactics.展开更多
基于正项级数通项的比值 a n+p/ a n ≤ b n+p /b n 的分析,得到了 Kummer 判别法的一种推广形式,进一步给出了其极限表示.对推广的 Kummer 判别法中的赋值,分别得到推广的达朗贝尔判别法,推广的拉贝判别法及推广的贝特朗判别法.类似得...基于正项级数通项的比值 a n+p/ a n ≤ b n+p /b n 的分析,得到了 Kummer 判别法的一种推广形式,进一步给出了其极限表示.对推广的 Kummer 判别法中的赋值,分别得到推广的达朗贝尔判别法,推广的拉贝判别法及推广的贝特朗判别法.类似得到高斯判别法的推广形式.最后通过若干例子验证了方法的有效性.展开更多
文摘We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient power, namely to the third power of the Fermat quotient. Using this result and the Gessel identity (2005) combined with our past work (2021), we are able to relate residues of some truncated convolutions of Bernoulli numbers with some Ernvall-Metsänkyla residues to residues of some full convolutions of the same kind. We also establish some congruences concerning other related weighted sums of powers of integers when these sums are weighted by some analogs of the Teichmüller characters.
文摘We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by 176 and show that there is a unique surface with 176 conics, all irreducible: it admits a faithful action of one of the Mukai groups. Therefore, we also discuss conics and lines on Mukai surfaces: we discover a double plane(ramified at a smooth sextic curve) that contains 8,910 smooth conics.
文摘An attempt has been made to study the heat and mass transfcr effects in a boundary layer flow through porous medtium of an electrically conducting viscoelastic fluid subject to transverse magnetic field in the presence of heat sourcelsink and chemical reaction.It has been considered the effects of radliation,viscous and Joule dissipations and intemal heat generation/absorption.Closed form solutions for the boundary layer equations of viscoelastic,second-grxle and Walters'B’fluid models are obtained.The method of solution involves similarity transformation.The ransfommed equations of thermal and mass transport are solved by applying Kummer's function.The solutions of temperature field for both prescribed surface temperature(PST)as well as prescribed surface heat flux(PHF)are obtained.It is important to remark that the interaction of magnetic field is found to be counterproductive in enhancing velocity and concentration distibution whereas the presence of chemical reaction as well as porous matrix with moderate values of magnetic parameter reduces the temperature and concentration fields at all points of flow domain.
文摘We discuss the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We here study the solution of that differential Equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation.
文摘Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.
文摘We discuss the solution of Laplace’s differential equation and a fractional differential equation of that type, by using analytic continuations of Riemann-Liouville fractional derivative and of Laplace transform. We show that the solutions, which are obtained by using operational calculus in the framework of distribution theory in our preceding papers, are obtained also by the present method.
基金This paper is supported partially by the 973 Program
文摘In this article, using Fontaine＇s ФГ-module theory, we give a new proof of Coleman＇s explicit reciprocity law, which generalizes that of Artin-Hasse, Iwasawa and Wiles, by giving a complete formula for the norm residue symbol on Lubin-Tate groups. The method used here is different from the classical ones and can be used to study the Iwasawa theory of crystalline representations.
文摘In this paper, we develop an algebraic independence method originated from a work of Mordoukhay-Boltovskoy, which allows us to establish the algebraic independence of certain numbers connected with Liouville numbers. This method depends either on elementary results of the Kummer theory or on transcendence measures for certain classes of numbers.
基金supported in part by the National High-Tech Research Plan of China(863 Plan)(Grant Nos.2002AA123031 and 2003AA123310)in part by the National Natural Science Foundation of China(Grant No.60471016).
文摘In this paper, a hybrid algorithm for accelerating the double series of Floquet vector modes arising in the analysis of frequency selective surfaces （FSS） is presented. The asymptotic terms with slow convergence in the double series are first accelerated by Poisson transformation and Ewald method, and then the remained series is accelerated by Shank transformation. It results in significant savings in memory and computing time. Numerical examples verify the validity of the hybrid acceleration algorithm.
文摘In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation. We there considered derivatives of a function on , when is locally integrable on , and the integral converges. We now discard the last condition that should converge, and discuss the same problem. In Appendices, polynomial form of particular solutions are given for the differential equations studied and Hermite’s differential equation with special inhomogeneous terms.
文摘This paper deals with the study of the composite Humbert matrix function with matrix arguments . The convergence and integral form this function is established. An operational relation between a Humbert matrix function and Kummer matrix function is studied. Also, integral expressions of this relation are deduced. Finally, we define and study of the composite Humbert Kummer matrix functions.
基金Supported by National Natural Science Foundation of China(Grant No.10601039)
文摘Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.
基金supported by the National Natural Science Foundation of China (Grant No. 11025211)the Natural Science Foundation of Zhejiang Province (Grant No. 26090125)the Special Fund for National Excellent PhD Dissertation
文摘First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise excitations is studied. First, by using the stochastic averaging method based on the generalized harmonic functions, the averaged It stochastic differential equation for the amplitudes of the nonlinear oscillators can be derived. Then the associated backward Kolmogorov equation of the conditional reliability function is established, and the conditional reliability is approximately expressed as a series expansion in terms of Kummer functions with time-dependent coefficients. By using the Galerkin method, the time dependent coefficients of the associated conditional reliability function can be solved by a set of differential equations. Finally, the proposed procedure is applied to Duffing-Van der Pol systems under external and/or parametric excitations of Gaussian white noises. The results are also verified by those obtained from Monte Carlo simulation of the original system. The effects of system parameters on first-passage failure are discussed briefly.
基金sponsored by the National Natural Science Foundation of China under grant No.61171089the Training Program of the Major Research Plan of the National Natural Science Foundation of China under grant No.91438104
文摘With the deployment of small cells and device to device communications in future heterogeneous networks,in many situations we would encounter mobile radio channels with partly blocked line of sight component,which are well modeled by the Rician shadowed(RS) fading channel.In this paper,by the usage of Kummer transformation,a simplified representation of the RS fading channel with integral fading parameter is given.It is a finite series representation involving only exponential function and low order polynomials.This allows engineers not only the closed-form expressions for exact performance analysis over RS fading channel,but also the insights on the system design tactics.
文摘基于正项级数通项的比值 a n+p/ a n ≤ b n+p /b n 的分析,得到了 Kummer 判别法的一种推广形式,进一步给出了其极限表示.对推广的 Kummer 判别法中的赋值,分别得到推广的达朗贝尔判别法,推广的拉贝判别法及推广的贝特朗判别法.类似得到高斯判别法的推广形式.最后通过若干例子验证了方法的有效性.
