on twisted q hurwitz zeta function and q two variable l function abstract in this study by applying the mellin transformation to the generating function of the h q bernoulli polynomials we construct integral representation of the twisted h q hurwitz function and twisted h q two variable l function these functions are interpolate the twisted h q bernoulli polynomials and generalized twisted h q bernoulli numbers at non positive integers respectively we also give the relation between twisted h q hurwitz zeta function and twisted h q two variable l function

a quadratic bolza type problem in a riemannian manifold abstract a classical nonlinear equation d s x x v x s 0 on a complete riemannian manifold m is considered the existence of solutions connecting any two points x 0 x 1 m is studied i e for t 0 the critical points of the functional j t x 1 2 0 t x x ds 0 t v x s ds with x 0 x0 x t x1 when the potential v has a subquadratic growth with respect to x jt admits a minimum critical point for any t 0 infinitely many critical points if the topology of m is not trivial when v has an at most quadratic growth i e v x s d 2 x x k this property does not hold but an optimal arrival time t 0 exists such that if 0 m can be joined by a critical point of the corresponding functional for the existence and multiplicity results variational methods and ljusternik schnirelman theory are used the optimal value t 2 is fulfilled by the harmonic oscillator these ideas work for other related problems

on the existence of geodesics on stationary lorentz manifolds with convex boundary abstract in this paper we consider the problem of the existence and multiplicity for geodesics not touching the boundary of a stationary lorentz manifold having convex boundary a physical example of a stationary and nonstatic lorentz manifold having convex boundary is the stationary axisymmetric asymptotically flat gravitational field outside a rotating massive object whenever its angular speed is small and its mean radius is close to the schwarzschild radius

q dedekind type sums related to q zeta function and basic l series abstract the main purpose of this paper is to define new generating functions by applying the mellin transformation formula to these generating functions we define q analogue of riemann zeta function q analogue hurwitz zeta function q analogue dirichlet l function and two variable q l function in particular by using these generating functions we will construct new generating functions which produce q dedekind type sums and q dedekind type sums attached to dirichlet character we also give the relations between these sums and dedekind sums furthermore by using product which is given in this paper we will give the relation between dedekind sums and q l function as well

on the q extension of euler and genocchi numbers abstract carlitz has introduced an interesting q analogue of frobenius euler numbers in l carlitz q bernoulli numbers and polynomials duke math j 15 1948 987 1000 l carlitz q bernoulli and eulerian numbers trans amer math soc 76 1954 332 350 he has indicated a corresponding stadudt clausen theorem and also some interesting congruence properties of the q euler numbers a recent author s study of more general q euler and genocchi numbers can be found in previous publication t kim l c jang h k pak a note on q euler and genocchi numbers proc japan acad ser a math sci 77 2001 139 141 in this paper we give a new construction of q euler numbers which are different from carlitz s q extension and author s q extension in previous publication see t kim l c jang h k pak a note on q euler and genocchi numbers proc japan acad ser a math sci 77 2001 139 141 by using our q extension of euler numbers we can also consider a new q extension of genocchi numbers and obtain some interesting relations between q extension of euler numbers and q extension of genocchi numbers

twisted h q bernoulli numbers and polynomials related to twisted h q zeta function and l function abstract in this paper by using q volkenborn integral we construct new generating functions of the new twisted h q bernoulli polynomials and numbers by applying the mellin transformation to these generating functions we obtain integral representations of the new twisted h q zeta function and twisted h q l function which interpolate the twisted h q bernoulli numbers and generalized twisted h q bernoulli numbers at non positive integers respectively furthermore relation between twisted h q zeta function and twisted h q l function are proved some new relations related to twisted h q bernoulli polynomials and numbers are given

some new identities for the apostol bernoulli polynomials and the apostol genocchi polynomials in this paper we present a further investigation for the apostol bernoulli polynomials and the apostol genocchi polynomials by making use of the generating function methods and summation transform techniques we establish some new identities involving the products of the apostol bernoulli polynomials and the apostol genocchi polynomials many of the results presented here are the corresponding generalizations of some known formulas on the classical bernoulli polynomials and the classical genocchi polynomials

on smooth cauchy hypersurfaces and geroch s splitting theorem given a globally hyperbolic spacetime m we show the existence of a smooth spacelike cauchy hypersurface s and thus a global diffeomorphism between m and r s

the determinants of some multilevel vandermonde and toeplitz matrices the closed algebraic expressions of the determinants of some multivariate multilevel vandermonde matrices and the associated toeplitz karle hauptman matrices are worked out the formula can usefully be applied to evaluate the determinant of the karle hauptman matrix generated by a principal basic set of reflections the knowledge of which determines the full diffraction pattern of an ideal crystal

new changhee q euler numbers and polynomials associated with p adic q integrals using non archimedean q integrals on z p defined in t kim on a q analogue of the p adic log gamma functions and related integrals j number theory 76 1999 320 329 t kim q volkenborn integration russ j math phys 9 2002 288 299 we define new changhee q euler polynomials and numbers which are different from those of kim t kim p adic q integrals associated with the changhee barnes q bernoulli polynomials integral transforms spec funct 15 2004 415 420 and carlitz l carlitz q bernoulli and eulerian numbers trans amer math soc 76 1954 332 350 we define generating functions of multiple q euler numbers and polynomials furthermore we construct a multivariate hurwitz type zeta function which interpolates the multivariate q euler numbers or polynomials at negative integers

on the analogs of euler numbers and polynomials associated with p adic q integral on zp at q 1 abstract the purpose of this paper is to construct euler numbers and polynomials by using fermionic expression of p adic q integral at q 1 from these euler polynomials we derive the harmonic sums of higher order finally we investigate several interesting properties and relationships involving the classical as well as the generalized euler numbers and polynomials as an application we will treat p adic invariant integrals on z p involving trigonometric functions

iteration of closed geodesics in stationary lorentzian manifolds following the lines of bott in commun pure appl math 9 171 206 1956 we study the morse index of the iterates of a closed geodesic in stationary lorentzian manifolds or more generally of a closed lorentzian geodesic that admits a timelike periodic jacobi field given one such closed geodesic we prove the existence of a locally constant integer valued map on the unit circle with the property that the morse index of the iterated n is equal up to a correction term e 0 1 to the sum of the values of at the n th roots of unity the discontinuities of occur at a finite number of points of the unit circle that are special eigenvalues of the linearized poincare map of we discuss some applications of the theory

complete subsets of a diffraction pattern a positive atomic density r j 1nnj r rj in a d dimensional space can be exactly reconstructed from an appropriate finite subset complete set of its fourier series coefficients uh hd or even limited to the support rj j 1 n from a finite subset of moduli uh it is necessary first to determine a complete set of fourier coefficients uh possibly inside the unavoidable high resolution cut off h l and then by these coefficients to determine the unknown density we report some procedures which are able to single out complete sets they are based on a property of goedkoop s vector lattice ah hd defined so that ah ak uk h the property states that if the vector with index h h1 hd is a linear combination of the vectors relevant to a set of indices with a particular shape then all the vectors relevant to the hyperquadrant h h h h 1 d are linear combinations of the vectors relevant to 0 h moreover the determination of from a complete set passes through the solution of a system of polynomial equations in d variables whose roots determine the position vectors we show how to convert this problem into the simpler problem of sequentially solving a set of polynomial equations in one variable

global hyperbolicity and palais smale condition for action functionals in stationary spacetimes abstract in order to apply variational methods to the action functional for geodesics of a stationary spacetime some hypotheses useful to obtain classical palais smale condition are commonly used pseudo coercivity bounds on certain coefficients of the metric etc we prove that these technical assumptions admit a natural interpretation for the conformal structure causality of the manifold as a consequence any stationary spacetime with a complete timelike killing vector field and a complete cauchy hypersurface thus globally hyperbolic is proved to be geodesically connected

generalizing caratheodory s uniqueness of harmonic parameterization to n dimensions consider a sum of f exponentials in n dimensions and let i sub n be the number of equispaced samples taken along the nth dimension it is shown that if the frequencies or decays along every dimension are distinct and spl sigma sub n 1 sup n i sub n spl ges 2f n 1 then the parameterization in terms of frequencies decays amplitudes and phases is unique the result can be viewed as generalizing a classic result of caratheodory to n dimensions the proof relies on a recent result regarding the uniqueness of low rank decomposition of n way arrays

some generalizations of the apostol bernoulli and apostol euler polynomials abstract the main object of this paper is to give analogous definitions of apostol type see t m apostol on the lerch zeta function pacific j math 1 1951 161 167 and h m srivastava some formulas for the bernoulli and euler polynomials at rational arguments math proc cambridge philos soc 129 2000 77 84 for the so called apostol bernoulli numbers and polynomials of higher order we establish their elementary properties derive several explicit representations for them in terms of the gaussian hypergeometric function and the hurwitz or generalized zeta function and deduce their special cases and applications which are shown here to lead to the corresponding results for the classical bernoulli numbers and polynomials of higher order

on the twisted q euler numbers and polynomials associated with basic q l functions one of the purposes of this paper is to construct the twisted q euler numbers by using p adic invariant integral on zp in the fermionic sense moreover we consider the twisted euler q zeta functions and q l functions which interpolate the twisted q euler numbers and polynomials at a negative integer

a unified presentation of certain meromorphic functions related to the families of the partial zeta type functions and the l functions abstract the aim of this paper is to construct a unified family of meromorphic functions which is related to many known functions such as a unified family of partial zeta type functions a unified family of l functions and so on we investigate and derive many properties of this family of meromorphic functions moreover we compute the residues of this family of meromorphic functions at their poles we also give some applications and remarks involving this family of meromorphic functions

a new approach to q genocchi numbers and their interpolation functions abstract the aim of this paper is to define generating functions of higher order q genocchi numbers by using a p adic q deformed fermionic integral on z p we give witt s type integral of these numbers furthermore we give the interpolation functions of these numbers

a korovkin based approximation of multilevel toeplitz matrices with rectangular unstructured blocks via multilevel trigonometric matrix spaces in this paper we are concerned with the approximation of multilevel toeplitz matrices generated by multivariate rectangular matrix valued continuous also l2 functions f i p rightarrow cal c s times t with i pi pi we first define a class cal a t of multilevel trigonometric matrix spaces with unstructured s times t blocks second we introduce a multi sequence of linear approximation operators cal p n x n n 1 n 2 ldots n p acting on complex matrices of dimensions n 1 cdots n p s times n 1 cdots n p t n j in cal n and giving the minimizer of the distance of x from a fixed representative of cal a t with regard to the frobenius norm then by stating and proving new versions of the korovkin theorem for f ranging in the banach space bf c i p cal c s times t cdot infty and by linking these theorems to the operators cal p n we prove the goodness of the proposed approximation in terms of the strong and weak equidistribution of the eigenvalues singular values of a n f and cal p n a n f the discussed results provide a very uniform tool for treating the preconditioning problem with applications to a wide variety of structures as analyzed in the twin paper s serra capizzano calcolo in press

unified apostol bernoulli euler and genocchi polynomials in this paper we present a unified family of polynomials including not only the apostol bernoulli euler and genocchi polynomials but also a general family of polynomials suggested by ozden et al h ozden y simsek h m srivastava a unified presentation of the generating functions of the generalized bernoulli euler and genocchi polynomials comput math appl 60 10 2010 2779 2787 we obtain the explicit representation of this unified family in terms of a gaussian hypergeometric function some symmetry identities and multiplication formula are also given

almost sure identifiability of multidimensional harmonic retrieval two dimensional 2 d and more generally multidimensional harmonic retrieval is of interest in a variety of applications including transmitter localization and joint time and frequency offset estimation in wireless communications the associated identifiability problem is key in understanding the fundamental limitations of parametric methods in terms of the number of harmonics that can be resolved for a given sample size consider a mixture of 2 d exponentials each parameterized by amplitude phase and decay rate plus frequency in each dimension suppose that i equispaced samples are taken along one dimension and likewise j along the other dimension we prove that if the number of exponentials is less than or equal to roughly ij 4 then assuming sampling at the nyquist rate or above the parameterization is almost surely identifiable this is significant because the best previously known achievable bound was roughly i j 2 for example consider i j 32 our result yields 256 versus 32 identifiable exponentials we also generalize the result to n dimensions proving that the number of exponentials that can be resolved is proportional to total sample size

smoothness of time functions and the metric splitting of globally hyperbolic spacetimes the folk questions in lorentzian geometry which concerns the smoothness of time functions and slicings by cauchy hypersurfaces are solved by giving simple proofs of a any globally hyperbolic spacetime m g admits a smooth time function open image in new window whose levels are spacelike cauchy hyperfurfaces and thus also a smooth global splitting open image in new window if a spacetime m admits a continuous time function t then it admits a smooth time function open image in new window with timelike gradient open image in new window on all m