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

some results on the apostol bernoulli and apostol euler polynomials the main object of this paper is to investigate the apostol bernoulli polynomials and the apostol euler polynomials we first establish two relationships between the generalized apostol bernoulli and apostol euler polynomials it can be found that many results obtained before are special cases of these two relationships moreover we have a study on the sums of products of the apostol bernoulli polynomials and of the apostol euler polynomials

absolutely γ summing multilinear operators abstract in this paper we introduce an abstract approach to the notion of absolutely summing multilinear operators we show that several previous results on different contexts absolutely summability almost summability cohen summability are particular cases of our general results

multilinear variants of pietsch s composition theorem various concepts of multilinear summing operators were introduced in the last years by extending the well known one from the linear case in this paper we prove that as in the linear case there is a splitting theorem for dominated operators as a consequence of this result we prove various multilinear variants of pietsch s composition theorem

on p adic interpolating function for q euler numbers and its derivatives abstract in this paper we study a two variable p adic q l function l p q s t for dirchlet s character with the property that l p q n t e n n q p t 2 q 2 q p n p p q n e n n q p t for positive integers n and t c p with t p 1 and e n n q x generalized euler polynomials finally we prove that l p q s t is analytic in s and t for s c p with s p p 1 1 p 1 and t c p with t p 1

nurbs enriched contact finite elements abstract a novel enrichment of finite elements for contact computations based on isogeometric analysis is presented each body is divided into two parts an enriched contact surface and the bulk domain together with surfaces that are not in contact the latter part comprises the large majority of the domain and is treated in the usual manner with standard linear basis function preserving the efficiency of classical finite element techniques the enriched contact surface is discretized using nurbs basis functions of at least second order allowing for a locally differentiable surface representation this avoids the problem of suddenly changing normal vectors between element boundaries on the contact surface following the concept of isogeometric analysis the smooth basis functions are not only used to describe the surface geometry but also to approximate the solution on the surface this leads to higher accuracy in the contact integral evaluation numerical results are presented for 2d and 3d contact computations including frictionless sliding adhesive peeling and cohesive debonding the presented contact element enrichment exhibits a major gain in numerical accuracy and stability without loss of efficiency compared to standard linear finite elements the enrichment technique offers some advantages over hermite and higher order lagrangian contact element enrichment techniques such as locally differentiable surface representations in 3d while featuring competitive accuracy and performance

modelling unilateral frictionless contact using the null space method and cubic b spline interpolation the analysis of unilateral sliding contact in elasticity is equivalent to a minimisation problem subjected to a set of inequality constraints however the presence of boundary discontinuities such as those stemming from the spatial discretisation appears as a major problem to determine the set of active constraints this work introduces a smoothing technique of the master surface resorting to cubic b spline interpolation which is c 1 continuous in contact situations between elastic and rigid bodies and g 1 continuous in elastic elastic contact problems the technique is applied in conjunction with the null space method where the solution is searched in an unconstrained manifold the resulting formulation eases the contact transition along the master surface and recovers the quadratic convergence of the iterative newton raphson process the robustness of the method is demonstrated using 2d and 3d examples

shape optimal design using b splines abstract shape optimal design of an elastic structure is formulated using a design element technique it is shown that bezier and b spline curves typical of the cad philosophy are well suited to the definition of design elements complex geometries can be described in a very compact way by a small set of design variables and a few design elements because of the b splines flexibility it is no longer necessary to piece design elements together in order to agree with the shape complexity nor to restrict the shape variations moreover the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh are automatically taken into account in the new formulation an analytical derivation of the sensitivity analysis will be established giving rise to numerical efficiency it will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables so that simple mathematical programming algorithms can be applied to solve it some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper

pade approximation and apostol bernoulli and apostol euler polynomials using the pade approximation of the exponential function we obtain recurrence relations between apostol bernoulli and between apostol euler polynomials as applications we derive some new lacunary recurrence relations for bernoulli and euler polynomials with gap of length 4 and lacunary relations for bernoulli and euler numbers with gap of length 6

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

a multiplication theorem for the lerch zeta function and explicit representations of the bernoulli and euler polynomials abstract a multiplication theorem for the lerch zeta function s a is obtained from which when evaluating at s n for integers n 0 explicit representations for the bernoulli and euler polynomials are derived in terms of two arrays of polynomials related to the classical stirling and eulerian numbers as consequences explicit formulas for some special values of the bernoulli and euler polynomials are given

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

a set of finite order differential equations for the appell polynomials let r n x n 0 denote the set of appell polynomials which includes among others hermite bernoulli euler and genocchi polynomials in this paper by introducing the generalized factorization method for each k n we determine the differential operator l n k x n 0 such that l n k x r n x l n kr n x where l n k n k n k the special case k 1 reduces to the result obtained in m x he p e ricci differential equation of appell polynomials via the factorization method j comput appl math 139 2002 231 237 the differential equations for the hermite and bernoulli polynomials are exhibited for the case k 2

some techniques on nonlinear analysis and applications in this paper we present two different results in the context of nonlinear analysis the first one is essentially a nonlinear technique that in view of its strong generality may be useful in different practical problems the second result more technical but also connected to the first one is an extension of the well known pietsch domination theorem the last decade witnessed the birth of different families of pietsch domination type results and some attempts of unification our result that we call full general pietsch domination theorem is potentially a definitive pietsch domination theorem which unifies the previous versions and delimits what can be proved in this line the connections to the recent notion of weighted summability are traced

subdivision schemes for smooth contact surfaces of arbitrary mesh topology in 3d this paper presents a strategy to parameterize contact surfaces of arbitrary mesh topology in 3d with at least c1 continuity for both quadrilateral and triangular meshes in the regular mesh domain four quadrilaterals or six triangles meet in one node even c2 continuity is attained therefore we use subdivision surfaces for which non physical pressure jumps are avoided for contact interactions they are usually present when the contact kinematics is based on facet elements discretizing the interacting bodies the properties of subdivision surfaces give rise to basically four different implementation strategies each strategy has specific features and requires more or less efforts for an implementation in a finite element program one strategy is superior with respect to the others in the sense that it does not use nodal degrees of freedom of the finite element mesh at the contact surface instead it directly uses the degrees of freedom of the smooth surface thereby remarkably it does not require an interpolation we show how the proposed method can be used to parameterize adaptively refined meshes with hanging nodes this is essential when dealing with finite element models whose geometry is generated by means of subdivision techniques three numerical 3d problems demonstrate the improved accuracy robustness and performance of the proposed method over facet based contact surfaces in particular the third problem adopted from biomechanics shows the advantages when designing complex contact surfaces by means of subdivision techniques copyright 2004 john wiley sons ltd

another discrete fourier transform pairs associated with the lipschitz lerch zeta function abstract it is demonstrated that the alternating lipschitz lerch zeta function and the alternating hurwitz zeta function constitute a discrete fourier transform pair this discrete transform pair makes it possible to deduce as special cases and consequences many mainly new transformation relations involving the values at rational arguments of alternating variants of various zeta functions such as the lerch and hurwitz zeta functions and legendre chi function

an explicit formula for the generalized bernoulli polynomials abstract the object of the present note is to prove a new explicit formula for the generalized bernoulli polynomials the main result 3 below provides an interesting extension of a representation for the generalized bernoulli numbers given recently by p g todorov c r acad sci paris ser i math 301 1985 665 666

divided differences and a general explicit formula for sequences of mansour mulay shattuck divided differences is a very important tool often used both in theory and in practice for the approximation of functions in this paper we employ divided differences with repetitions to find a general explicit formula for the sequences satisfying mansour mulay shattuck s two term recurrence with arbitrary b i i 0

genocchi polynomials associated with the umbral algebra abstract the aim of this paper is to study on the genocchi polynomials of higher order on p the algebra of polynomials in the single variable x over the field c of characteristic zero and p the vector spaces of all linear functional on p by using the action of a linear functional l on a polynomial p x sheffer sequences and appell sequences we obtain some fundamental properties of the genocchi polynomials furthermore we give relations between the first and second kind stirling numbers euler polynomials of higher order and genocchi polynomials of higher order

the impact of surface higher order differentiability in two dimensional contact elements the aim of this work is to propose new contact elements of higher order of differentiability for analysing two dimensional frictionless contact problems several methods were proposed in the literature to solve the problem caused by the lack of continuity resulting from the discretization among them are bezier interpolation hermitian interpolation and splines one of the difficulties in using hermitian interpolation is to verify the partition of unity therefore new elements that satisfy the c 1 and c 2 continuity at the interface are presented in this paper these new contact elements are based on hermitian polynomials for ensuring a higher order of continuity the advantage is that this approach can be easily developed not only for linear elements but also for quadratic elements with higher order of differentiability the performance of different surface representations is assessed through a comparison with a c 0 surface discretization some numerical examples are used for assessing the accuracy and the convergence behaviour

a new unified family of generalized apostol euler bernoulli and genocchi polynomials in this paper we introduce a new unified family of polynomials including unified apostol bernoulli euler and genocchi polynomials see luo and srivastava 2006 and a unified family of polynomials defined by ozden et al 2010 also by applying the mellin transformation for the generating function of the new unified family of polynomials we deduced a unified class of zeta function finally we derive some relationships between our new unified family of polynomials and some types of generalized polynomials

a contact smoothing method for arbitrary surface meshes using nagata patches abstract this paper presents a contact surface smoothing method combined with the node to segment discretization technique to solve large deformation frictional contact problems between deformable bodies the nagata patch interpolation is used to smooth the surface mesh providing a master surface with quasi g 1 continuity between patches moreover the local support of the interpolation method allows to deal with surface meshes of arbitrary topology regular and irregular finite element discretizations as well as hybrid meshes the non physical oscillations in the contact force evolution induced by the faceted contact surface representation are reduced using the proposed smoothing method furthermore the smooth representation of the master surface allows a more accurately evaluation of the resulting stresses and forces while providing an important improvement in convergence behaviour four representative numerical examples are used to demonstrate the advantages of the proposed contact smoothing method the results show a significant improvement in the accuracy robustness and performance of the numerical simulations using the smoothing approach when compared with the piecewise faceted contact surface description

q hardy berndt type sums associated with q genocchi type zeta and q l functions abstract the aim of this paper is to define new generating functions by applying a derivative operator and the mellin transformation to these generating functions we define q analogue of the genocchi zeta function q analogue hurwitz type genocchi zeta function and q genocchi type l function we define partial zeta function by using this function we construct p adic interpolation functions which interpolate generalized q genocchi numbers at negative integers we also define p adic meromorphic functions on c p furthermore we construct new generating functions of q hardy berndt type sums and q hardy berndt type sums attached to dirichlet character we also give some new relations related to these sums

p adic distribution of the unification of the bernoulli euler and genocchi polynomials abstract the aim of this paper is to construct p adic distribution on x c p of the unification of the bernoulli euler and genocchi polynomials y n x k a b which is given by n k a b j dp n z p a b dp n p dp n n k a jb y n dp n j dp n k a dp n b where y n x k a b are defined by 1 1 we give some applications related to these functions and distribution

a class of hurwitz lerch zeta distributions and their applications in reliability abstract in this paper we revisit the study of the hurwitz lerch zeta hlz distribution by investigating its structural properties reliability properties and statistical inference more specifically we explore the reliability properties of the hlz distribution and investigate the monotonic structure of its failure rate mean residual life function and the reversed hazard rate it is shown that the hlz distribution is log convex and hence that it is infinitely divisible both the hazard rate and the reversed hazard rate are found to be decreasing the maximum likelihood estimation of the parameters is discussed and an example is provided in which the hlz distribution fits the data remarkably well

interpolation function of the h q extension of twisted euler numbers in h ozden y simsek i n cangul generating functions of the h q extension of euler polynomials and numbers acta math hungarica in press doi 10 1007 510474 008 7139 1 by using p adic q invariant integral on z p in the fermionic sense ozden et al constructed generating functions of the h q extension of euler polynomials and numbers they defined h q euler zeta functions and h q euler l functions they also raised the following problem find ap adic twisted interpolation function of the generalized twisted h q euler numbers e n g w h q the aim of this paper is to give a partial answer to this problem therefore we constructed twisted h q partial zeta function and twisted p adic h q euler l functions l e p x q h s g 2 m 1 m p 1 g m 1 m x mq h mm s which interpolate h q extension of euler numbers at negative integers l e p x q h n g e n x g n h q p n g n p e n x p g n h q p by using this interpolation function and twisted h q partial zeta function we proved distribution relations of the h q extension of generalized euler polynomials consequently we find a partial answer to the above question

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

certain results for the 2 variable apostol type and related polynomials in this article the 2 variable general polynomials are taken as base with apostol type polynomials to introduce a family of 2 variable apostol type polynomials these polynomials are framed within the context of monomiality principle and their properties are established certain summation formulae for these polynomials are also derived examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored

some relationships between the apostol bernoulli and apostol euler polynomials recently srivastava and pinter 1 investigated several interesting properties and relationships involving the classical as well as the generalized or higher order bernoulli and euler polynomials they also showed among other things that the main relationship proven earlier by cheon 2 can easily be put in a much more general setting the main object of the present sequel to these earlier works is to derive several general properties and relationships involving the apostol bernoulli and apostol euler polynomials some of these general results can indeed be suitably specialized in order to deduce the corresponding properties and relationships involving the generalized bernoulli and generalized euler polynomials other relationships associated with the stirling numbers of the second kind are also considered

extendible polynomials on banach spaces abstract we are concerned with the following question when can a polynomial p e x e and x are banach spaces be extended to a banach space containing e we prove that the polynomials that are extendible to any larger space are precisely those which can be extended to c b e if x is complemented in its bidual and l b e in general we also show that the extendibility is a property that is preserved by aron berner extensions and composition with linear operators we construct a predual of the space of extendible polynomials for the case that x is a dual space

a monolithic smoothing gap algorithm for contact impact based on the signed distance function a new algorithm has been developed for smoothing the surfaces in finite element formulations of contact impact a key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies these functions are then employed for the computation of the gap and other variables needed for implementation of contact impact the smoothed signed distance functions are constructed by a moving least squares approximation with a polynomial basis results show that when nodes are placed on a surface the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis with a quadratic basis the method exactly reproduces a circle or a sphere even for coarse meshes results are presented for contact problems involving the contact of circular bodies copyright c 2002 john wiley sons ltd

novel identities involving genocchi numbers and polynomials arising from applications of umbral calculus abstract the aim of this paper is to deal with applications of umbral calculus on fermionic p adic integral on z p from those applications we derive some new identities on genocchi numbers and polynomials moreover a systemic study of the class of sheffer sequences on the generating function of genocchi polynomials are given

construction a new generating function of bernstein type polynomials abstract main purpose of this paper is to reconstruct generating function of the bernstein type polynomials some properties of this generating functions are given by applying this generating function not only derivative of these polynomials but also recurrence relations of these polynomials are found interpolation function of these polynomials is also constructed by mellin transformation this function interpolates these polynomials at negative integers which are given explicitly moreover relations between these polynomials the stirling numbers of the second kind and bernoulli polynomials of higher order are given furthermore some remarks associated with the bezier curves are given

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

modification and unification of the apostol type numbers and polynomials and their applications abstract in this paper we construct generating functions for modification and unification of the apostol type polynomials y n v x k a b of order v by using these generating functions we derive many new identities related to the generalized stirling type numbers of the second kind array type polynomials eulerian polynomials and the modification and unification of the apostol type polynomials and numbers we give many applications related to these numbers and polynomials and pdes

a general 3d contact smoothing method based on radial point interpolation this paper presents a general 3d contact smoothing method based on the meshfree radial point interpolation method to improve the numerical simulation of contact problems in particular a locally smooth contact surface is constructed from the scattered surface nodes by point interpolation using the combination of polynomial and radial bases with such bases this method reproduces smooth surfaces even for coarse meshes and the constructed surface passes exactly through the surface nodes results for contact problems involving deformable bodies are included to demonstrate its advantages

a family of p adic twisted interpolation functions associated with the modified bernoulli numbers the main purpose of this paper is to construct a family of modified p adic twisted functions which interpolate the modified twisted q bernoulli polynomials and the generalized twisted q bernoulli numbers at negative integers we also give some applications and examples related to these functions and numbers

cn continuous modelling of smooth contact surfaces using nurbs and application to 2d problems this paper presents a strategy for the finite element implementation of cn continuous contact surfaces for deformable bodies undergoing finite deformations whereby n represents an arbitrary level of continuity the proposed novel approach avoids the non physical oscillations of contact forces which are induced by the traditional enforcement of kinematic contact constraints via faceted surfaces discretizing the interacting boundaries in particular for certain problems the level of continuity may influence the rate of convergence significantly within a non linear solution scheme a hierarchical tree data structure is proposed for an efficient search algorithm to find the neighbour elements on adaptively refined meshes which are involved in the smoothing process of a particular finite element the same data structure is used for the automatic detection of the contact surfaces of a body three representative numerical examples demonstrate the increased rate of convergence the ability to trace the actual surface more accurately and the prevention of pressure jumps of the proposed method copyright 2003 john wiley sons ltd

isogeometric contact analysis geometric basis and formulation for frictionless contact this paper introduces an isogeometric framework for the numerical analysis of contact problems in this approach nurbs is utilized as basis for geometric representation and analysis the contact surfaces and the underlying solids are parameterized in an identical paradigm the use of nurbs geometry eliminates at the onset the geometric discontinuities induced by the traditional faceted approximation contact detection is carried out patch wise instead of element wise leading to an efficient and robust numerical algorithm a strategy for smoothing sharp corners is also described the algorithm does not rely on fillets but entails only a minor perturbation to the nurbs parameters a variationally consistent surface to surface formulation is developed in the context of frictionless contact numerical examples are presented to demonstrate the performance and utility of the method

several identities for the generalized apostol bernoulli polynomials the purpose of this paper is to give several symmetric identities on the generalized apostol bernoulli polynomials by applying the generating functions these results extend some known identities

some identities of symmetry for the generalized q euler polynomials abstract by the symmetric properties of drichlet s type multiple q l function we establish various identities concerning the generalized higher order q euler polynomials furthermore we give some interesting relationship between the power sums and the generalized higher order q euler polynomials

unbounded violation of tripartite bell inequalities we prove that there are tripartite quantum states constructed from random unitaries that can lead to arbitrarily large violations of bell inequalities for dichotomic observables as a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model this is in sharp contrast with the bipartite case where all violations are bounded by grothendieck s constant we will discuss the possibility of determining the hilbert space dimension from the obtained violation and comment on implications for communication complexity theory moreover we show that the violation obtained from generalized greenberger horne zeilinger ghz states is always bounded so that in contrast to many other contexts ghz states do not lead to extremal quantum correlations in this case in order to derive all these physical consequences we will have to obtain new mathematical results in the theories of operator spaces and tensor norms in particular we will prove the existence of bounded but not completely bounded trilinear forms from commutative c algebras finally we will relate the existence of diagonal states leading to unbounded violations with a long standing open problem in the context of banach algebras

on the modelling of smooth contact surfaces using cubic splines in this paper a new strategy for the smooth representation of 2d contact surfaces is developed and implemented the contact surfaces are modelled using cubic splines which interpolate the nite element nodes these splines provide a unique surface normal vector and do not require prior knowledge of surface tangents and normals c continuous cubic splines are suitable for representing rigid contact surfaces while c continuous overhauser splines are shown to be most suitable for representing exible contact surfaces a consistent linearization of the kinematic contact constraints based on the spline interpolation is derived the new spline based contact surface interpolation scheme does not in uence the element calculations consequently it can be easily implemented in standard fe codes several numerical examples are used to illustrate the advantages of the proposed smooth representation of contact surfaces the results show a signi cant improvement in accuracy compared to traditional piecewise element based surface interpolation the predicted contact stresses are also less sensitive to the mismatch in the meshes of the di erent contacting bodies this property is useful for problems where the contact area is unknown a priori and when there is signi cant tangential slip copyright 2001 john wiley sons ltd

a one mesh method for the cell centered discretization of sliding abstract a new method is described to treat slide lines in cell centered lagrangian schemes for the modeling of sliding problems between two fluids in the framework of compressible hydrodynamics the method is an extension of the one proposed in clair et al 2013 1 and is conservative in momentum and total energy we illustrate our method which is based on the minimization of an objective function over a specific set that models the sliding constraint by several basic problems

large deformation analysis of contact in degenerate shell elements a new formulation is presented for the analysis of contact in degenerate shell elements this formulation accounts for the transverse stress and strain through the shell thickness and can accommodate double sided shell contact the kinematic contact conditions are expressed accurately in terms of the physical shell contacting surfaces and the problem is formulated in terms of variational inequalities vi large deformations and rotations are accounted for by invoking the appropriate stress and strain measures the solution of the variational inequality is obtained using lagrange multipliers this guarantees that the kinematic contact constraints are accurately satisfied and that the solution is free from user defined parameters two examples involving three beams in contact and ring compression are simulated to establish the validity of the developed formulations and the solution technique 1998 john wiley sons ltd

applying nagata patches to smooth discretized surfaces used in 3d frictional contact problems the accurate solution of large deformation frictional contact problems using the finite element method is still a challenging task due to the strong nonlinearities involved this paper presents a smoothing method applicable to 3d contact surfaces discretized with an arbitrary mesh topology the quadratic nagata patch interpolation is adopted to define the smooth surface the resulting contact surface passes through all nodes of the mesh while providing a smooth description with at least g 1 continuity at the nodes and quasi g 1 continuity between the patches thus the proposed method avoids the non physical oscillations in the contact force which are induced by the traditionally used faceted contact surfaces description when slave nodes slide over several master segments moreover it allows the accurate evaluation of kinematic variables leading to important improvements in terms of convergence rate within the newton raphson iteration loop the developed global and local contact search algorithms designed for contact surfaces described by nagata patches are described in detail three numerical examples were selected to illustrate the advantages of the proposed smoothing method including a complex industrial example of sheet metal forming process the results show the significant improvements attained with the proposed approach in terms of efficiency robustness and accuracy when compared with the traditional faceted contact surfaces description 2014 published by elsevier b v

on the behavior of two variable twisted p adic euler q l functions abstract in this paper we study on h q euler zeta and l functions we give relations between twisted h q partial zeta function twisted h q euler zeta and twisted two variable h q euler l functions we also give the value of twisted two variable h q euler l function at s 0 the main purpose of this paper is to construct two variable twisted p adic euler h q l function which interpolates twisted h q euler polynomials at negative integers we give p adic fermionic integral representation of this functions

carlitz s q bernoulli and q euler numbers and polynomials and a class of generalized q hurwitz zeta functions in this paper we systematically recover the identities for the q eta numbers h k and the q eta polynomials h k x presented by carlitz l carlitz q bernoulli numbers and polynomials duke math j 15 1948 987 1000 which we define here via generating series rather than via the difference equations of carlitz following a method developed by kaneko et al m kaneko n kurokawa m wakayama a variation of euler s approach to the riemann zeta function kyushu j math 57 2003 175 192 for a canonical q extension of the riemann zeta function we investigate a similarly constructed q extension of the hurwitz zeta function the details of this investigation disclose some interesting connections among q eta polynomials carlitz s q bernoulli polynomials b k x e polynomials and the q bernoulli polynomials that emerge from the q extension of the hurwitz zeta function discussed here

on the von staudt clausen s theorem associated with q genocchi numbers recently the von staudt clausen s theorem for q euler numbers was introduced by kim 2013 andq genocchi numbers were constructed by araci et al 2013 in this paper we give the corresponding von staudt clausen s theorem for q genocchi numbers and also get the kummer type congruence for q genocchi numbers

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

certain classes of series associated with the zeta and related functions a fascinatingly large number of seemingly independent solutions of the so called basler problem of evaluating the riemann zeta function z s when s 2 which was of vital importance to leonhard euler 1707 1783 and the bernoulli brothers jakob bernoulli 1654 1705 and johann bernoulli 1667 1748 have appeared in the mathematical literature ever since euler first solved this problem in the year 1736 the main object of this two part series of lectures is to present some recent developments on the evaluations and representations of z s when email protected email protected 1 n being the set of natural numbers we emphasize upon several interesting classes of rapidly convergent series representations for z 2n 1 email protected n which have been developed in recent years in two of many computationally useful special cases considered here it is observed that z 3 can be represented by means of series which converge much more rapidly than that in euler s celebrated formula as well as the series used recently by roger apery 1916 1994 in his proof of the irrationality of z 3 symbolic and numerical computations using mathematica version 4 0 for linux show among other things that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places

some generalizations of the apostol genocchi polynomials and the stirling numbers of the second kind abstract recently the authors introduced some generalizations of the apostol bernoulli polynomials and the apostol euler polynomials see q m luo h m srivastava j math anal appl 308 2005 290 302 and q m luo taiwanese j math 10 2006 917 925 the main object of this paper is to investigate an analogous generalization of the genocchi polynomials of higher order that is the so called apostol genocchi polynomials of higher order for these generalized apostol genocchi polynomials we establish several elementary properties provide some explicit relationships with the apostol bernoulli polynomials and the apostol euler polynomials and derive various explicit series representations in terms of the gaussian hypergeometric function and the hurwitz or generalized zeta function we also deduce their special cases and applications which are shown here to lead to the corresponding results for the genocchi and euler polynomials of higher order by introducing an analogue of the stirling numbers of the second kind that is the so called stirling numbers of the second kind we derive some basic properties and formulas and consider some interesting applications to the family of the apostol type polynomials furthermore we also correct an error in a previous paper q m luo h m srivastava comput math appl 51 2006 631 642 and pose two open problems on the subject of our investigation

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 the generating functions of the generalized bernoulli euler and genocchi polynomials the goal of this paper is to unify and extend the generating functions of the generalized bernoulli polynomials the generalized euler polynomials and the generalized genocchi polynomials associated with the positive real parameters a and b and the complex parameter b by using this generating function we derive recurrence relations and other properties for these polynomials by applying the mellin transformation to the generating function of the unification of bernoulli euler and genocchi polynomials we construct a unification of the zeta functions furthermore we give many properties and applications involving the functions and polynomials investigated in this paper

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

computational model for 3 d contact problems with friction based on the penalty method the friction forces are assumed to follow the coulomb law with a slip criterion treated in the context of a standard return mapping algorithm consistent linearization of the field equations is performed which leads to a fully implicit scheme with non symmetric tangent stiffness which preserves asymptotic quadratic convergence of the newton raphson method

generalized higher order bernoulli number pairs and generalized stirling number pairs abstract from a delta series f t and its compositional inverse g t hsu defined the generalized stirling number pair s n k s n k in this paper we further define from f t and g t the generalized higher order bernoulli number pair b n z b n z making use of the bell polynomials the potential polynomials as well as the lagrange inversion formula we give some explicit expressions and recurrences of the generalized higher order bernoulli numbers present the relations between the generalized higher order bernoulli numbers of both kinds and the corresponding generalized stirling numbers of both kinds and study the relations between any two generalized higher order bernoulli numbers moreover we apply the general results to some special number pairs and obtain series of combinatorial identities it can be found that the introduction of generalized bernoulli number pair and generalized stirling number pair provides a unified approach to lots of sequences in mathematics and as a consequence many known results are special cases of ours

some families of the hurwitz lerch zeta functions and associated fractional derivative and other integral representations the main object of this paper is to present in a unified manner a number of fractional derivative and other integral representations for several general families of the hurwitz lerch zeta functions relevant connections of the results presented here with those obtained in earlier works are also indicated precisely

identities of symmetry for q bernoulli polynomials in this paper we derive eight basic identities of symmetry in three variables related to q bernoulli polynomials and the q analogue of power sums these and most of their corollaries are new since there have been results only concerning identities of symmetry in two variables these abundant symmetries shed new light even on the existing identities so as to yield some further interesting ones the derivations of the identities are based on the p adic integral expression of the generating function for the q bernoulli polynomials and the quotient of integrals that can be expressed as the exponential generating function for the q analogue of power sums

hahn banach extension of multilinear forms and summability the aim of this paper is to investigate close relations between the validity of hahn banach extension theorems for multilinear forms on banach spaces and summability properties of sequences from these spaces a case of particular importance occurs when we consider banach spaces which have the property that every bilinear form extends to any superspace

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

compatible description of tool surfaces and fem meshes for analysing sheet forming operations implementation of the 3 d finite element method fem of sheet forming operations has proceeded slowly in particular describing the arbitrary tool surfaces in an accurate and smooth manner with well behaved first and second derivatives has been a major obstacle a new geometric method suitable for representing any rigid tool surface has been developed and shown to be superior to the usual schemes the new method relies on the described tool surface for position data only the spatial derivatives are obtained by considering only the sheet mesh nodal positions this new scheme has been implemented with a rigid viscoplastic fem program using general surface descriptions based on b splines and linear inter polation analytic representations of a hemispherical and rounded square punch were also compared the comparisons show that the proposed method offers several advantages over other general formulations 1 the new representation is the proper one for formulating the equilibrium condition alternate forms can produce spurious results 2 the proposed method introduces inherently smooth surface derivatives that improve numerical stability even with crude surface resolution suitable test problems show covergence with the new method far past the divergence points of the simulations using the standard general surface description 3 the method is reasonably efficient with a time penalty of approximately 30 50 per cent unoptimized with respect to analytic surface descriptions

a consistent tangent stiffness matrix for three dimensional non linear contact analysis a consistent tangent stiffness matrix for the analysis of non linear contact problems is presented the associated element has three or four nodes and establishes contact between three dimensional structures like solids and shells it accounts for the non linear kinematics of large deformation analysis and guarantees a quadratic convergence rate two formulations the penalty method and the lagrange multiplier method are investigated

some series identities involving the generalized apostol type and related polynomials a unification and generalization of various apostol type polynomials was introduced and investigated recently by luo and srivastava q m luo h m srivastava some generalizations of the apostol genocchi polynomials and the stirling numbers of the second kind appl math comput 217 2011 5702 5728 in this paper we prove several symmetry identities for these generalized apostol type polynomials by using their generating functions as special cases and consequences of our results we obtain the corresponding symmetry identities for the apostol euler polynomials of higher order the apostol bernoulli polynomials of higher order and the apostol genocchi polynomials of higher order and also for another family of generalized apostol type polynomials which were investigated systematically 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 2010 2779 2787 we also derive several relations between the apostol type polynomials the generalized sum of integer powers and the generalized alternating sum it is shown how each of these results would extend the corresponding known identities

some array type polynomials associated with special numbers and polynomials abstract the main objective in this paper is first to establish new identities for the stirling type numbers of the second kind the array type polynomials the apostol bernoulli polynomials and the apostol bernoulli numbers we then construct a delta operator and investigate various generating functions for the bell type numbers and for some new polynomials associated with the array type polynomials we also derive several other identities and relations for these polynomials and numbers

reverse inclusions for multiple summing operators abstract multiple summing operators have been proven to be useful in several areas of analysis and mathematical physics in this paper we prove reverse inclusions for this class of operators completing the work already initiated in d perez garcia the inclusion theorem for multiple summing operators studia math 165 3 2004 275 290

an augmented lagrangian technique combined with a mortar algorithm for modelling mechanical contact problems summary a finite element formulation for three dimensional 3d contact mechanics using a mortar algorithm combined with a mixed penalty duality formulation from an augmented lagrangian approach is presented in this method no penalty parameter is introduced for the regularisation of the contact problem the contact approach based on the mortar method gives a smooth representation of the contact forces across the bodies interface and can be used in arbitrarily curved 3d configurations the projection surface used for integrating the equations is built using a local cartesian basis defined in each contact element a unit normal to the contact surface is defined locally at each element simplifying the implementation and linearisation of the equations the displayed examples show that the algorithm verifies the contact patch tests exactly and is applicable to large displacements problems with large sliding motions copyright 2012 john wiley sons ltd

twisted p adic h q l functions by using the q volkenborn integral on z p in simsek 2006 33 and simsek 2007 34 generating functions for the h q bernoulli polynomials and numbers were defined by using these functions we define a new twisted h q partial zeta function which interpolates the twisted h q bernoulli polynomials and generalized twisted h q bernoulli numbers at negative integers we give a relation between twisted h q partial zeta functions and the twisted h q two variable l function we find the value of this function at s 0 we also find the residue of this function at s 1 we construct a p adic twisted h q l function which interpolates the twisted h q bernoulli polynomials l x p q h 1 n t g b n g n x h p t q email protected n p p n 1b n g n 1 h p 1p t q p n furthermore we construct an integral representation of the twisted h q two variable l function we give some applications related to the p adic twisted h q l function and the twisted h q bernoulli polynomials

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

notes on generalization of the bernoulli type polynomials abstract recently srivastava et al introduced a new generalization of the bernoulli euler and genocchi polynomials see h m srivastava m garg s choudhary russian j math phys 17 2010 251 261 and h m srivastava m garg s choudhary taiwanese j math 15 2011 283 305 they established several interesting properties of these general polynomials the generalized hurwitz lerch zeta functions and also in series involving the familiar gaussian hypergeometric function by the same motivation of srivastava s et al 11 12 we introduce and derive multiplication formula and some identities related to the generalized bernoulli type polynomials of higher order associated with positive real parameters a b and c we also establish multiple alternating sums in terms of these polynomials moreover by differentiating the generating function of these polynomials we give a interpolation function of these polynomials

application of a composition of generating functions for obtaining explicit formulas of polynomials abstract using notions of composita and composition of generating functions we obtain explicit formulas for the chebyshev polynomials the legendre polynomials the gegenbauer polynomials the associated laguerre polynomials the stirling polynomials the abel polynomials the bernoulli polynomials of the second kind the generalized bernoulli polynomials the euler polynomials the peters polynomials and the narumi polynomials

fourier expansions and integral representations for the apostol bernoulli and apostol euler polynomials we investigate fourier expansions for the apostol bernoulli and apostol euler polynomials using the lipschitz summation formula and obtain their integral representations we give some explicit formulas at rational arguments for these polynomials in terms of the hurwitz zeta function we also derive the integral representations for the classical bernoulli and euler polynomials and related known results

some q extensions of the apostol bernoulli and the apostol euler polynomials of order n and the multiple hurwitz zeta function abstract in this paper we first investigate several further interesting properties of the multiple hurwitz lerch zeta function n z s a which was introduced recently by choi et al j choi d s jang h m srivastava a generalization of the hurwitz lerch zeta function integral transform spec funct 19 2008 we then introduce and investigate some q extensions of the multiple hurwitz lerch zeta function n z s a the apostol bernoulli polynomials b k n x of order n and the apostol euler polynomials e k n x of order n relevant connections of the results presented here with those obtained in earlier works are also indicated precisely

difference equations of q appell polynomials in this paper we study some properties of the q appell polynomials including the recurrence relations and the q difference equations which extend some known classical q 1 results we also provide the recurrence relations and the q difference equations for q bernoulli polynomials q euler polynomials q genocchi polynomials and for q hermite polynomials as special cases of q appell polynomials