convergence of time stepping schemes for passive and extended linear complementarity systems generalizing recent results in m k camlibel complementarity methods in the analysis of piecewise linear dynamical systems ph d thesis center for economic research tilburg university tilburg the netherlands 2001 m k camlibel w p m h heemels and j m schumacher ieee trans circuits systems i fund theory appl 49 2002 pp 349 357 and j s pang and d stewart math program ser a 113 2008 pp 345 424 this paper provides an in depth analysis of time stepping methods for solving initial value and boundary value non lipschitz linear complementarity systems lcss under passivity and broader assumptions the novelty of the methods and their analysis lies in the use of least norm solutions in the discrete time linear complementarity subproblems arising from the numerical scheme these subproblems are not necessarily monotone and are not guaranteed to have convex solution sets among the principal results it is shown that using such least norm solutions of the discrete time subproblems an implicit euler scheme is convergent for passive initial value lcss generalizations under a strict copositivity assumption and for boundary value lcss are also established

multiple correction and continued fraction approximation abstract the main aim of this paper is to further develop a multiple correction method formulated in a previous work 6 as applications we find a kind of hybrid type finite continued fraction approximations in two cases of landau constants and lebesgue constants in addition we refine the previous results of lu 29 and xu and you 48 for the euler mascheroni constant

some new asymptotic approximations of the gamma function based on nemes formula ramanujan s formula and burnside s formula in this paper we construct some new approximations of the gamma function based on nemes formula ramanujan s formula and burnside s formula using these approximations some inequalities are established finally for demonstrating the superiority of our new approximation over mortici s formula and other classical ones some numerical computations are also given

some new convergent sequences and inequalities of euler s constant abstract in this paper some new convergent sequences and inequalities of euler s constant are provided to demonstrate the superiority of our new convergent sequence over detemple s sequence vernescu s sequence and mortici s sequences some numerical computations are also given

complete characterizations of the gamma function abstract in this paper we obtain the complete monotonicities regarding both the functions x and x defined by x 1 2 x x e x e x 12 x 2 x x e x 1 x as direct consequences x is strictly increasing and strictly concave on 0 and x is strictly decreasing and strictly convex on 0 furthermore we show that x consists the properties lim x 0 x 0 and lim x x 1 as well as x holds the properties lim x 0 x and lim x x 0

continued fractions and the polygamma functions abstract in a previous study we have shown that the polygamma functions derivatives of the logarithm of the gamma function relate to stieltjes transforms in the square of the argument these transforms in turn may be converted to stieltjes continued fractions in the background is a determined stieltjes moment problem in the present study we use the hamburger form of the stieltjes integral to produce a set of real monotonic increasing and monotonic decreasing approximants to each of the real and imaginary parts of a polygamma function when the argument is complex the approximants involve rational fractions which appear to be new special attention is given to ln z and the psi function

on stirling s formula remainder let the sequence r n be defined by n 2 n n e n e r n we establish new estimates for stirling s formula remainder r n this improves some known results let x be defined by the relation x 1 2 x e x e x 12 x we prove that x is completely monotonic on 0 this implies the result given by mortici who proved that x 1 x is completely monotonic on 0

new sequences with continued fraction towards euler s constant in this paper using the continued fraction some new convergent sequences towards euler s constant are given in order to demonstrate the superiority of the new sequences over detemple s sequence mortici s sequences and lu s sequences some numerical simulations are given at the end of this article

bifurcation points for a reaction diffusion system with two inequalities abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability we show that obstacles e g a unilateral membrane for both quantities modeled in terms of inequalities introduce a new bifurcation of spatially non homogeneous steady states in the domain of stability of the trivial solution of the corresponding classical problem without obstacles

smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem the implicit function theorem is applied in a nonstandard way to abstract variational inequalities depending on a possibly infinite dimensional parameter in this way results on smooth continuation of solutions as well as of eigenvalues and eigenvectors are established under certain particular assumptions the abstract results are applied to a linear second order elliptic eigenvalue problem with nonlocal unilateral boundary conditions schrodinger operator with the potential as the parameter

stieltjes continued fractions for polygamma functions speed of convergence it is well known that the polygamma functions k z dk 1 dzk 1 log z k 0 1 2 can be represented in the hall plane region arg z 0 in the present paper it is shown that the coefficients am k have the asymptotic behavior am k m2 16 m from this it is deduced that the nth approximant gn k z of g k z converges at the rate g k z gn k z a nb n 1 where the positive constants a and b depend upon k and z but are independent of n

on the ramanujan lodge harmonic number expansion the aim of this paper is to extend and refine the ramanujan lodge harmonic number expansion into negative powers of a triangular number we construct a faster asymptotic series and some new sharp inequalities for the harmonic numbers

asymptotic expansions of the gamma function related to windschitl s formula we develop windschitl s approximation formula for the gamma function to two asymptotic expansions and provide a formula for determining the coefficients of each asymptotic expansion

inequalities asymptotic expansions and completely monotonic functions related to the gamma function abstract in this paper we present some completely monotonic functions and asymptotic expansions related to the gamma function based on the obtained expansions we provide new bounds for x 1 x 1 2 and x 1 2

sharp approximation formulas and inequalities for the wallis ratio by continued fraction abstract in this paper we present a new continued fraction approximation of the wallis ratio this approximation is fast in comparison with the recently discovered asymptotic series we also establish the inequalities related to this approximation finally some numerical computations are provided for demonstrating the superiority of our approximation

inequalities and asymptotic expansions associated with the ramanujan and nemes formulas for the gamma function we present some inequalities and asymptotic expansions associated with the ramanujan and nemes formulas for the gamma function

on the asymptotic expansions of the gamma function related to the nemes gosper and burnside formulas in this paper we present new asymptotic expansions of the gamma function related to the nemes gosper and burnside formulas

monotonicity properties inequalities and asymptotic expansions associated with the gamma function we define x by the equality x 1 x e x 8 x 3 4 x 2 x 1 30 1 6 e x we call x the remainder of ramanujan s formula in this paper we present some properties for x including monotonicity properties inequalities and asymptotic expansions furthermore we present some full asymptotic expansions for the gamma function related to the nemes ramanujan and burnside formulas

a generated approximation related to gosper s formula and ramanujan s formula abstract in this paper based on gosper s formula and ramanujan s formula a generated approximation of the factorial function and some inequalities for the gamma function are established finally for demonstrating the superiority of our new series over the classical stirling s series some numerical computations are given

continued fraction approximation for the gamma function based on the tri gamma function abstract in this paper we present a continued fraction product approximation for the gamma function via the tri gamma function this approximation is fast in comparison with the recently discovered asymptotic series we also establish the inequalities related to this approximation finally some numerical computations are provided for demonstrating the superiority of our approximation

estimates of the function and quotient by minc sathre we present some approximations of minc sathre quotient and some related lower and upper bounds then we establish some estimates of minc sathre function and the nth root of the volume of the unit n dimensional ball some applications and comparison with other results are given

some new improved classes of convergence towards euler s constant in this paper using continued fractions some new quicker sequences convergent to euler s constant are provided finally for demonstrating the superiority of our new convergent sequence over detemple s sequence vernescu s sequence and mortici s sequences some numerical computations are also given

on a special class of regularized central paths for semidefinite programs we present a special class of regularized central paths for standard primal dual semidefinite program sdp that can be used to design path following algorithms for finding the projection of any symmetric matrix vector onto the solution set of the sdp we will study the existence convergence and analytical properties of these paths

completely monotonic functions and inequalities associated to some ratios of the pochhammer k symbol abstract in this paper we study some ratios of the pochhammer k symbol we prove that some functions associated to these ratios are completely monotonic and obtain some sharp inequalities

some inequalities for the trigamma function in terms of the digamma function in the paper the authors establish three kinds of inequalities for the trigamma function in terms of the exponential function to powers of the digamma function these newly established inequalities extend some known results the method in the paper utilizes some facts from the asymptotic theory and is a natural way to solve problems for approximating some quantities for large values of the variable

some quicker classes of sequences convergent to euler s constant in this paper some quicker classes of sequences convergent to euler s constant are provided finally for demonstrating the superiority of our new convergent sequences over detemple s sequence vernescu s sequence and mortici s sequences some numerical computations are also given

a high order path following method for locating the least 2 norm solution of monotone lcps a high order path following method is proposed for finding the least 2 norm solution of a monotone lcp this method follows the regularized central paths introduced in y b zhao and d li siam j control optim 40 2001 pp 898 924 by using the analyticity of these paths we showed the global convergence under the assumption that the lcp has at least one solution and the superlinear rate of local convergence under the assumption that the least 2 norm solution is maximally complementary