leaf languages and string compression tight connections between leaf languages and strings compressed by straight line programs slps are established it is shown that the compressed membership problem for a language l is complete for the leaf language class defined by l via logspace machines a more difficult variant of the compressed membership problem for l is shown to be complete for the leaf language class defined by l via polynomial time machines as a corollary it is shown that there exists a fixed linear visibly pushdown language for which the compressed membership problem is pspace complete for xml languages it is shown that the compressed membership problem is conp complete furthermore it is shown that the embedding problem for slp compressed strings is hard for pp probabilistic polynomial time

new bounds for the first inequality of ostrowski gruss type and applications abstract some new bounds for the first inequality of ostrowski gruss type are derived these new bounds can be much better than some recently obtained bounds applications in numerical integration are also given

on an iyengar type inequality involving quadratures in n knots abstract in this short note we give an iyengar type inequality involving quadratures in n knots where n is an arbitrary natural number

on an inequality of ostrowski type in three independent variables in the present paper a new inequality of ostrowski type in three independent variables is established the discrete analogue of the main result is also given

comparing two integral means for absolutely continuous functions whose absolute value of the derivative are convex and applications abstract some new estimates for the difference between the integral mean of a function and its mean over a subinterval are established and new applications for special means and probability density functions are also given

on sharp inequalities of simpson type and ostrowski type in two independent variables in this paper two sharp inequalities are derived the first is a sharp simpson inequality and the second is a sharp inequality of ostrowski type in two independent variables

weighted ostrowski integral inequalities for mappings whose derivatives belong to l p a b in this paper we establish some weighted ostrowski integral inequalities for mappings whose derivatives belong to l p a b

comparing two integral means for absolutely continuous mappings whose derivatives are in l a b and applications estimates of the difference of two integral means on a b c d with c d a b in terms of the sup norm of the derivative and applications for pdfs special means jeffreys divergence and continuous streams are given

some remarks on the chebyshev functional identities are provided for the chebyshev functional defined on a real linear space equipped with a bilinear form in addition some inequalities for the functional are discussed

global solution to the compressible isothermal multipolar fluid abstract the global existence of weak solutions of the initial boundary value problem in bounded domains to the system of partial differential equations for viscous compressible isothermal bipolar and multipolar fluids is proved some other properties as cavitation regularity up to the strong solution and uniqueness are discussed

on the optimal constants of ostrowski like inequalities involving n knots we compute the optimal constants of ostrowski like inequalities involving n knots given by huy and ngo

new weighted ostrowski and cebysev type inequalities abstract on utilizing a generalization of the weighted montgomery identity obtained by barnett and dragomir published in n s barnett s s dragomir on the weighted inequalities j inequal pure appl math 8 4 2007 art 96 new weighted ostrowski and cebysev type inequalities are established

a new generalization of ostrowski type inequality involving functions of two independent variables the main purpose of this paper is to derive a new inequality of ostrowski type involving functions of two independent variables by using certain integral inequalities

gruss type inequalities in normed spaces abstract generalizations of the classic gruss inequality in normed spaces are given the results are illustrated with some specific examples

new results concerning chebyshev gruss type inequalities via discrete oscillations the classical form of gruss inequality was first published by g gruss and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions in the subsequent years many variants of this inequality appeared in the literature the aim of this paper is to consider some new bivariate chebyshev gruss type inequalities via discrete oscillations and to apply them to different tensor products of linear not necessarily positive well known operators we also compare the new inequalities with some older results in the end we give a chebyshev gruss type inequality with discrete oscillations for more than two functions

a generalization of levy s concentration variance inequality sharp lower bounds are found for the concentration of a probability distribution as a function of the expectation of any given convex symmetric function in the case x x c 2 wherec is the expected value of the distribution these bounds yield the classical concentration variance inequality of levy an analogous sharp inequality is obtained in a similar linear search setting where a sharp lower bound for the concentration is found as a function of the maximum probability swept out from a fixed starting point by a path of given length

a generalization of gruss s inequality in inner product spaces and applications a generalization of the classical gruss s integral inequality in inner product spaces is given some applications for positive linear functionals and integrals are also pointed out

a note on some ostrowski like type inequalities abstract error estimate plays an important role for numerical integration some ostrowski like type inequalities concerning a new type of quadrature formula are established recently by huy and ngo 2009 2010 6 7 in this note improvement and extension to these inequalities are given

an iterative method for solving nonlinear equations an iterative method for finding a solution of the equation f x 0 is presented the method is based on some specially derived quadrature rules it is shown that the method can give better results than the newton method

a generalization of the ostrowski integral inequality for mappings whose derivatives belong to lp a b and applications in numerical integration a generalization of ostrowski integral inequality for mappings whose derivatives belong to l 1 a b and applications for general quadrature formulae are given

improvement of some inequalities of euler gruss type abstract we prove an inequality of gruss type and use it to improve strictly some general euler gruss type inequalities all improved inequalities are sharp

new bounds for moments of continuous random variables in this paper some gruss and ostrowski gruss type inequalities are applied to estimate the moments of continuous random variables whose probability density function is in l p space some results of kumar are generalized p kumar inequalities involving moments of a continuous random variable defined over a finite interval comput math appl 48 2004 257 273 p kumar the ostrowski type moment integral inequalities and moment bounds for continuous random variables comput math appl 49 2005 1929 1940

the ostrowski type moment integral inequalities and moment bounds for continuous random variables we establish ostrowski type integral inequalities involving moments of a continuous random variable defined on a finite interval we also derive bounds for moments from these inequalities further we discuss applications of these bounds to the euler s beta mappings and illustrate their behaviour

a survey on some inequalities for expectation and variance inequalities for continuous random variables having the probability density function defined on a finite interval obtained recently by the authors are surveyed

tomographic analysis of sign altering functions by maximum entropy method abstract generalization of the maximum entropy method mem for the reconstruction of sign altering functions from two dimensional tomographic measurement data is developed three dimensional algorithms for parallel beam geometry are considered results of numerical simulations for composite model are presented

remarks on ostrowski like inequalities abstract we show the error inequalities on quadrature formulas obtained by huy and ngo can be improved if m is even

inequalities involving moments of a continuous random variable defined over a finite interval some results based on the korkine s identity and integral inequalities of holder and gruss are obtained for the moments of a continuous random variable whose probability distribution is a convex function on the interval of real numbers applications of these results are considered in deriving the inequalities involving higher moments and special means and also in evaluating moments of a beta random variable

several error inequalities for a quadrature formula with a parameter and applications in this paper we will derive several error inequalities for a quadrature formula with a parameter which will not only provide some generalizations of the known results but also give some other interesting quadrature formulae as special cases furthermore sharp upper and lower error bounds for the double error inequalities are obtained applications in numerical integration are also given

a generalization of two sharp inequalities in two independent variables a generalization of two sharp inequalities of simpson type and ostrowski type in two independent variables is established

improvement of some ostrowski gruss type inequalities abstract in this paper we improve and further generalize some ostrowski gruss type inequalities involving bounded once and twice differentiable mappings

an inequality for monotonic functions generalizing ostrowski and related results in this paper we establish a genralisation of the ostrowski inequality for monotonic functions that also includes various recent results and apply it for quadrature formulae in numerical integration

some generalized ostrowski gruss type integral inequalities in this paper we establish some new ostrowski gruss type integral inequalities involving k 1 interior points in 1d case which are generalizations of some known results in the literature and one of which is sharp then we deduce an ostrowski gruss type integral inequality in 2d case involving k 1 2 interior points for the first time we also present one application on the estimate of error bound for numerical integration formula in which a sharp error bound for a new numerical integration formula is provided by the results established

some ostrowski gruss type inequalities and applications new generalizations of ostrowski gruss type inequalities for functions of lipschitzian type are established applications for cumulative distribution functions are given

a representation of the peano kernel for some quadrature rules and applications a general interpolating formula is established from this formula all newton cotes quadrature rules of the closed type can be derived some corrected interpolating polynomials are also derived and used for obtaining corresponding quadrature rules a new effective representation of the peano kernel is derived estimation of errors for these quadrature rules is established

a note to inequalities of euler gruss type following the main ideas of wang 1 we generalize matie s results and establish our inequalities for functions with n t h derivatives of bounded p variation all of our error bounds are sharp in the sense that they cannot be replaced by smaller ones

new inequalities of ostrowski type for mappings whose derivatives are s convex in the second sense via fractional integrals a new identity similar to an identity proved in alomari et al 2010 15 for fractional integrals is established then by making use of the established identity some new ostrowski type inequalities for riemann liouville fractional integral are established our results have some relationships with the results of alomari et al 2010 proved in 15 and the analysis used in the proofs is simple

a generalization of ostrowski inequality on time scales for k points abstract in this paper we first generalize the ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions we also point out some particular ostrowski type inequalities on time scales as special cases

a new ostrowski gruss inequality involving 3n knots abstract this is the fifth and last in our series of notes concerning some classical inequalities such as the ostrowski simpson iyengar and ostrowski gruss inequalities in r in the last note we propose an improvement of the ostrowski gruss inequality which involves 3 n knots where n 1 is an arbitrary numbers more precisely suppose that x k k 1 n 0 1 y k k 1 n 0 1 and k k 1 n 0 n are arbitrary sequences with k 1 n k n and k 1 n k x k n 2 the main result of the present paper is to estimate 1 n k 1 n k f a b a y k 1 b a a b f t d t f b f a n k 1 n k y k x k in terms of either f or f unlike the standard ostrowski gruss inequality and its known variants which basically estimate f x a b f t d t b a in terms of a correction term as a linear polynomial of x and some derivatives of f our estimate allows us to freely replace f x and the correction term by using 3 n knots x k k 1 n y k k 1 n and k k 1 n as far as we know this is the first result involving the ostrowski gruss inequality with three sequences of parameters

a new inequality of ostrowski gruss type and applications to some numerical quadrature rules in this paper we derive some gruss and ostrowski gruss type inequalities for functions in l p spaces as applications we provide some new estimates for the error in some numerical integration rules in particular we deal with the mid point and trapezoid quadrature rules

sharp inequalities of simpson type and ostrowski type two sharp inequalities are derived the first is a sharp simpson s inequality and the second is a sharp inequality of ostrowski type the mentioned inequalities give error bounds for some known quadrature rules these results enlarge applicability email protected the corresponding quadrature rules with respect to the obtained error bounds applications in numerical integration are also given

on some generalizations of an ostrowski gruss type integral inequality in this paper we improve and extend a new ostrowski gruss type integral inequality obtained recently by feng and meng 2012 26 to be precise we show that a condition imposed on the inequality can be removed furthermore we provide a two dimensional generalization of this ostrowski gruss type inequality which is sharp

ostrowski s inequality for vector valued functions and applications abstract in this paper we obtain some ostrowski type inequalities for vector valued functions which both generalise and improve the scalar case and show that the midpoint inequality is the best possible inequality in the class a quadrature formula of the riemann type for the bochner integral and the error bounds are considered applications to operator inequalities and numerical approximation for the mild solution of inhomogeneous vector valued differential equations are also pointed out in the last section a numerical example is analysed

a generalization of the corrected midpoint trapezoid rule and error bounds a generalization of the corrected midpoint trapezoid rule is derived various error bounds for this generalization are established

weighted quadrature rules via gruss type inequalities for weighted lp spaces new estimates of gruss type for weighted ebysev functional in weighted lp spaces are presented by using the sonin s identity these results are applied to obtain new ostrowski type inequalities and further to weighted numerical rules for functions whose derivative belongs to weighted lp spaces

finite monoids from word to circuit evaluation the problem of evaluating a circuit whose wires carry values from a finite monoid m and whose gates perform the monoid operation provides a meaningful generalization to the well studied problem of evaluating a word over m evaluating words over monoids is closely tied to the fine structure of the complexity class nc 1 and in this paper analogous ties between evaluating circuits over monoids and the structure of the complexity class p are exhibited it is shown that circuit evaluation in the case of any nonsolvable monoid is p complete while circuits over solvable monoids can be evaluated in det subseteq nc 2 then the case of aperiodic monoids is completely elucidated their circuit evaluation problems are either in ac 0 or l or nl complete depending on the precise algebraic properties of the monoids finally it is shown that the evaluation of circuits over the cyclic group bbb z q for fixed q geq 2 is complete for the logspace counting class co mod ql that the problem for p groups p a prime is complete for mod pl and that the more general case of nilpotent groups of exponent q belongs to the boolean closure of mod ql

the aα spread of a graph abstract let a g and d g be the adjacency matrix and the degree diagonal matrix of a graph g respectively for any real number 0 1 nikiforov defined the a matrix of a graph g as a g d g 1 a g the a spread of a graph is the difference between the largest eigenvalue and the smallest eigenvalue of the a matrix of the graph in this paper we obtain some new lower bounds on a spread and characterize the extremal graphs for certain cases which extend the results of a spread and q spread moreover some graph operations on a spread are presented

gruss type inequalities abstract a connection between gruss inequality and the error of best approximation is revealed a gruss type inequality that unifies the continuous and discrete versions of the classical gruss inequalities is established

sharp inequalities of ostrowski type for convex functions defined on linear spaces and application an ostrowski type inequality for convex functions defined on linear spaces is generalised some inequalities which improve the hermite hadamard type inequality for convex functions defined on linear spaces are derived using the obtained result the results in normed linear spaces are used to obtain some inequalities which are related to the given norm and associated semi inner products and to prove the sharpness of the constants in those inequalities

sharp bounds for integral means we introduce a bound m of f f m 2 f which allows us to give for 0 p sharp upper bounds and for p 0 sharp lower bounds for the average of f p over e if the average of f over e is zero as an application we give a new proof of gruss s inequality estimating the covariance of two random variables we also give a new estimate for the error term in the trapezoidal rule

an inequality of ostrowski gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules abstract in this paper we derive a new inequality of ostrowski gruss type and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules

improvements of the ostrowski integral inequality for mappings of bounded variation i in this paper we establish some improvements of the ostrowski integral inequality for mappings of bounded variation

an ostrowski gruss type inequality on time scales we derive a new inequality of ostrowski gruss type on time scales by using the gruss inequality on time scales and thus unify corresponding continuous and discrete versions we also apply our result to the quantum calculus case

on ostrowski type inequalities for stieltjes integrals with absolutely continuous integrands and integrators of bounded variation some ostrowski type inequalities are given for the stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation the case when f is convex is explored applications for the mid point rule and a generalised trapezoid type rule are also presented

word problems and membership problems on compressed words we consider a compressed form of the word problem for finitely presented monoids where the input consists of two compressed representations of words over the generators of a monoid m and we ask whether these two words represent the same monoid element of m words are compressed using straight line programs i e context free grammars that generate exactly one word for several classes of finitely presented monoids we obtain completeness results for complexity classes in the range from p to expspace as a by product of our results on compressed word problems we obtain a fixed deterministic context free language with a pspace complete compressed membership problem the existence of such a language was open so far finally we will investigate the complexity of the compressed membership problem for various circuit complexity classes

error inequalities for a quadrature formula and applications an optimal two point quadrature formula of open type is derived it is shown that the optimal quadrature formula has a better error bound than the well known two point gaus quadrature formula various error inequalities for this formula are established applications in numerical integration are given

improvement and further generalization of inequalities of ostrowski gruss type abstract we improve some inequalities of ostrowski gruss type and further generalize them we apply the obtained results to the estimation of error bounds for some numerical quadrature rules also some bounds for the differences of some special means are discussed

a unified approach to some inequalities of ostrowski gruss type based on the euler maclaurin formula in the spirit of 1 we provide a unified approach to some inequalities of ostrowski gruss type which include some existing results as special cases some illustrative examples are also included

a new way to think about ostrowski like type inequalities in this present paper by considering some known inequalities of ostrowski like type we propose a new way to treat a class of ostrowski like type inequalities involving n points and m th derivative to be precise the following inequality email protected a bf x email protected i 1nf a x i b a 2m 54 b a m 1 m 1 s s holds where email protected sup a x bf m x email protected inf a x bf m x and for suitable x 1 x 2 x n it is worth noticing that n m are arbitrary numbers this means that the estimate in is more accurate when m is large enough our approach is also elementary

a method for solving nonlinear equations a method for finding a solution of the equation f x 0 is presented the method is based on some specially derived quadrature rules it is shown that the method can give better results than the newton method

on generalized gruss type inequalities for k fractional integrals the aim of the present paper is to investigate some new integral inequalities of gruss type for k riemann liouville fractional integrals from our results new weighted or classical gruss type inequalities have been established for some special cases moreover special cases of the integral inequalities in this paper have been obtained by dahmani and tabharit 2010 in 5

generalizations of weighted ostrowski type inequalities for mappings of bounded variation and their applications abstract in this paper we establish some generalizations of weighted ostrowski type inequalities

logspace and logtime leaf languages the computation tree of a nondeterministic machinemwith inputxgives rise to aleaf stringformed by concatenating the outcomes of all the computations in the tree in lexicographical order we may characterize problems by considering for a particular leaf language y the set of allxfor which the leaf string ofmis contained iny in this way in the context of polynomial time computation leaf languages were shown to capture many complexity classes in this paper we study the expressibility of the leaf language mechanism in the contexts of logarithmic space and of logarithmic time computation we show that logspace leaf languages yield a much finer classification scheme for complexity classes than polynomial time leaf languages capturing also many classes withinp in contrast logtime leaf languages basically behave like logtime reducibilities both cases are more subtle to handle than the polynomial time case we also raise the issue of balanced versus nonbalanced computation trees underlying the leaf language we indicate that it is a nontrivial problem to obtain information about the leaf string of a nonbalanced computation tree and present conditions under which it does not matter whether the computation tree is balanced or not

on the generalization of ostrowski and gruss type discrete inequalities abstract the main purpose of this paper is to establish a generalization of discrete inequalities of the ostrowski and gruss type involving two functions the analysis used in the proofs is fairly elementary

gruss and ostrowski type inequalities abstract in this paper we use a method originated in s s dragomir some gruss type inequalities in inner product spaces j inequal pure appl math 4 2 2003 article 42 to establish some gruss and ostrowski type inequalities

a sharp estimate for the peano error representation we provide a sharp estimate of the peano error representation formula for linear functionals as applications we obtain sharp estimates for the remainder term in general quadrature formulae and expand some ostrowski like type inequalities to linear functionals the new approach extends and unifies many earlier results on the subject dragomir and wang 1997 cheng 2001 matic 2003 vong 2011 gonska et al 2012