alternative proof for the localization of sinai s walk we give an alternative proof of the localization of sinai s random walk in random environment under weaker hypothesis than the ones used by sinai moreover we give estimates that are stronger than the one of sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood

integral inequalities for concave functions with applications to special functions in this paper we prove refinements extensions and counterparts of known integral inequalities for concave functions furthermore we apply our results to find new inequalities for some special functions and mean values

inequalities for the tails of some elementary series we prove that if dn k x n k 2 n k 2 in k x in k x n 2 in x 2 with formula then we have for all x 0 dn k x k 0 and dn 1 k x 2 dn k x dn 2 k x n k 1 0

inequalities involving generalized interpolation polynomials the generalized vandermonde determinant and the generalized interpolation polynomial are defined we establish inequalities involving generalized interpolation polynomials under the proper hypotheses our main result is j 1nv n x j u a v n x a y j 2n n 1 i 0 n 12 j 1 n 12 1i j n n 1 2 v n x n q x 1 q qx n q a j 1n y j v n xx n a the approach used is able to combine algebraic and analytical theories

a refinement of the cauchy schwarz inequality abstract we prove if xk and yk k 1 n are real numbers satisfying 0 x 0 1 x 2 2 x n n and 0 n y n 1 y 1 then k 1 n x k y k 2 k 1 n y k k 1 n x 2 k 1 4 x k x k 1 y k with equality holding if and only if xk kx1 k 1 n and y1 yn inequality is valid in particular if the sequence xk is positive and convex

quenched annealed and functional large deviations for one dimensional random walk in random environment suppose that the integers are assigned random variables i taking values in the unit interval which serve as an environment this environment defines a random walk x n called a rwre which when at i moves one step to the right with probability i and one step to the left with probability 1 i when the i sequence is i i d greven and den hollander 1994 proved a large deviation principle for x n n conditional upon the environment with deterministic rate function we consider in this paper large deviations both conditioned on the environment quenched and averaged on the environment annealed for the rwre in the ergodic environment case the annealed rate function is the solution of a variational problem involving the quenched rate function and specific relative entropy we also give a detailed qualitative description of the resulting rate functions our techniques differ from those of greven and den hollander and allow us to present also a trajectorial quenched large deviation principle

input forces estimation of beam structures by an inverse method an on line recursive inverse method to estimate the input forces of beam structures is presented the inverse method is based on the kalman filter and a recursive least squares algorithm the filter models the system dynamics in a linear set of state equations the state equations of the beam structures were constructed using the finite element method the practicability and accuracy of the estimation method were examined with numerical simulations from which the input forces of a cantilever beam with a lumped mass on the free end were estimated from the output responses in the numerical experiments the cantilever beam was subjected to five types of input forces i e sinusoidal triangular impulse rectangular impulse a series of impulses and random the simulation results show that the inverse method has an excellent performance to estimate the input forces of beam structural systems from the noisy measurements

an inverse non linear force vibration problem of estimating the external forces in a damped system with time dependent system parameters abstract an inverse non linear force vibration problem based on the iterative regularization method i e the conjugate gradient method cgm is used to estimate the unknown time dependent external forces in a damped system having time dependent system parameters by using the measured system displacement it is assumed that no prior information is available on the functional form of the unknown external forces in the present study thus it is classified as the function estimation in inverse calculation the accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements the numerical simulations are performed to test the validity of present algorithm by using different types of external forces and measurements results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses within a couple of seconds of cpu time at pentium ii 300 mhz pc

inequalities for residuals of power expansions for the exponential function and completely monotone functions letin x be the residual after thenth term of power series for a functionf in the casef x ex x 0 inequalities forinhave been studied by many authors but there are almost no results forx 0 in this paper we present some bounds forinwithf x e xand we give some results for completely monotone functions

force identification of dynamic systems using genetic programming one obvious limitation of the traditional force identification techniques is that they are unable to obtain the explicit expression of the force moreover some techniques need both the displacement and velocity data of all freedoms and some need the markov parameters from numerical calculation or experimental test before the force identification can be carried out this paper presents a genetic programming gp based method for excitation force identification of dynamic systems to overcome these traditional methods disadvantages gp is employed as a search and optimization method to obtain the optimal if not the best force expression from the known dynamic response one obvious merit of the proposed method is that it can obtain the explicit expression of the unknown force another advantage is that it only needs the dynamic response data at one point i e displacement or velocity or acceleration of one freedom illustrative examples demonstrate that the gp based method is able to identify the excitation force of a single degree a three degree dynamic systems and a frame structure depicting its potential for force forecast problems

chebyshev type inequalities involving permanents and their applications abstract we extend the well known chebyshev s inequality to some new cases involving permanents under the proper hypotheses our main results are per a b n per a n per b n and per a i 1 n j 1 n a i j per b i 1 n j 1 n b i j as applications we consider the problem of finding bounds of the ratios of two functions involving permanents

functional inequalities for the incomplete gamma function abstract we present several inequalities for f a x a x a 0 a 0 x 0 where a x is the incomplete gamma function one of our theorems states that the inequalities f a s p x 1 x n f a x 1 f a x n f a s q x 1 x n p q 0 hold for all nonnegative real numbers x 1 x n n 2 if and only if p m i n a 1 and q m a x a 1 here s t x 1 x n denotes the power sum of order t this extends and complements a result published by ismail and laforgia in 2006

inequalities involving modified bessel functions of the first kind ii the intrinsic properties including logarithmic convexity concavity of the modified bessel functions of the first kind and some other related functions are obtained several inequalities involving functions under discussion are established

random walks in random environments random walks in random environments and their diffusion analogues have been a source of surprising phenomena and challenging problems especially in the non reversible situation since they began to be studied in the 1970s we review the model available results and techniques and point out several gaps in the understanding of these processes

quenched sub exponential tail estimates for one dimensional random walk in random environment suppose that the integers are assigned i i d random variables x taking values in the unit interval which serve as an environment this environment defines a random walk x n called a rwre which when at x moves one step to the right with probability x and one step to the left with probability 1 x solomon 1975 determined the almost sure asymptotic speed v rate of escape of a rwre greven and den hollander 1994 have proved a large deviation principle for x n n conditional upon the environment with deterministic rate function for certain environment distributions where the drifts 2 x 1 can take both positive and negative values their rate function vanisheson an interval 0 v we find the rate of decay on this interval and prove it is a stretched exponential of appropriate exponent that is the absolute value of the log of the probability that the empirical mean x n n is smaller than v v 0 v behaves roughly like a fractional power of n the annealed estimates of dembo peres and zeitouni 1996 play a crucial role in the proof we also deal with the case of positive and zero drifts and prove there a quenched decay of the form

precise large deviation estimates for a one dimensional random walk in a random environment suppose that the integers are assigned i i d random variables f xg taking values in the interval 1 2 1 which serve as an environment thisenvironmentdenesarandomwalk fxkg calledarwre which when at x moves one step to the right with probability x and one step to the left withprobability1 x solomon 1975 determinedthealmost sureasymp totic speed rate of escape of a rwre in a more general set up dembo peres and zeitouni 1996 following earlier work by greven and den hol lander 1994 on the quenched case have computed rough tail asymptotics for the empirical mean of the annealed rwre they conjectured the form of the rate function in a full ldp we prove in this paper their conjecture the proof is based on a icoarse graining schemei together with comparison techniques

a new approach for fuzzy information retrieval based on weighted power mean averaging operators an information retrieval system can help users to retrieve documents relevant to the users queries in recent years some researchers used averaging operators i e infinite one operators waller kraft operators p norm operators and gma operators to handle and and or operations of users fuzzy queries for fuzzy information retrieval but they still have some drawbacks e g sometimes query results do not coincide with the intuition of the human being in this paper we present new averaging operators called weighted power mean averaging wpma operators based on the weighted power mean for dealing with fuzzy information retrieval to overcome the drawbacks of the existing methods furthermore we also extend the proposed wpma operators into the extended wpma operators to handle weighted fuzzy queries for fuzzy information retrieval the proposed wpma operators are more flexible and more intelligent than the existing averaging operators to handle users fuzzy queries for fuzzy information retrieval

some gamma function inequalities a class of completely monotonic functions are presented involving the gamma function as well as the derivative of the psi function as a consequence new upper and lower bounds for the ratio f x 1 f x s are obtained and compared with related bounds given in part by j d keckic and p m vasic our results are further applied to obtain functions which are laplace transforms of infinitely divisible probability measures

estimation of modal loads using structural response in this study an analytical procedure is developed based on the kalman filtering approach to estimate modal loads applied on a structure using limited measured response of the structure the effect of various variables such as the type of response the noise level and the level of uncertainty in dynamic properties of the structure on the modal load estimation is evaluated in the frequency domain through numerical analysis for a single degree of freedom sdof and a multi degree of freedom mdof system it is observed that the acceleration response is relatively more stable and robust in external load estimation than other response components the noise is amplified at the high frequency range for the displacement or velocity response whereas in the case of acceleration response the noise is not amplified in the estimated external load it is also found that the discrepancy between dynamic characteristics derived for an analytical model and the actual structure causes the transfer function from the actual load to the estimated load to distort near and below the structural natural frequency the estimation of external loads is extended to a mdof system the results show that the modal loads can be estimated accurately from limited measurements of acceleration response on the basis of the assumption that the measured response can be transformed to the modal response by a proper orthogonal decomposition and the corresponding modal properties used for the transformation can be obtained by a system identification technique

aggregation operators for selection problems this paper describes and compares aggregation techniques for multi expert multi criteria decision making the process of selecting applicants for a ph d program using different aggregation operators is presented as a case study the focus is on applying these operators using only ordinal sorted information a heuristic for determining weights in these situations is discussed the results obtained with different aggregation methods are compared and analyzed

generalization and sharpness of the power means inequality and their applications abstract in this paper we generalize and sharpen the power means inequality by using the theory of majorization and the analytic techniques our results unify some optimal versions of the power means inequality as application a well known conjectured inequality proposed by janous et al is proven furthermore these results are used for studying a class of geometric inequalities for simplex from which some interesting inequalities including the refined euler inequality and the reversed finsler hadwiger type inequality are obtained

geometrically concave univariate distributions in this paper our aim is to show that if a probability density function is geometrically concave convex then the corresponding cumulative distribution function and the survival function are geometrically concave convex too under some assumptions the proofs are based on the so called monotone form of l hospital s rule and permit us to extend our results to the case of the concavity convexity with respect to holder means to illustrate the applications of the main results we discuss in details the geometrical concavity of the probability density function cumulative distribution function and survival function of some common continuous univariate distributions moreover at the end of the paper we present a simple alternative proof to schweizer s problem related to the mulholland s generalization of minkowski s inequality

log concavity for bernstein type operators using stochastic orders abstract this paper aims to study the preservation of log concavity for bernstein type operators in particular attention is focused on positive linear operators defined on the positive semi axis admitting a probabilistic representation in terms of a process with independent increments this class includes the classical gamma szasz and szasz durrmeyer operators with respect to the first and second operators the results of this paper correct two erroneous counterexamples in 10 as a main tool in our results we use stochastic order techniques our results include as a particular case the log concavity of certain functions related to the incomplete gamma function

inequalities for the chi square distribution function abstract letpa x 1 x a0 e ttx 1 dtbe the chi square distribution function and letmt u v be the weighted power mean of ordert we prove the following ifx y 0 x y and 0 1 are fixed real numbers then the inequalities formula are valid for all real numbersa 0 if and only ifr 0 ands in particular we obtain that for alla 0 the functionx pa x is log concave on 0 this proves a conjecture of m merkle

large deviations for a random walk in random environment let px x z be an i i d collection of 0 1 valued random variables given let x n n 0 be the markov chain on z defined by x 0 0 and x n 1 x n 1 resp x n n 1 with probability px n resp 1 px n it is shown that x n n satisfies a large deviation principle with a continuous rate function that is lim n 1 n log p x n n n i a s for n 1 1 first we derive a representation of the rate function i in terms of a variational problem second we solve the latter explicitly in terms of random continued fractions this leads to a classification and qualitative description of the shape of i in the recurrent case i is nonanalytic at 0 in the transient case i is nonanalytic at c 0 c for some c 0 with linear pieces in between

a variant of jensen steffensen s inequality and quasi arithmetic means a variant of jensen steffensen s inequality is proved necessary and sufficient conditions for the equality in jensen steffensen s inequality are established several inequalities involving more than two monotonic functions and generalized quasi arithmetic means with not only positive weights are proved it is shown that such generalized quasi arithmetic means have the same comparability properties as those with positive weights

power geometric operators and their use in group decision making the power average pa operator and the power ordered weighted average powa operator are the two nonlinear weighted average aggregation tools whose weighting vectors depend on the input arguments in this paper we develop a power geometric pg operator and its weighted form which are on the basis of the pa operator and the geometric mean and develop a power ordered geometric pog operator and a power ordered weighted geometric powg operator which are on the basis of the powa operator and the geometric mean and study some of their properties we also discuss the relationship between the pa and pg operators and the relationship between the powa and powg operators then we extend the pg and powg operators to uncertain environments i e develop an uncertain pg upg operator and its weighted form and an uncertain power ordered weighted geometric upowg operator to aggregate the input arguments taking the form of interval of numerical values furthermore we utilize the weighted pg and powg operators respectively to develop an approach to group decision making based on multiplicative preference relations and utilize the weighted upg and upowg operators respectively to develop an approach to group decision making based on uncertain multiplicative preference relations finally we apply both the developed approaches to broadband internet service selection

an essay on the history of inequalities abstract we look at the rise of a discipline of inequalities trying to answer several questions when did it become respectable to write a paper whose intent was the proof of an inequality when were inequalities first given names who is responsible for the growth in the inequality literatures what are the events that shaped the discipline we give first answers to these questions

large deviation principle for random walk in a quenched random environment in the low speed regime we consider a one dimensional random walk x n n n in a random environment of zero or strictly positive drifts we establish a full large deviation principle for x n n of the correct order n log n 2 in the low speed regime valid for almost every environment this completes the large deviation picture obtained earlier by greven and den hollander and gantert and zeitouni in the case of zero and positive drifts the proof uses coarse graining along with concentration of measure techniques

a contribution to the study of the metric and euclidean structures of dissimilarities this paper is concerned with the geometric properties of dissimilarity coefficients defined on finite sets and especially with their euclidean nature we present several particular transformations which preserve euclideanarity and we complete through the study of a one parameter family the current knowledge of the metric and euclidean structure of coefficients based on binary data these results are directly deduced from two theorems which prove the positive semi definite status of some quadratic forms which play a large role in some definitions of dissimilarity commonly used

tail estimates for one dimensional random walk in random environment suppose that the integers are assigned i i d random variables x taking values in the unit interval which serve as an environment this environment defines a random walk x k called a rwre which when atx moves one step to the right with probability x and one step to the left with probability 1 x solomon 1975 determined the almost sure asymptotic speed rate of escape of a rwre for certain environment distributions where the drifts 2 x 1 can take both positive and negative values we show that the chance of the rwre deviating below this speed has a polynomial rate of decay and determine the exponent in this power law for environments which allow only positive and zero drifts we show that these large deviation probabilities decay like exp cn1 3 this differs sharply from the rates derived by greven and den hollander 1994 for large deviation probabilities conditioned on the environment as a by product we also provide precise tail and moment estimates for the total population size in a branching process with random environment

rates of convergence of diffusions with drifted brownian potentials we are interested in the asymptotic behaviour of a diffusion process with drifted brownian potential the model is a continuous time analogue to the random walk in random environment studied in the classical paper of kesten kozlov and spitzer we not only recover the convergence of the diffusion process which was previously established by kawazu and tanaka but also obtain all the possible convergence rates an interesting feature of our approach is that it shows a clear relationship between drifted brownian potentials and bessel processes

slowdown and neutral pockets for a random walk in random environment we consider a d dimensional random walk in random environment for which transition probabilities at each site are either neutral or present an effective drift pointing to the right we obtain large deviation estimates on the probability that the walk moves in a too slow ballistic fashion both under the annealed and quenched measures these estimates underline the key role of large neutral pockets of the medium in the occurrence of slowdowns of the walk

inequalities for the generalized marcum q function abstract in this paper we consider the generalized marcum q function of order 0 real defined by q a b 1 a 1 b t e t 2 a 2 2 i 1 at d t where a b 0 i stands for the modified bessel function of the first kind and the right hand side of the above equation is replaced by its limiting value when a 0 our aim is to prove that the function q a b is strictly increasing on 0 for each a 0 b 0 and to deduce some interesting inequalities for the function q moreover we present a somewhat new viewpoint of the generalized marcum q function by showing that satisfies the new is better than used nbu property which arises in economic theory

beam selection gain versus antenna selection gain we consider beam selection using a fixed beamforming network fbn at a base station with m array antennas in our setting a butler matrix is deployed at the rf stage to form m beams and then the best beam is selected for transmission we introduce some properties of the noncentral chi square distribution and prove the resulting properties of the beam selection gain verifying that beam selection is superior to antenna selection in rician channels with any k factors furthermore we find asymptotically tight stochastic bounds of the beam selection gain which yield approximate closed form expressions of the expected selection gain and the ergodic capacity beam selection has the order of growth of the ergodic capacity logm regardless of user location in contrast to log logm for antenna selection

theory of surround system and associated inequalities in this paper we define the surround system s m c l and the surround system with a center s 2 p c l under the proper hypotheses we establish several geometric inequalities for s 2 p c l as applications we give the background of the surround system with a center s 2 p c l in space science

bayesian force reconstruction with an uncertain model this paper presents a bayesian approach for force reconstruction which can deal with both measurement noise and model uncertainty in particular an uncertain model is considered for inversion in the form of a matrix of frequency response functions whose modal parameters originate from either measurements or a finite element model the model uncertainty and the regularization parameter are jointly determined with the unknown force through monte carlo markov chain methods bayesian credible intervals of the force are built from its posterior probability density function by taking into account the quantified model uncertainty and measurement noise the proposed approach is illustrated and validated on numerical and experimental examples

some properties of generalized exponential entropies with applications to data compression abstract the scale of exponential entropies of order is introduced it unifies a number of notions of generalized differential entropies for continuous distributions the properties of this scale are derived from results in the theory of means we show that the scale can represent the extent of a probability distribution i e its degree of concentration with regard to a reference measure this fact has several consequences that are of interest in the theory of data or signal compression the aspects of data compression considered are the intrinsic extent of a probability distribution introduced by l l campbell and the properties of entropy series we investigate specially the exponential families of distributions in particular the miller thomas or generalized gaussian family of distributions

two optimal double inequalities between power mean and logarithmic mean for email protected r the power mean m p a b of order p the logarithmic mean l a b and the arithmetic mean a a b of two positive real values a and b are defined by m p a b a p b p2 1 p p 0 ab p 0 l a b b alogb loga a b a a b and a a b a b2 respectively in this article we answer the questions what are the greatest values p and r and the least values q and s such that the inequalities m p a b 13a a b 23l a b m q a b and m r a b 23a a b 13l a b m s a b hold for all a b 0

properties of the probability density function of the non central chi squared distribution abstract in this paper we consider the probability density function pdf of a non central 2 distribution with arbitrary number of degrees of freedom for this function we prove that can be represented as a finite sum and we deduce a partial derivative formula moreover we show that the pdf is log concave when the degrees of freedom is greater or equal than 2 at the end of this paper we present some turan type inequalities for this function and an elegant application of the monotone form of l hospital s rule in probability theory is given

generalized convexity and inequalities abstract let r 0 and let m be the family of all mean values of two numbers in r some examples are the arithmetic geometric and harmonic means given m 1 m 2 m we say that a function f r r is m 1 m 2 convex if f m 1 x y m 2 f x f y for all x y r the usual convexity is the special case when both mean values are arithmetic means we study the dependence of m 1 m 2 convexity on m 1 and m 2 and give sufficient conditions for m 1 m 2 convexity of functions defined by maclaurin series the criteria involve the maclaurin coefficients our results yield a class of new inequalities for several special functions such as the gaussian hypergeometric function and a generalized bessel function

on multidimensional branching random walks in random environment we study branching random walks in random i i d environment in z d d geq 1 for this model the population size cannot decrease and a natural definition of recurrence is introduced we prove a dichotomy for recurrence transience depending only on the support of the environmental law we give sufficient conditions for recurrence and for transience in the recurrent case we study the asymptotics of the tail of the distribution of the hitting times and prove a shape theorem for the set of lattice sites which are visited up to a large time

review of force reconstruction techniques abstract an important engineering problem is the recovery of the input of a system given its output this is a difficult problem to solve in that it is often an ill defined problem such ill posedness is problematic since noise becomes very influential and results in inaccurate or non unique solutions to combat this ill posedness additional constraints are typically applied to redefine the problem leading to a well defined problem with a unique solution current input reconstruction methods span the spectrum of analysis and computation and we have grouped them into three categories direct regularization and probabilistic statistical each of these groups is divided into several subsets that offer different perspectives in which to view the reconstruction problem our primary interests lie in the behavior of mechanical systems and as such we have focused on the literature in these fields however applicability includes other fields with the same and similar governing equations

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

lagrangian mean type mappings for which the arithmetic mean is invariant we determine the class of all pairs of the lagrangian means forming mean type mappings which are invariant with respect to the arithmetic mean

schur convexity and schur geometrically concavity of gini means the schur convexity and the schur geometric convexity with variables x y r 2 for fixed s t of gini means g r s x y are discussed some new inequalities are obtained

generalized golden ratios defined by means abstract golden ratio is defined by a proportion corresponding to the geometric mean we introduce a generalized golden ratio as a fixed point of an operator defined by an arbitrary mean satisfying certain conditions an algorithm for the evaluation of the generalized golden ratio is obtained using banach s fixed point theorem as applications we show that some problems in shape optimization correspond to some aesthetic standards introduced in the paper

why does the kronecker model result in misleading capacity estimates many recent works that study the performance of multiple input multiple output mimo systems in practice assume a kronecker model where the variances of the channel entries upon decomposition on to the transmit and the receive eigenbases admit a separable form measurement campaigns however show that the kronecker model results in poor estimates for capacity motivated by these observations a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better in this paper we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates the transmit and or the receive eigenbases using tools from random matrix theory we then establish the theoretical basis behind the kronecker mismatch at the low and the high snr extremes 1 sparsity of the dominant statistical degrees of freedom dof in the true channel at the low snr extreme and 2 nonregularity of the sparsity structure disparities in the distribution of the dof across the rows and the columns at the high snr extreme

monotonicity theorems and inequalities for the complete elliptic integrals we prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind k and e these results lead to sharp symmetrical bounds for k and e which improve recently discovered inequalities

sharp power mean bounds for the gaussian hypergeometric function sharp inequalities are established between the gaussian hypergeometric function and the power mean these results extend known inequalities involving the complete elliptic integral and the hypergeometric mean

a mean value theorem and its applications abstract for a function f defined in an interval i satisfying the conditions ensuring the existence and uniqueness of the lagrange mean l f we prove that there exists a unique two variable mean m f such that f x f y x y m f f x f y for all x y i x y the mean m f is closely related l f necessary and sufficient condition for the equality m f m g is given a family of means m t t r relevant to the logarithmic means is introduced the invariance of geometric mean with respect to mean type mappings of this type is considered a result on convergence of the sequences of iterates of some mean type mappings and its application in solving some functional equations is given a counterpart of the cauchy mean value theorem is presented some relations between stolarsky means and m t means are discussed

lyapounov exponents and quenched large deviations for multidimensional random walk in random environment assign to the lattice sizes z z d i i d random 2d dimensional vectors z z e e 1 whose entries take values in the open unit interval and add up to one given a realization of this environment let x n n 0 be a markov chain on z d which when at z moves one step to its neighbor z e with transition probability z z e we derive a large deviation principle for x n n by means of a result similar to the shape theorem of first passage percolation and related models this result produces certain constants that are the analogue of the lyapounov exponents known from brownian motion in poissonian potential or random walk in random potential we follow a strategy similar to sznitman