about some new generalizations of bellman bihari results for integro functional inequalities with discontinuous functions and applications abstract in this article we present some new nonlinear bellman bihari type integral inequalities with delay for discontinuous functions integro sum inequalities impulse integral inequalities some applications of the results are included conditions of boundedness uniformly stability by lyapunov uniformly practical stability by chetaev uniformly for the solutions of impulsive differential and integro differential systems of ordinary differential equations

computing motivic zeta functions on log smooth models we give an explicit formula for the motivic zeta function in terms of a log smooth model it generalizes the classical formulas for snc models but it gives rise to much fewer candidate poles in general this formula plays an essential role in recent work on motivic zeta functions of degenerating calabi yau varieties by the second named author and his collaborators as a further illustration we explain how the formula for newton non degenerate polynomials can be viewed as a special case of our results

vanishing of principal value integrals on surfaces principal value integrals are associated to multi valued rational differential forms with normal crossings support on a non singular algebraic variety we prove their vanishing on rational surfaces in the context of a conjecture of denef jacobs as an appli cation we obtain a strong vanishing result for candidate poles of p adic and motivic igusa zeta functions

on the smallest poles of igusa s p adic zeta functions let k be a p adic field we explore igusa s p adic zeta function which is associated to a k analytic function on an open and compact subset of k n first we deduce a formula for an important coefficient in the laurent series of this meromorphic function at a candidate pole afterwards we use this formula to determine all values less than 1 2 for n 2 and less than 1 for n 3 which occur as the real part of a pole

on euler characteristics associated to exceptional divisors let k be an algebraically closed field and f e k x1 x fix an embedded resolution h x an i of f i o and denote by ei i e s the irreducible components of h l f l o with multiplicity ni in the 0 0 visor of f o h put also es ei uj1iej and denote by x ei its euler characteristic several conjectures concerning igusa s local zeta function and the topological zeta function of f motivate the study of euler characteristics associated to subsets uie tei of uiese1 which are maximal connected with respect to the property that dini for all i e t here d e n d 1 we prove that if h maps uiet ei to a point then

estimates for operator norms on weighted spaces and reverse jensen inequalities we examine the dependence on the a p norm of w of the operator norms of singular integrals maximal functions and other operators in l p w we also examine connections between some fairly general reverse jensen inequalities and the a p and rh p weight conditions

two weight extrapolation via the maximal operator abstract we give several extrapolation theorems for pairs of weights of the form w m k w and w mw w r w where w is any non negative function r 1 and m k is the k th iterate of the hardy littlewood maximal operator as an application we show that our results can be used to extend and sharpen results for square functions and singular integral operators by chang et al 1985 comment math helv 60 217 246 chanillo and wheeden 1987 indiana univ math j 36 277 294 wilson 1987 duke math j 55 879 887 1989 trans amer math soc 314 661 692 1989 illinois j math 33 361 366 and uchiyama 1995 studia math 115 135 149 in the process we prove a conjecture due to wilson

investigations of the properties motion for essential nonlinear systems perturbed by impulses on some hypersurfaces abstract in this work sufficiently conditions boundedness stability asymptotical stability exponential stability attraction practical stability nondisturbed motion systems with impulse perturbations on some hypersurfaces are obtained we formulate the conditions which guarantee that no beating motion of hypersurfaces will be present estimates of cauchy matrix system of variation for approximated system are obtained for different kinds of right side shorted system these estimates are used as one parametric scale increasing functions moreover we also consider two parametric scale such as proposed by demidovich

multiparameter operators and sharp weighted inequalities this article is concerned with the operators from harmonic analysis which are naturally associated to a multiple parameter family of dilations we are especially interested here in dealing with questions from the theory of such operators whose answers cannot be obtained by a reduction to the case of product operators we also introduce a new tool in order to carry out this multiparameter analysis which comes from the classical theory this is the concept of sharp weighted inequalities where for operators such as the hilbert transform or classical square function one asks for hilbert space inequalities which imply the correct estimates of the norm on lp of these operators as p becomes large 0 introduction in this article our main goal is to study classes of oper ators associated with multiparameter groups of dilations on rn in some sense the consideration of these operators is a natural next step or simplest case after those of the classical calderon zygmund theory and the product space theory it turns out that in order to obtain estimates for the multiparameter operators we shall be led to the following type of extremely classical question how does one obtain l2 estimates on r1 for the hilbert transform or other singular integrals which yield sharp estimates on the lp rl operator norm of h as p approaches 1 or oc these sharp weighted inequalities are of some independent interest and their study will be seen to be essentially equivalent to the deep work of chang wilson and wolff 3 on the exponential square integrability of functions whose area integral is bounded they also have other applications for example they provide an immediate extension of the chang wilson wolff estimates to product spaces as given by pipher in 12 at this point let us be more specific about the exact nature of the multipa rameter operators which we shall consider consider in r3 the dilations given by ps t x y z sx ty9 stz for s91 0 then there is a maximal operator first considered by zygmund ml and singular integrals tl introduced by ricci and stein 13 naturally associated to these dilations the maximal operator af3 is defined by

the motivic zeta function and its smallest poles abstract let f be a regular function on a nonsingular complex algebraic variety of dimension d we prove a formula for the motivic zeta function of f in terms of an embedded resolution this formula is over the grothendieck ring itself and specializes to the formula of denef and loeser over a certain localization we also show that the space of n jets satisfying f 0 can be partitioned into locally closed subsets which are isomorphic to a cartesian product of some variety with an affine space of dimension d n 2 finally we look at the consequences for the poles of the motivic zeta function

growth in an impulsive integral inequality abstract in this paper we study a finite sum integral inequality with a sequence of impulses making a sequential monotonization we give recursively defined functions to estimate solutions of the inequality piecewise in order to use the estimate to study boundedness and asymptotics of solutions for differential equations we regard the estimating function as a solution of a nonautonomous difference equation simplify the equation with composition of operators and reduce our discussion to qualitative analysis of the difference equation so that we give results on monotonicity boundedness and weighted boundedness for solutions of the inequality as applications we study boundedness and asymptotics of solutions for two impulsive differential equations

about new analogies of gronwall bellman bihari type inequalities for discontinuous functions and estimated solutions for impulsive differential systems abstract in this article we present new integral gronwall bellman bihari type inequalities for discontinuous functions integro sum inequalities as applications we investigate estimated solutions for impulsive differential systems conditions of boundedness stability practical stability

boundary value problems for a class of impulsive functional equations this paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions we study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times by the use of the monotone method some of the options included in this formulation are differential equations with maximum and integro differential equations in this paper we also prove that the lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval the corresponding results are established for the impulsive case the general formulation includes several types of functional dependence delay equations equations with maxima integro differential equations finally we consider the case of functional dependence which is given by nonincreasing and bounded functions

on muckenhoupt wheeden conjecture abstract let m denote the dyadic maximal function we show that there is a weight w and haar multiplier t for which the following weak type inequality fails sup t 0 t w x r t f x t c r f m w x d x with t replaced by m this is a well known fact this shows that a dyadic version of the so called muckenhoupt wheeden conjecture is false this accomplished by using current techniques in weighted inequalities to show that a particular l 2 consequence of the inequality above does not hold

mixed a1 a bounds for fractional integrals abstract for a fractional integral operator i we show that i f l q w q c w a q 1 p w a 1 q 1 q f l p w p where w a q sup q 1 w q q q m q w q d x is wilson a q s constant which is smaller than the a 1 q constant we also prove a weak type 1 1 bound for a couple of weights of the form w m w assuming that w a

monodromy eigenvalues and zeta functions with differential forms abstract for a complex polynomial or analytic function f there is a strong correspondence between poles of the so called local zeta functions or complex powers f 2 s where the are c differential forms with compact support and eigenvalues of the local monodromy of f in particular barlet showed that each monodromy eigenvalue of f is of the form exp 2 1 s 0 where s 0 is such a pole we prove an analogous result for similar p adic complex powers called igusa local zeta functions but mainly for the related algebro geometric topological and motivic zeta functions

zeta functions for curves and log canonical models the topological zeta function and igusa s local zeta function are respectively a geometrical invariant associated to a complex polynomial f and an arithmetical invariant associated to a polynomial f over a p adic field when f is a polynomial in two variables we prove a formula for both zeta functions in terms of the so called log canonical model of f 1 0 in bbb a 2 this result yields moreover a conceptual explanation for a known cancellation property of candidate poles for these zeta functions also in the formula for igusa s local zeta function appears a remarkable non symmetric q deformation of the intersection matrix of the minimal resolution of a hirzebruch jung singularity 1991 mathematics subject classification 32s50 11s80 14e30 14g20

motivic zeta functions of abelian varieties and the monodromy conjecture we prove for abelian varieties a global form of denef and loeser s motivic monodromy conjecture in arbitrary characteristic more precisely we prove that for every tamely ramified abelian variety a over a complete discretely valued field with algebraically closed residue field its motivic zeta function has a unique pole at chai s base change conductor c a of a and that the order of this pole equals one plus the potential toric rank of a moreover we show that for every embedding of ql in c the value exp 2 ic a is an l adic tame monodromy eigenvalue of a the main tool in the paper is edixhoven s filtration on the special fiber of the neron model of a which measures the behavior of the neron model under tame base change

integro sum inequalities and motion stability of systems with impulse perturbations abstract this article is devoted to the investigation of the properties of motion represented by essential nonlinear system of differential equations with impulse effect the results based on the solvability problem by s a chaplygin for discontinuous functions satisfy integro sum inequalities the conditions of boundedness stability asymptotical stability practical stability attraction motion for different kinds of nonlinearities of systems are obtained

the l log l e endpoint estimate for maximal singular integral operators abstract we prove in this paper the following estimate for the maximal operator t associated to the singular integral operator t t f l 1 w 1 r n f x m l log l w x d x w 0 0 1 this follows from the sharp l p estimate t f l p w p 1 1 p f l p m l log l p 1 w 1 p w 0 0 1 as a consequence we deduce that t f l 1 w w a 1 log e w a r n f w d x extending the endpoint results obtained in 23 and 15 to maximal singular integrals another consequence is a quantitative two weight bump estimate

on gronwall bellman bihari type integral inequalities in several variables with retardation the celebrated gronwall bellman bihari inequality and its various linear and nonlinear generalizations have been of vital importance in the study of existence uniqueness continuous dependence comparison perturbation boundedness and stability results of ordinar differential equations and integral equations 2 6 14 15 18 20 22 23 371 in recent years the more than one variable generalizations of this inequality have evoked considerable interest since they are handy tools in the theory of partial differential and integral equations specifically we refer to the results of bondge and pachpatte 7 11 131 bondge et 121 chu and metcalf 161 colan and diaz 171 headley 21 agarwal 11 pachpatte 24 301 rasmussen 31 shih and yeh 32 41 singare and pachpatte 33 snow 34 35 than dapani and agarwal 36 yeh 39 40 42 young 43 and zahariev and bainov 44 among others in this paper we establish some new nonlinear integral inequalities with delay in n independent variables which include and unify recent results on integral inequalities in several variables by shih and yeh 41 yeh 42 and zahariev and bainov 44 we also deduce from our results new generalizations of earlier results of bihari 6 bellman 4 dhongade and deo 18 191 and pachpatte 22 231 some applications of our results to a certain class of nonlinear hyperbolic functional partial differential equations are also given

sharp a2 inequality for haar shift operators as a corollary to the main result of the paper we give a new proof of the inequality rm t f l 2 w lesssim w a 2 f l 2 w where t is either the hilbert transform amer j math 129 5 1355 1375 2007 a riesz transform proc amer math soc 136 4 1237 1249 2008 or the beurling operator duke math j 112 2 281 305 2002 the weight w is non negative and the linear growth in the a2 characteristic on the right is sharp prior proofs relied strongly on haar shift operators cr acad sci paris ser i math 330 6 455 460 2000 and bellman function techniques the new proof uses haar shifts and then uses an elegant two weight t 1 theorem of nazarov treil volberg math res lett 15 3 583 597 2008 to immediately identify relevant carleson measure estimates which are in turn verified using an appropriate corona decomposition of the weight w

several integral inequalities and their applications in nonlinear differential systems in this paper several new integral inequalities are presented which are effective in dealing with the integro differential inequalities whose variable exponents are greater than one compared with existing integral inequalities those proposed here can be applied to more complicated differential equations the notions of uniform lipschitz stability are generalized and the relations between these notions are analyzed several sufficient conditions about uniform lipschitz asymptotic stability of nonlinear systems are established by the proposed integral inequalities these sufficiently conditions can be similarly generalized to linearly perturbed differential systems that appear in the literature finally an example of uniform lipschitz asymptotic stability of nonlinear differential systems is shown

poles of the topological zeta function associated to an ideal in dimension two to an ideal in mathbb c x y one can associate a topological zeta function this is an extension of the topological zeta function associated to one polynomial but in this case we use a principalization of the ideal instead of an embedded resolution of the curve in this paper we will study two questions about the poles of this zeta function first we will give a criterion to determine whether or not a candidate pole is a pole it turns out that we can know this immediately by looking at the intersection diagram of the principalization together with the numerical data of the exceptional curves afterwards we will completely describe the set of rational numbers that can occur as poles of a topological zeta function associated to an ideal in dimension two the same results are valid for related zeta functions as for instance the motivic zeta function

toroidal varieties and the weak factorization theorem we develop the theory of stratified toroidal varieties which gives together with the theory of birational cobordisms 73 a proof of the weak factorization conjecture for birational maps in characteristic zero a birational map between complete nonsingular varieties over an algebraically closed field k of characteristic zero is a composite of blow ups and blow downs with smooth centers

about a generalization of bellman bihari type inequalities for discontinuous functions and their applications abstract in the present paper we introduce the conditions of solvability for chaplygin s problem with discontinuous functions in two independent variables satisfying integro sum inequalities the new type of nonlinear integral and wendroff s inequality for discontinuous functions are investigated as applications the conditions of boundedness solutions of partial differential equations of hyperbolic type with impulse influence on some hypersurfaces j r 2 are obtained some historical aspects of the theory of integro sum inequalities are presented

relations between numerical data of an embedded resolution introduction let k be an algebraically closed field of characteristic zero and f x y e k x y let x h be an embedded resolution of f 0 in the affine plane a2 constructed by successive blowing ups and denote by ei i e i the irreducible components of h f 0 we associate to each ei i e i a pair of numerical data n vi where ni and vi 1 are the multiplicities of ei in the divisor of respectively f o h and h dx a dy on x fix one exceptional curve e with numerical data n v and say e intersects k times another irreducible component denote these components by e1 ek then we have