series estimation under cross sectional dependence an asymptotic theory is developed for series estimation of nonparametric and semiparametric regression models for cross sectional data under conditions on disturbances that allow for forms of cross sectional dependence and hetero geneity including conditional and unconditional heteroskedascity along with conditions on regressors that allow dependence and do not require existence of a density the conditions aim to accommodate various settings plausible in economic applications and can apply also to panel spatial and time series data a mean square rate of convergence of nonparametric regression estimates is established followed by asymptotic normality of a quite general statistic data driven studentizations that rely on single or double indices to order the data are justified in a partially linear model setting monte carlo investigation of finite sample properties and two empirical applications are carried out

tauberian theorems and the central limit theorem 1 results let xn be independent and identically distributed random variables with law p mean 0 and variance a2 00 s 1 xk write p qn 1 for the laws of sn sn nyi a n and the standard normal n o 1 thus qn 1d weak convergence by the global central limit theorem we shall need the local central limit theorem see e g ibragimov and linnik 1971 theorems 4 4 1 4 2 1 4 2 2 we shall assume either llt i some pk has an absolutely continuous component in which case qn 11 3 0 as n x oo variation norm or llt ii p is lattice supported by some arithmetic progression a hk with k integer and h maximal we shall suppose for simplicity that a 0 and h 1 when writing pnk for pn k

on topological dynamics of turing machines abstract we associate to a turing machine two dynamical systems which we call turing machine with moving tape tmt and turing machine with moving head tmh tmt are equivalent to generalized shifts of moore 1990 and they include two sided full shifts tmh are shift commuting maps of two sided sofic systems in both classes we characterize systems with the shadowing property show that a bijective expansive tmt is conjugate to a subshift of finite type and that topological entropy of every tmh is zero we conjecture that every tmt has a periodic point

the expansion of functions under transformation and its application to optimization abstract this paper proposes the expansion of functions under transformation which represents infinite kinds of extensions of taylor s expansion based on this duffin s condensation formula is developed as a condensation formula of high order furthermore a theorem of efficiently solving mathematical programming by using the expansion of functions is proposed according to the condensation formula of high order two kinds of second order primal algorithms are proposed for solving generalized geometric programming with rapid and stable convergence which could be applied to a wide range of structural optimization problems finally an efficient fully stressed design method under the function transformation is proposed using these expansions of functions

weighted versions of beurling s tauberian theorem wiener s well known tauberian theorem is equivalent to the following assertion for f l the relation lim k f x 0 holds true for the convolution with x coo any k e l 1 whenever it holds true for some k1 li r having a fourier transform which does not vanish at any point beurling suggested such an implication to be true if convolution is replaced by certain related methods of taking moving averages with variable band widths cf 5 6 for details appropriately reformulated results and proofs as given in 6 even hold true in the m dimensional setting m 1 in the present note weighted quantitative versions are to be discussed showing that a certain speed of convergence for a sufficiently smooth kernel k with nonvanishing fourier transform implies the same order of convergence for all kernels satisfying an appropriate decay condition for an illustrating set of equivalent conditions for m 1 the reader is referred to theorem 3 below

two sided bounds on the rate of convergence to a stable law we derive necessary and sufficient conditions for several characterizations of the rate of convergence of a sum of independent variables to a stable law the technique used is to obtain upper and lower bounds on the rate in terms of functions depending in a very simple way on the common underlying distribution this permits a general approach to the problem of rates of convergence

a new accelerating method for global non convex quadratic optimization with non convex quadratic constraints abstract in this paper we combine the new global optimization method proposed by qu et al s j qu k c zhang y ji a global optimization algorithm using parametric linearization relaxation appl math comput 186 2007 763 771 with a suitable deleting technique to propose a new accelerating global optimization algorithm for solving the non convex quadratic optimization problems with non convex quadratic constraints nqp this technique offers a possibility to cut away a large part of the currently investigated region in which the global optimal solution of nqp does not exist and can be seen as an accelerating device for the global optimization algorithm of the nqp problems compared with the method in qu et al 2007 numerical results show that the computational efficiency is obviously improved by using this new technique in the number of iterations the required list length and the overall execution time of the algorithm

second order method of generalized geometric programming for spatial frame optimization to design concrete sectional sizes of beams the optimization model of the spatial frame is transformed into a problem of ggp generalized geometric programming in terms of the duffin s condensation formula adopting the strategy of two stages the problem is solved by the structure stage and the elements stage alternately the first and the second order primal algorithm for the ggp which are based on the first and the second order expansions under the logarithmic transformation in the logarithmic space are applied in the elements stage and the structure stage respectively numerical results including a large scale structure of the electrostatic precipitator show satisfactory efficiency of the method

general regular variation popa groups and quantifier weakening abstract we introduce general regular variation a theory of regular variation containing the existing karamata bojanic karamata de haan and beurling theories as special cases the unifying theme is the popa groups of our title viewed as locally compact abelian ordered topological groups together with their haar measure and fourier theory the power of this unified approach is shown by the simplification it brings to the whole area of quantifier weakening so important in this field

universality of a reversible two counter machine abstract a k counter machine cm k is an automaton having k counters as an auxiliary memory it has been shown by minsky that a cm 2 can simulate any turing machine and thus it is universal in this paper we investigate the computing ability of reversible i e backward deterministic cms we first show that any irreversible cm k can be simulated by a reversible cm k 2 in this simulation however the reversible cm k 2 leaves a large number as a garbage in some counter when it halts we then show that if k more counters are added this garbage information is erased reversibly finally we prove that any reversible cm k k 1 2 3 can be simulated by a reversible cm 2 from these results computation universality of a reversible cm 2 is established

weighted sums of i i d random variables attracted to integrals of stable processes under the assumption of the convergence of partial sum processesz n t of i i d random variables to an stable levy processz t 0 2 the convergence of weighted sums f n u dz n u to f u dz u is studied the general convergence result is then applied to examine the domain of attraction of the fractional stable process

functional limit theorems for weighted sums of i i d random variables on etudie des theoremes limites fonctionnels pour des sommes ponderees specialement pour des poids concernant les methodes de sommabilite classiques telles que celles de cesaro abel borel et euler

some undecidability results for asynchronous transducers and the brin thompson group 2v using a result of kari and ollinger we prove that the torsion problem for elements of the brin thompson group 2v is undecidable as a result we show that there does not exist an algorithm to determine whether an element of the rational group r of grigorchuk nekrashevich and sushchanskii has finite order a modification of the construction gives other undecidability results about the dynamics of the action of elements of 2v on cantor space arzhantseva lafont and minasyanin prove in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem to our knowledge 2v furnishes the first concrete example of such a group and gives an example of a direct undecidability result in the extended family of r thompson type groups

higher dimensional generalizations of the thompson groups abstract motivated by the goal of generalizing the cuntz krieger algebras and making heavy use of the pioneering work of robertson and steger kumjian and pask generalized the notion of a directed graph to what they termed a higher rank graph the c algebras constructed from such higher rank graphs have proved to be highly interesting higher rank graphs are in fact a class of cancellative categories and so the one vertex higher rank graphs are therefore a class of cancellative monoids in this paper we call them k monoids finite direct products of free monoids belong to this family but there are many examples not of this form it is well known that the classical thompson groups arise from the free monoids and it is easy to show that brin s higher dimensional thompson groups arise from finite direct products of free monoids in this paper we generalize these constructions and show how to construct a family of new groups with simple commutator subgroups from arbitrary aperiodic k monoids thereby subsuming all the above examples although we give simple direct constructions of our groups a key feature of our paper is that we also show that they arise as topological full groups of the usual etale groupoids associated with k monoids in this way our groups are naturally associated with c algebras the question of the mutual isomorphisms amongst this family of groups appears to be a delicate one and is not handled here

stochastic random walk summability on etudie les proprietes limites des sommes partielles ponderees lorsque les poids sont donnes par une procedure de sommation en marche aleatoire

statistical gap tauberian theorems in metric spaces abstract by using the concept of statistical convergence we present statistical tauberian theorems of gap type for the cesaro euler borel family and the hausdorff families applicable in arbitrary metric spaces in contrast to the classical gap tauberian theorems we show that such theorems exist in the statistical sense for the convolution methods which include the taylor and the borel matrix methods we further provide statistical analogs of the gap tauberian theorems for the hausdorff methods and provide an explanation as to how the tauberian rates over the gaps may differ from those of the classical tauberian theorems

probabilistic and worst case analyses of classical problems of combinatorial optimization in euclidean space the classical problems reviewed are the traveling salesman problem minimal spanning tree minimal matching greedy matching minimal triangulation and others each optimization problem is considered for finite sets of points in d and the feature of principal interest is the value of the associated objective function special attention is given to the asymptotic behavior of this value under probabilistic assumptions but both probabilistic and worst case analyses are surveyed

a parametric linear relaxation algorithm for globally solving nonconvex quadratic programming abstract in this article we present a parametric linear relaxation algorithm for globally solving the nonconvex quadratic programming nqp in this algorithm a new parametric linearized technique is proposed for generating parametric linear relaxation programming plrp of the nqp which can be used to determine the lower bound of global minimum value of the nqp to improve the convergent speed of the proposed algorithm a pruning operation is employed to compress the investigated region by subdividing subsequently the initial domain and solving subsequently a series of parametric linear relaxation programming problems over the subdivided domain the proposed algorithm is convergent to the global minimum of the nqp finally an engineering problem for the design of heat exchanger network and some test examples are used to verify the effectiveness of the proposed algorithm

presentations of higher dimensional thompson groups in a previous paper we defined a higher dimensional analog of thompson s group v and proved that it is simple infinite finitely generated and not isomorphic to any of the known thompson groups there are other thompson groups that are infinite simple and finitely presented here we show that the new group is also finitely presented by calculating an explicit finite presentation

a new rectangle branch and pruning approach for generalized geometric programming generalized geometric programming ggp problem occurs frequently in engineering design and management in this paper a branch and pruning global optimization algorithm is proposed for ggp by utilizing some transformations a linear relaxation of the problem ggp is obtained based on the linear lower bound functions of objective and constraint functions inside some hyperrectangle region then a new pruning technique is given to accelerate the convergence of the given algorithm and this pruning technique offers the possibility to cut away a large part of the current investigated region in which there no exist global optimum solution the proposed algorithm which connects branch and bound method with the pruning technique successfully is convergent to the global minimum according to the successive refinement of the linear relaxation of feasible region of the objective function and the solutions of a series of linear relaxation problems and finally numerical experiment is given to illustrate the feasibility and efficiency of the proposed algorithm

abelian tauberian and mercerian theorems for arithmetic sums we consider abelian results passing from behaviour of f to that of single or double sums as above tauberian theorems converse implications under additional conditions tauberian conditions and mercerian theorems in which we pass from some comparison statement between f and a sum to a conclusion on f alone this line of work may be traced to a seminal paper of polya in 1917 p see also polya szego ps part ii ch 4 no 156 our two main tools are the karamata theory of regular variation originated in 1930 see bgt and the wiener tauberian theory originated in 1932 see hardy h widder w polya s achievement is all the more striking in that neither of these tools was available to him this study arises from a fusion of two recent lines of work on the arithmetic sums side our interest was stimulated by a series of studies by de koninck ivic deki1 2 3 on the abelian tauberian mercerian side we make use of recent work of our own bi5

computational method for the profit bounds of inventory model with interval demand and unit cost changing economic conditions make the selling price and demand quantity more and more uncertain in the market the conventional inventory models determine the selling price and order quantity for a retailer s maximal profit with exactly known parameters this paper develops a solution method to derive the imprecise profit of the inventory model when the demand quantity and unit cost are imprecise since imprecise parameters contained in the inventory model lie in intervals the profit value calculated from the model should be in a range as well we formulate a pair of two level mathematical programming model to derive the upper bound and lower bound of the profit based on the duality theorem of geometric programming the pair of two level mathematical programs is transformed into a pair of conventional geometric programs solving the corresponding pair of geometric programs produces the interval of profit an example illustrates the idea in this paper that example also shows that the interval profit contains more information for determining inventory policy

a global optimization using linear relaxation for generalized geometric programming many local optimal solution methods have been developed for solving generalized geometric programming ggp but up to now less work has been devoted to solving global optimization of ggp problem due to the inherent difficulty this paper considers the global minimum of ggp problems by utilizing an exponential variable transformation and the inherent property of the exponential function and some other techniques the initial nonlinear and nonconvex ggp problem is reduced to a sequence of linear programming problems the proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of ggp on a microcomputer

deciding stability and mortality of piecewise affine dynamical systems in this paper we study problems such as given a discrete time dynamical system of the form x t 1 f x t where f r n r n is a piecewise affine function decide whether all trajectories converge to 0 we show in our main theorem that this attractivity problem is undecidable as soon as n greater than or equal to2 the same is true of two related problems stability is the dynamical system globally asymptotically stable and mortality do all trajectories go through 0 we then show that am activity and stability become decidable in dimension 1 for continuous functions c 2001 elsevier science b v all rights reserved

tauberian theorems via statistical convergence the concept of statistical convergence which is related to the usual concept of convergence in probability provides a regular summability method for abstract metric spaces by using probabilistic tools we provide some tauberian theorems which have best possible order tauberian conditions furthermore these methods can be used to unify and improve the classical pointwise tauberian theorems of summability theory for the random walk type methods as proved by bingham and hausdorff methods as proved by lorentz

relative entropy relaxations for signomial optimization signomial programs sps are optimization problems specified in terms of signomials which are weighted sums of exponentials composed with linear functionals of a decision variable sps are nonconvex optimization problems in general and families of np hard problems can be reduced to sps in this paper we describe a hierarchy of convex relaxations to obtain successively tighter lower bounds of the optimal value of sps this sequence of lower bounds is computed by solving increasingly larger sized relative entropy optimization problems which are convex programs specified in terms of linear and relative entropy functions our approach relies crucially on the observation that the relative entropy function by virtue of its joint convexity with respect to both arguments provides a convex parametrization of certain sets of globally nonnegative signomials with efficiently computable nonnegativity certificates via the arithmetic geometric mean inequality by appealing to representation theorems from real algeb

a milp formulation for generalized geometric programming using piecewise linear approximations abstract generalized geometric programming ggp problems are converted to mixed integer linear programming milp problems using piecewise linear approximations our approach is to approximate a multiple term log sum function of the form log x 1 x 2 x n in terms of a set of linear equalities or inequalities of log x 1 log x 2 and log x n where x 1 x n are strictly positive the advantage of this approach is its simplicity and readiness to implement and solve using commercial milp solvers while milp problems in general are no easier than ggp problems this approach is justified by the phenomenal progress of computing power of both personal computers and commercial milp solvers the limitation of this approach is discussed along with numerical tests

freeness of automaton groups vs boundary dynamics abstract we prove that the boundary dynamics of the semi group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group we specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to the existence of a finite schreier graph in the boundary of the enriched dual pointed at some essentially non trivial point from these results we derive some consequences from the algebraic algorithmic and dynamical points of view

logarithmic moving averages abstract we introduce a moving average summability method which is proved to be equivalent to the logarithmic l method several equivalence and tauberian theorems are given a strong law of large numbers is also proved

global optimization of signomial geometric programming problems abstract this paper presents a global optimization approach for solving signomial geometric programming problems in most cases nonconvex optimization problems with signomial parts are difficult np hard problems to solve for global optimality but some transformation and convexification strategies can be used to convert the original signomial geometric programming problem into a series of standard geometric programming problems that can be solved to reach a global solution the tractability and effectiveness of the proposed successive convexification framework is demonstrated by seven numerical experiments some considerations are also presented to investigate the convergence properties of the algorithm and to give a performance comparison of our proposed approach and the current methods in terms of both computational efficiency and solution quality

weighted sums of random variables attracted to stable laws on etudie des sommes ponderees de variables aleatoires en relation avec la loi des grands nombres et la loi du logarithme itere

range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems many global optimization approaches for solving signomial geometric programming problems are based on transformation techniques and piecewise linear approximations of the inverse transformations since using numerous break points in the linearization process leads to a significant increase in the computational burden for solving the reformulated problem this study integrates the range reduction techniques in a global optimization algorithm for signomial geometric programming to improve computational efficiency in the proposed algorithm the non convex geometric programming problem is first converted into a convex mixed integer nonlinear programming problem by convexification and piecewise linearization techniques then an optimization based approach is used to reduce the range of each variable tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using fewer break points in the linearization process therefore decreasing the required cpu time several numerical experiments are presented to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality

an automaton group with undecidable order and engel problems abstract for every turing machine we construct an automaton group that simulates it precisely starting from an initial configuration of the turing machine we explicitly construct an element of the group such that the turing machine stops if and only if this element is of finite order if the turing machine is universal the corresponding automaton group has an undecidable order problem this solves a problem raised by grigorchuk the above group also has an undecidable engel problem there is no algorithm that given g h in the group decides whether there exists an integer n such that the n iterated commutator g h h h is the identity or not this solves a problem raised by bartholdi

a new bound and reduce approach of nonconvex quadratic programming problems abstract for the nonconvex quadratic programming problem a new linear programming relaxation bound and reduce algorithm is proposed and its convergence is proved in this algorithm a new hyper rectangle partition technique and a new linear programming relaxation tactics are used at the same time the hyper rectangular reduction method is used to raise its convergent speed the numerical results demonstrate the effectiveness and feasibility of the proposed algorithm

linearization method of global optimization for generalized geometric programming many methods for solving generalized geometric programming ggp problem can only find locally optimal solutions but up to now less work has been devoted to solving global optimization of ggp due to the inherent difficulty this paper gives a method for finding the globally optimal solutions of ggp utilizing an exponentially variable transformation and some other techniques the initial nonlinear and nonconvex ggp problem is reduced to a sequence of linear programming problems the proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems several ggp examples in the literatures are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a prespecified error