refined proximity and sensitivity results in linearly constrained convex separable integer programming abstract we define a new measure of the structure of a linear constraint matrix and establish some propertie we then use the measure to refine proximity and sensitivity results in the literature in particular we refine bounds on the distance between continuous and discrete optima of linearly constrained convex separable programming problems and on the size of the feasible region for a linear program we apply the results to improve the computational complexity of hochbaum and shanthikumar s algorithm for integer nonlinear programming reducing the computational effort for certain problems from exponential to polynomial

approximate tolerance limits for zipf mandelbrot distributions abstract zipf mandelbrot distributions are commonly used to model natural phenomena where the frequency of an event s occurrence is inversely proportional to its rank based on that frequency of occurrence this discrete distribution typically exhibits a large number of rare events however it may be of interest to obtain reasonable limits that bound the majority of the number of different events we propose the use of statistical tolerance limits as a way to quantify such a bound the tolerance limits are constructed using wald confidence limits for the zipf mandelbrot parameters and are shown through a simulation study to have coverage probabilities near the nominal levels we also calculate zipf mandelbrot tolerance limits for two real datasets and discuss the associated computer code developed for the r programming language

extremal solutions of φ laplacian diffusion scalar problems with nonlinear functional boundary conditions in a unified way abstract the aim of this paper is to ensure the existence of extremal solutions lying between a pair of lower and upper solutions for a second order differential equation that includes both the laplacian and some classes diffusion equations the results hold from a suitable change of variables an example is given to expose the applicability of the obtained results

existence of solutions for weighted p r laplacian system boundary value problems this paper investigates the existence of solutions for weighted p r laplacian ordinary system boundary value problems via leray schauder degree the sufficient conditions for the existence of solutions be given as an application we obtain the existence of the radial solutions for the p x laplacian partial differential system dirichlet problems

random growth urban model with geographical fitness abstract this paper formulates a random growth urban model with a notion of geographical fitness using techniques of complex network theory we study our system as a type of preferential attachment model with fitness and we analyze its macro behavior to clarify the properties of the city size distributions it predicts first restricting the geographical fitness to take positive values and using a continuum approach we show that the city size distributions predicted by our model asymptotically approach pareto distributions with coefficients greater than unity then allowing the geographical fitness to take negative values we perform local coefficient analysis to show that the predicted city size distributions can deviate from pareto distributions as is often observed in actual city size distributions as a result the model we propose can generate a generic class of city size distributions including but not limited to pareto distributions for applications to city population projections our simple model requires randomness only when new cities are created not during their subsequent growth this property leads to smooth trajectories of city population growth in contrast to other models using gibrat s law in addition a discrete form of our dynamical equations can be used to estimate past city populations based on present day data this fact allows quantitative assessment of the performance of our model further study is needed to determine appropriate formulas for the geographical fitness

on the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions abstract we prove the existence of extremal solutions for the third order discontinuous functional nonlinear problem u t f t u u t u t for a e t a b u a a a r l 1 u u u a u b u a 0 l 2 u u a u b u b 0 by using a fixed point theorem after having established some existence results for some auxiliary second order nonlinear problems we observe that together with the discontinuities allowed on the spacial variable u with adequate modifications of technical type analogous results can be obtained when the equation has a second member not necessarily continuous in u

existence of infinitely many solutions for a neumann problem involving the p x laplacian abstract in this paper we consider the neumann problem involving the p x laplacian of the type div u p x 2 u x u p x 2 u f x u g x u in u 0 on we prove the existence of infinitely many solutions of the problem under weaker hypotheses by applying a variational principle due to b ricceri and the theory of the variable exponent sobolev spaces our results are an improvement and generalization of the relative results obtained by b ricceri for the p laplacian case

existence of positive solutions for a class of p x laplacian systems abstract we mainly consider the system p x u f x v in p x v g x u in u v 0 on where r n is a bounded domain p x is a function which satisfies some conditions p x u div u p x 2 u is called p x laplacian we give the existence of positive solutions under some conditions in particular we do not assume radial symmetric conditions on the system

eigenvalues of p x laplacian dirichlet problem abstract this paper studies the eigenvalues of the p x laplacian dirichlet problem div u p x 2 u u p x 2 u in u 0 on where is a bounded domain in rn and p x is a continuous function on such that p x 1 we show that the set of eigenvalues is a nonempty infinite set such that sup we present some sufficient conditions for inf 0 and for inf 0 respectively

hartman type results for p t laplacian systems consider the weighted p t laplacian ordinary system w t u t p t 2u t w t f t u t 0 in a b u a u b 0 where f c a b rn rn w c a b r p c a b r and p t 1 for t a b it is proved that if r 0 such that f t u u 0 t a b u rn with u r then the problem has a solution u such that u t r for t a b as a corollary of this result taking w t tn 1 we obtain the existence of the radial solutions for the elliptic systems our result generalized the corresponding results obtained by hartman and mawhin

a multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids the goal of this correction is to correct a mistake that appears in the proof of both lemma 3 9 and 3 10 in the article mih ilescu r dulescu 2006 1 the mistake in the proof of lemma 3 9 and 3 10 is mainly owing to the fact that we wrongly computed the expression of function g x t

sensitivity theorems in integer linear programming we consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right hand side vector among our results we show that for any optimal solution to a linear program max wx ax b the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixa using this we strengthen several integer programming proximity results of blair and jeroslow graver and wolsey we also show that the chvatal rank of a polyhedron x ax b can be bounded above by a function of the matrixa independent of the vectorb a result which as blair observed is equivalent to blair and jeroslow s theorem that each integer programming value function is a gomory function

singular solutions of the p laplace equation soit un sous ensemble ouvert de r n n 1 et p un nombre reel plus grand que 1 on suppose que 0 o et u est p harmonique dans on etudie le comportement de la solution faible u pres de o de l equation apu div u p 2 u 0

the method of upper lower solutions for nonlinear second order differential inclusions abstract in this paper we consider a second order differential inclusion driven by the ordinary p laplacian with a subdifferential term a discontinuous perturbation and nonlinear boundary value conditions assuming the existence of an ordered pair of appropriately defined upper and lower solutions and respectively using truncations and penalization techniques and results from nonlinear and multivalued analysis we prove the existence of solutions in the order interval and of extremal solutions in we show that our problem incorporates the dirichlet neumann and sturm liouville problems moreover we show that our method of proof also applies to the periodic problem

eigenvalues of the p x laplacian steklov problem abstract consider steklov eigenvalue problem involving the p x laplacian on a bounded domain the open subset of r n with n 2 as follows p x u u p x 2 u in u p x 2 u u p x 2 u on where p x constant we prove that the existence of infinitely many eigenvalue sequences unlike the p laplacian case for a variable exponent p x constant there does not exist a principal eigenvalue and the set of all eigenvalues is not closed under some assumptions finally we present some sufficient conditions for the infimum of all eigenvalues is zero and positive respectively

existence of positive solutions for elliptic systems with nonstandard p x growth conditions via sub supersolution method abstract we mainly consider the system p x u f v in p x v g u in u v 0 on where p x c 1 r n is a radial symmetric function which satisfies sup p x and 1 inf p x sup p x where p x u div u p x 2 u is called p x laplacian b 0 r r n is a bounded radial symmetric domain where r is sufficiently large we prove the existence of a positive solution when lim u f m g u 1 p 1 u p 1 0 in particular we do not assume any sign condition on f 0 and g 0

distances between optimal solutions of mixed integer programs a classic result of cook et al math program 34 251 264 1986 bounds the distances between optimal solutions of mixed integer linear programs and optimal solutions of the corresponding linear relaxations their bound is given in terms of the number of variables and a parameter vardelta which quantifies sub determinants of the underlying linear inequalities we show that this distance can be bounded in terms of vardelta and the number of integer variables rather than the total number of variables to this end we make use of a result by olson j number theory 1 8 10 1969 in additive combinatorics and demonstrate how it implies feasibility of certain mixed integer linear programs we conjecture that our bound can be improved to a function that only depends on vardelta in general

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

calibrating confidence coefficients abstract two approaches for dealing with the problem of poor coverage probabilities of certain standard confidence intervals are proposed the first is a recommendation that the actual coverage be estimated directly from the data and its value reported in addition to the nominal level this is achieved through a combination of computer simulation and density estimation the asymptotic validity of the procedure is proved for a number of common situations a classical example is the nonparametric estimation of the variance of a population using the normal theory interval here it is shown that the estimated coverage probability consistently estimates the true coverage probability if the population distribution possesses a finite sixth moment the second approach is more traditional it is a procedure for modifying an interval to yield improved coverage properties given a confidence interval its estimated coverage probability obtained in the first approach is used to alter the nominal level of the interval

inverse optimization for linearly constrained convex separable programming problems abstract in this paper we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas for a given feasible point of a convex separable program the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem and when the answer is positive find the parameter values that have the smallest adjustments a sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values inverse optimization formulations are presented with l 1 and l 2 norms these inverse optimization problems are either linear programming when l 1 norm is used in the formulation or convex quadratic separable programming when l 2 norm is used

extremal solutions for nonlinear functional ϕ laplacian impulsive equations abstract in this paper we deal with some nonlinear laplacian second order boundary value problems with impulses subject to a general type of boundary value conditions which cover dirichlet and periodic boundary data as particular cases our approach is that of upper and lower solutions together with growth restrictions of nagumo s type the impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear in both cases functional dependence on the solution is allowed

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

the relationship between integer and real solutions of constrained convex programming we prove the following theorem which gives a bound on the proximity of the real and the integer solutions to certain constrained optimization programs

existence of solutions for some nonlinear problems with p laplacian like operators abstract the purpose of this paper is to obtain some existence results of solutions for the nonlinear boundary value problems with p laplacian like operators

a strong maximum principle for differential equations with nonstandard p x growth conditions abstract in this paper with some special technics we give a strong maximum principle for the equations with nonstandard p x growth conditions div x u u d x f x u 0 in where x s d x f x u satisfy some conditions

existence of periodic solutions for p t laplacian systems abstract in this paper by using minimax methods in critical point theory we obtain some existence theorems for periodic solutions of p t laplacian system u t p t 2 u t f t u t 0 u 0 u t u 0 u t 0 and our results generalize some existed theorems

existence of multiple solutions for weighted p r laplacian equation dirichlet problems abstract this paper deals with the existence of multiple solutions for weighted p r laplacian equation dirichlet problems several sub super solution type results have been given via leray schauder s degree method in particular we give a counterexample which means that 2 in paper j henderson h b thompson existence of multiple solutions for second order boundary value problems j differential equations 166 2000 443 454 is not an open subset of c 0 1

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

beyond the zipf mandelbrot law in quantitative linguistics abstract in this paper the zipf mandelbrot law is revisited in the context of linguistics despite its widespread popularity the zipf mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of words contained in some given corpus in particular we focus our attention on the important deviations that become statistically relevant as larger corpora are considered and that ultimately could be understood as salient features of the underlying complex process of language generation finally it is shown that all the different observed regimes can be accurately encompassed within a single mathematical framework recently introduced by c tsallis

existence of multiple solutions for second order boundary value problems we give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y f x y y 0 x epsilon 0 1 y 0 0 y 1 in the special case f x y y f y greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions we give an example showing this latter result is sharp our results extend those of avery and of lakshmikantham et al