fluid dynamic limits of kinetic equations i formal derivations the connection between kinetic theory and the macroscopic equations of fluid dynamics is described in particular our results concerning the incompressible navier stokes equations are based on a formal derivation in which limiting moments are carefully balanced rather than on a classical expansion such as those of hilbert or chapman enskog the moment formalism shows that the limit leading to the incompressible navier stokes equations like that leading to the compressible euler equations is a natural one in kinetic theory and is contrasted with the systematics leading to the compressible navier stokes equations some indications of the validity of these limits are given more specifically the connection between the diperna lions renormalized solution of the classical boltzmann equation and the leray solution of the navier stokes equations is discussed

existence of global weak solutions for a 2d viscous shallow water equations and convergence to the quasi geostrophic model we consider a two dimensional viscous shallow water model with friction term existence of global weak solutions is obtained and convergence to the strong solution of the viscous quasi geostrophic equation with free surface term is proven in the well prepared case the ill prepared data case is also discussed

von mises type conditions in second order regular variation we give a thorough treatment concerning sufficient conditions involving derivatives for extended regular variation of second order most of the results are new a summary of the analogous known results for first order extended regular variation is given first

extreme value distributions and renormalization group in the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent identically distributed random variables are studied the vast majority of the literature on the subject deals with affine normalization we argue that more general normalizations are natural from a mathematical and physical point of view and work them out the problem is approached using the language of renormalization group transformations in the space of probability densities the limit distributions are fixed points of the transformation and the study of its differential around them allows a local analysis of the domains of attraction and the computation of finite size corrections

on the existence of moments for the busy period in a single server queue we obtain sufficient conditions for the finiteness of the moments of the single server queue busy period in discrete and continuous time in the cases of power and exponential moments the conditions found coincide with the known necessary ones

renormalization group theory for finite size scaling in extreme statistics we present a renormalization group rg approach to explain universal features of extreme statistics applied here to independent identically distributed variables the outlines of the theory have been described in a previous paper the main result being that finite size shape corrections to the limit distribution can be obtained from a linearization of the rg transformation near a fixed point leading to the computation of stable perturbations as eigenfunctions here we show details of the rg theory which exhibit remarkable similarities to the rg known in statistical physics besides the fixed points explaining universality and the least stable eigendirections accounting for convergence rates and shape corrections the similarities include marginally stable perturbations which turn out to be generic for the fisher tippett gumbel class distribution functions containing unstable perturbations are also considered we find that after a transitory divergence they return to the universal fixed line at the same or at a different point depending on the type of perturbation

bit error resilient index assignment for multiple description scalar quantizers this paper addresses the problem of increasing the robustness to bit errors for two description scalar quantizers our approach is to start with an m diagonal index assignment and further apply a permutation to the indexes of each description to increase the minimum hamming distance d rm min of the set of valid index pairs in particular we show how to construct linear permutation pairs achieving d rm min geq 3 and establish a lower bound in terms of the description rate r for the highest value of m for which such permutations exist

boundary nlc graph grammars basic definitions normal forms and complexity node label controlled nlc grammars are graph grammars operating on node labeled undirected graphs which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only they define possibly infinite languages of undirected node labeled graphs or if we just omit the labels languages of unlabeled graphs here we consider a restriction of nlc grammars so called boundary nlc bnlc grammars distinguished by the property that whenever in a graph already generated two nodes may be rewritten then these nodes are not adjacent the graph languages generated by this type of grammars are called bnlc languages although we show that this restriction leads to a smaller class of languages still enough generative power remains to define interesting graph languages for example trees complete bipartite graphs maximal outerplanar graphs k trees graphs of bandwidth k graphs of cyclic bandwidth k graphs of binary tree bandwidth k graphs of cutwidth k always for a fixed positive integer k turn out all to be bnlc languages we prove a number of normal forms for bnlc grammars and then we indicate their usefulness by various applications in particular we show that for connected graphs of bounded degree the membership problem for bnlc languages is solvable in deterministic polynomial time

approximation bounds for a general class of precedence constrained parallel machine scheduling problems an important class of scheduling problems concerns parallel machines and precedence constraints we consider precedence delays which associate with each precedence constraint a certain amount of time that must elapse between the completion and start times of the corresponding jobs together with ordinary precedence constraints release dates and delivery times can be modeled in this manner we present a 4 approximation algorithm for the total weighted completion time objective for this general class of problems the algorithm is a rather simple form of list scheduling the list is in order of job midpoints derived from a linear programming relaxation our analysis unifies and simplifies that of a number of special cases heretofore separately studied while actually improving many of the former approximation results

second order regular variation and rates of convergence in extreme value theory rates of convergence of the distribution of the extreme order statistic to its limit distribution are given in the uniform metric and the total variation metric a second order regular variation condition is imposed by supposing a von mises type condition which allows a unified treatment rates are constructed from the parameters of the second order regular variation condition some connections with poisson processes are discussed

a multidimensional model for the combustion of compressible fluids we consider a multidimensional model for the combustion of compressible reacting fluids the flow is governed by the navier stokes in eulerian coordinates and the chemical reaction is irreversible and is governed by the arrhenius kinetics the existence of globally defined weak solutions is established by using weak convergence methods compactness and interpolation arguments in the spirit of feireisl 16 and p l lions 24

towards estimating extremal serial dependence via the bootstrapped extremogram abstract davis and mikosch 2009a introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series there we showed some standard statistical properties of the sample extremogram a major difficulty was the construction of credible confidence bands for the extremogram in this paper we employ the stationary bootstrap to overcome this problem the use of the stationary bootstrap for the extremogram and the resulting interpretations are illustrated with several financial time series

global existence of weak solutions for the multicomponent reaction flows abstract a multidimensional model is introduced for the dynamic reversible reaction of compressible multicomponent gaseous mixture the purpose of this work is to develop a complete existence result in the case where the pressure depends only on the mixture composition and the barotropic correction without any additional assumption the existence of globally weak solutions of the navier stokes for multicomponent reaction flows is established by using weak convergence methods in the spirit of mellet vasseur 14 and li xin 12

a non parametric entropy based approach to detect changes in climate extremes summary the paper focuses primarily on temperature extremes measured at 24 european stations with at least 90 years of data here the term extremes refers to rare excesses of daily maxima and minima as mean temperatures in this region have been warming over the last century it is automatic that this positive shift can be detected also in extremes after removing this warming trend we focus on the question of determining whether other changes are still detectable in such extreme events as we do not want to hypothesize any parametric form of such possible changes we propose a new non parametric estimator based on the kullback leibler divergence tailored for extreme events the properties of our estimator are studied theoretically and tested with a simulation study our approach is also applied to seasonal extremes of daily maxima and minima for our 24 selected stations

on the norming constants for normal maxima abstract given n independent standard normal random variables it is well known that their maxima m n can be normalized such that their distribution converges to the gumbel law in a remarkable study hall proved that the kolmogorov distance d n between the normalized m n and its associated limit distribution is less than 3 log n in the present study we propose a different set of norming constants that allow this upper bound to be decreased with d n c m log n for n m 5 furthermore the function c m is computed explicitly which satisfies c m 1 and lim m c m 1 3 as a consequence some new and effective norming constants are provided using the asymptotic expansion of a lambert w type function

global solutions to a model for exothermically reacting compressible flows with large discontinuous initial data we prove the global existence of solutions of the navier stokes equations describing the dynamic combustion of a compressible exothermically reacting fluid and we study the large time behavior of solutions giving necessary and sufficient conditions for complete combustion in certain cases the adiabatic constants and specific heats of the burned product and unburned reactant fluids may differ and the initial data may be large and discontinuous

chemically reacting mixtures in terms of degenerated parabolic setting the paper analyzes basic mathematical questions for a model of chemically reacting mixtures we derive a model of several finite component compressible gas taking rigorously into account the thermodynamical regime mathematical description of the model leads to a degenerate parabolic equation with hyperbolic deviation the thermodynamics implies that the diffusion terms are non symmetric not positively defined and cross diffusion effects must be strongly marked the mathematical goal is to establish the existence of weak solutions globally in time for arbitrary number of reacting species a key point is an entropy like estimate showing possible renormalization of the system

on some variants of the bandwidth minimization problem we consider the following variants of the bandwidth minimization problem 1 the cycle bandwidth problem which for a given graph g and positive integer k asks if there is a circular layout such that every pair of adjacent vertexes have a distance at most k 2 the separation problem which asks if there is a linear layout such that every pair of adjacent vertexes have a distance greater than k and 3 the cycle separation problem which asks if there is a circular layout such that every pair of adjacent vertexes have a distance greater than k we show that the cycle bandwidth problem is np complete for each fixed k geqslant 2 the separation and cycle separation problems are both np complete for each fixed k geqslant 1 and the directed separation problem is np complete for arbitrary k we give polynomial time algorithms for several special cases of the directed separation problem finally we show the relationships of the directed separation problem with several scheduling problems by giving reduct

steady compressible navier stokes fourier system for monoatomic gas and its generalizations we consider steady compressible navier stokes fourier system for a gas with pressure p and internal energy e related by the constitutive law p i 1 e 1 we show that for any 3 there exists a variational entropy solution i e solution satisfying the weak formulation of balance of mass and momentum entropy inequality and global balance of total energy this result includes the model for monoatomic gas 5 if 5 these solutions also fulfill the weak formulation of the pointwise total energy balance

on the steady compressible navier stokes fourier system we study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible navier stokes fourier system our main result is the existence of a weak solution to these equations for arbitrarily large data a key element of the proof is a special approximation of the original system guaranteeing pointwise uniform boundedness of the density as well as the positiveness of the temperature therefore the passage to the limit omits tedious technical tricks required by the standard theory basic estimates on the solutions are possible to obtain by a suitable choice of physically reasonable boundary conditions

extreme statistics for time series distribution of the maximum relative to the initial value the extreme statistics of time signals is studied when the maximum is measured from the initial value in the case of independent identically distributed iid variables we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn then we turn to correlated periodic gaussian signals with a 1 f ensuremath alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height mathrm mrh mathrm i the exact mathrm mrh mathrm i distribution is derived for ensuremath alpha 0 iid variables ensuremath alpha 2 random walk ensuremath alpha 4 random acceleration and ensuremath alpha ensuremath infty single sinusoidal mode for other intermediate values of ensuremath alpha the distribution is determined from simulations we find that the mathrm mrh mathrm i distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all ensuremath alpha the two main distinguishing features of the mathrm mrh mathrm i distribution are the much larger weight for small relative heights and the divergence at zero height for ensuremath alpha g3 we also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some nonperiodic boundary conditions finally we show that for signals arising from time translationally invariant distributions the density of near extreme states is the same as the mathrm mrh mathrm i distribution this is used in developing a scaling theory for the threshold singularities of the two distributions

heavy tail modeling and teletraffic data special invited paper huge data sets from the teletraffic industry exhibit many nonstandard characteristics such as heavy tails and long range dependence various estimation methods for heavy tailed time series with positive innovations are reviewed these include parameter estimation and model identification methods for autoregressions and moving averages parameter estimation methods include those of yule walker and the linear programming estimators of feigin and resnick as well estimators for tail heaviness such as the hill estimator and the qq estimator examples are given using call holding data and interarrivals between packet transmissions on a computer network the limit theory makes heavy use of point process techniques and random set theory

on the flow of chemically reacting gaseous mixture abstract we consider the cauchy problem for the system of equations governing flow of isothermal reactive mixture of compressible gases our main contribution is to prove sequential stability of weak solutions when the state equation essentially depends on the species concentration and the viscosity coefficients vanish on vacuum moreover under additional assumption on the cold component of the pressure in the regions of small density we prove the existence of weak solutions for arbitrary large initial data

maximal height statistics for 1 f alpha signals numerical and analytical results are presented for the maximal relative height distribution of stationary periodic gaussian signals one dimensional interfaces displaying a 1 f alpha power spectrum for 0 1 regime of strong correlations and a highly accurate picture gallery of distribution functions can be constructed numerically analytical results can be obtained in the limit alpha infinity and for large alpha by perturbation expansion furthermore using path integral techniques we derive a trace formula for the distribution function valid for alpha 2n even integer from the latter we extract the small argument asymptote of the distribution function whose analytic continuation to arbitrary alpha 1 is found to be in agreement with simulations comparison of the extreme and roughness statistics of the interfaces reveals similarities in both the small and large argument asymptotes of the distribution functions