analysis of a coupled system of kinetic equations and conservation laws rigorous derivation and existence theory via defect measures in this paper we introduce a coupled system of kinetic equations of b g k type and then study its hydrodynamic limit we obtain as a consequence the rigorous derivation and existence theory for a coupled system of kinetic equations and their hydrodynamic conservation laws limit the latter is a particular case of the coupled system of boltzmann and euler equations a fundamental element in this study is the rigorous derivation and justification of the interface conditions between the kinetic model and its hydrodynamic conservation laws limit which is obtained using a new regularity theory introduced herein

strong traces for solutions to scalar conservation laws with general flux in this paper we consider bounded weak solutions u of scalar conservation laws not necessarily of class bv defined in a subset omega subset mathbb r times mathbb r we define a strong notion of trace at the boundary of omega reached by l1 convergence for a large class of functionals of u g u the functionals g depend on the flux function of the conservation law and on the boundary of omega the result holds for a general flux function and a general subset

on a class of degenerate parabolic equations with dynamic boundary conditions we consider a quasi linear parabolic possibly degenerate equation with nonlinear dynamic boundary conditions the corresponding class of initial and boundary value problems has already been studied previously proving well posedness of weak solutions and the existence of the global attractor assuming that the nonlinearities are subcritical to a given exponent the goal of this article is to show that the previous analysis can be redone for supercritical nonlinearities by proving an additional l estimate on the solutions in particular we derive new conditions which reflect an exact balance between the internal and the boundary mechanisms involved even when both the nonlinear sources contribute in opposite directions then we show how to construct a trajectory attractor for the weak solutions of the associated parabolic system and prove that any solution belonging to the attractor is bounded which implies uniqueness finally we also prove for the semilinear reaction diffusion equation with nonlinear dynamic boundary conditions that the fractal dimension of the global attractor is of the order n 1 as diffusion 0 in any space dimension n 2 improving some recent results in gal 2012 23

mean variance portfolio selection with the ordered weighted average portfolio selection is the theory that studies the process of selecting the optimal proportion of different assets the first approach was introduced by harry markowitz and was based on a mean variance framework this paper introduces the ordered weighted average owa in the mean variance model the main idea is to replace the classical mean and variance by the owa operator by doing so the new model is able to study different degrees of optimism and pessimism in the analysis being able to develop an approach that considers the decision makers attitude in the selection process this paper also suggests a new framework for dealing with the attitudinal character of the decision maker based on the numerical values of the available arguments the main advantage of this method is the ability to adapt to many situations offering a more complete representation of the available data from the most pessimistic situation to the most optimistic one an illustrative with fictitious data and a real example are studied

coupling of the wang chang uhlenbeck equations with the multispecies euler system after having recalled the basic properties of the wang chang uhlenbeck equations we describe a class of relaxation schemes to solve the multispecies euler system closed with a non classical state equation system which is the fluid limit of these kinetic equations then we show how to couple the resolution of the wang chang uhlenbeck equations with the resolution of this euler system by using a particular relaxation scheme namely a kinetic scheme which allows to define a natural boundary condition at the kinetic fluid interface and by using a marshak condition to take into account the effect of the knudsen layer in the fluid domain through an asymptotic matching finally we show applications in the field of the atomic vapor laser isotopic separation avlis

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

aggregation of infinite sequences infinitary aggregation functions acting on sequences and possessing some a priori given properties as additivity comonotone additivity symmetry etc are investigated on the other side we discuss infinitary aggregation functions related to given extended aggregation functions where special attention is given to triangular norms triangular conorms and weighted means

weighted aggregation operators based on minimization minimization based aggregation operators a g d are discussed special attention is paid to weighting function g based cases related to some fixed dissimilarity function d when d 2 x y x y 2 we recognize mixture operators and we recall some sufficient conditions for g ensuring the monotonicity of a g d for d 1 x y x y and non decreasing non increasing g a g d is shown to be the upper lower median whenever a g d is an aggregation operator

characterization of the ordered weighted averaging operators this paper deals with the characterization of two classes of monotonic and neutral mn aggregation operators the first class corresponds to mn aggregators which are stable for the same positive linear transformations and presents the ordered linkage property the second class deals with mn idempotent aggregators which are stable for positive linear transformations with the same unit independent zeroes and ordered values these two classes correspond to the weighted ordered averaging operator owa introduced by yager in 1988 it is also shown that the owa aggregator can be expressed as a choquet integral

strong traces for solutions of multidimensional scalar conservation laws in this paper we consider multidimensional scalar conservation laws without bv estimates defined in a subset d we show that with a non degeneracy hypothesis on the flux we can define a strong notion of trace at the boundary of reached by l 1 convergence

an invariance of geometric mean with respect to lagrangian means abstract the invariance of the geometric mean g with respect to the lagrangian mean type mapping l f l g i e the equation g l f l g g is considered we show that the functions f and g must be of high class regularity this fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g

structure of entropy solutions for multi dimensional scalar conservation laws an entropy solution u of a multi dimensional scalar conservation law is not necessarily in bv even if the conservation law is genuinely nonlinear we show that u nevertheless has the structure of a bv function in the sense that the shock location is codimension one rectifiable this result highlights the regularizing effect of genuine nonlinearity in a qualitative way it is based on the locally finite rate of entropy dissipation the proof relies on the geometric classification of blow ups in the framework of the kinetic formulation

a rigorous derivation of the coupling of a kinetic equation and burgers equation in this article we investigate the kinetic fluid coupling on a toy model which we obtain rigorously from a hydrodynamical limit the idea is that at the level of the full kinetic model the coupling is obvious we then investigate the coupling obtained when passing into the limit we show that especially in presence of a shock stuck on the interface the coupling involves a kinetic layer known as the milne problem due to this layer the limit process is quite delicate and some blow up techniques are needed to ensure its strong convergence

a semilinear parabolic system with generalized wentzell boundary condition abstract in this paper we consider a weak coupled semilinear parabolic system with general wentzell boundary condition we prove the well posedness of the problem and derive different conditions in terms of the powers of the nonlinear terms under which the global solution exists and finite time blow up occurs

note on monotonicity of generalized weighted mean values in the note using the cauchy schwarz buniakowski inequality the authors prove that the generalized weighted mean values mp f r s x y are increasing with respect to the two parameters r and s for any given non negative weight p and positive function f

on the associativity functional equation abstract let a b be any bounded closed real interval the class of all continuous nondecreasing associative functions m a b 2 a b fulfilling the boundary conditions m a a a and m b b b is described

including importances in owa aggregations using fuzzy systems modeling ordered weighted averaging owa operators are described and are shown to provide a general class of parameterized aggregation operators that include the max min and average we suggest an approach to the inclusion of importances in the owa operator aggregation technique the methodology suggested involves a transformation of the scores to be aggregated by their respective importances we show how we can construct transformation functions with the aid of the fuzzy modeling technology

well posedness and singular limit of a semilinear hyperbolic relaxation system with a two scale discontinuous relaxation rate nonlinear hyperbolic systems with relaxations may encounter different scales of relaxation time which is a prototype multiscale phenomenon that arises in many applications in such a problem the relaxation time is of o 1 in part of the domain and very small in the remaining domain in which the solution can be approximated by the zero relaxation limit which can be solved numerically much more efficiently for the jin xin relaxation system in such a two scale setting we establish its wellposedness and singular limit as the smaller relaxation time goes to zero the limit is a multiscale coupling problem which couples the original jin xin system on the domain when the relaxation time is o 1 with its relaxation limit in the other domain through interface conditions which can be derived by matched interface layer analysis as a result we also establish the well posedness and regularity such as boundedness in sup norm with bounded total variation and l1 contraction of the coupling problem thus providing a rigorous mathematical foundation in the general nonlinear setting to the multiscale domain decomposition method for this two scale problem originally proposed in jin et al in math comp 82 749 779 2013

alpha as ambiguity robust mean variance portfolio analysis we derive the analogue of the classic arrow pratt approximation of the certainty equivalent under model uncertainty as described by the smooth model of decision making under ambiguity of klibano marinacci and mukerji 2005 we study its scope by deriving a tractable meanvariance model adjusted for ambiguity and solving the corresponding portfolio allocation problem in the problem with a risk free asset a risky asset and an ambiguous asset we nd that portfolio rebalancing in response to higher ambiguity aversion only depends on the ambiguous asset s alpha setting the performance of the risky asset as benchmark in particular a positive alpha corresponds to a long position in the ambiguous asset a negative alpha corresponds to a short position in the ambiguous asset and greater ambiguity aversion reduces optimal exposure to ambiguity the analytical tractability of the enhanced arrow pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of model uncertainty on equilibrium asset prices

mean variance approximations to expected utility abstract it is often asserted that the application of mean variance analysis assumes normal gaussian return distributions or quadratic utility functions this common mistake confuses sufficient versus necessary conditions for the applicability of modern portfolio theory if one believes as does the author that choice should be guided by the expected utility maxim then the necessary and sufficient condition for the practical use of mean variance analysis is that a careful choice from a mean variance efficient frontier will approximately maximize expected utility for a wide variety of concave risk averse utility functions this paper reviews a half century of research on mean variance approximations to expected utility the many studies in this field have been generally supportive of mean variance analysis subject to certain initially unanticipated caveats

entropy inequalities for evaporation condensation problem in rarefied gas dynamics the present paper is devoted mainly to the half space problem for stationary boltzmann type equations using only conservation laws and the boltzmann h theorem we derive an inequality for unknown constant fluxes of mass energy and momentum this inequality is expressed in terms of three parameters pressure p temperature t and the mach number m of the asymptotic maxwellian at infinity geometrically the inequality describes a physical domain with positive entropy production in the 3 d space of the parameters the domain appears to be qualitatively different for evaporation and condensation problems we show that for given m the curve p p m t t m of maximal entropy production practically coincides with the experimental evaporation curve obtained by sone et al on the basis of numerical solutions of bgk equation similar consideration for the condensation problem is also in qualitative agreement with known numerical results

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

one sided difference approximations for nonlinear conservation laws we analyze one sided or upwind finite difference approximations to hyperbolic partial differential equations and in particular nonlinear conservation laws second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions we show that no such stable approximation of order higher than two is possible these one sided schemes have desirable properties for shock calculations we show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance new and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles existence uniqueness and stability of discrete shocks numerical examples are given

on representations of 2 increasing binary aggregation functions in this paper we provide two different representations of 2 increasing binary aggregation functions by means of their lower and upper margins and a suitable copula

resolution d equations d evolution quasilineaires en dimension n d espace a l aide d equations lineaires en dimension n 1 on montre que l on peut calculer les solutions de l equation d evolution quasi lineaire dans r n d t u div b u a u 0 u x t r x r n t 0 et en particulier de l equation d ordre 1 d t u div b u 0 u x t r x r n t 0 a l aide d une equation d evolution lineaire dans r n r

a semilinear equation with generalized wentzell boundary condition abstract in this paper we consider a semilinear equation with a generalized wentzell boundary condition we prove the local well posedness of the problem and derive the conditions of the global existence of the solution and the conditions for finite time blow up we also derive an estimate for the blow up time

a kinetic construction of global solutions of first order quasilinear equations on considere le probleme de cauchy pour des equations quasilineaires d ordre 1 de type conservation dans la region t 0 u t i 1 u a i u x i 0 u x o u o x ou x x 1 x n u u x t et a i i 1 n sont des fonctions continument differentiables a valeurs reelles d une seule variable reelle

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

boundary conditions for scalar conservation laws from a kinetic point of view boundary conditions for multidimensional scalar conservation laws are obtained in the context of hydrodynamic limits from a kinetic point of view the initial boundary value kinetic problem is well posed since inward and outward characteristics of the domain can be distinguished the convergence of the first momentum of the distribution function to an entropy solution of the conservation law is established boundary conditions are obtained the equivalence with the bardos leroux and nedelec conditions is studied

a classification of well posed kinetic layer problems in the first part of this paper we study the half space boundary value problem for the boltzmann equation with an incoming distribution obtained when considering the boundary layer arising in the kinetic theory of gases as the mean free path tends to zero we linearize it about a drifting maxwellian and prove that as conjectured by cercignani 4 the problem is well posed when the drift velocity u exceeds the sound speed c but that one respectively four five additional conditions must be imposed when 0 u c respectively c u 0 and u c in the second part we show that the well posedness and the asymptotic behavior results for kinetic layers equations with prescribed incoming flux can be extended to more general and realistic boundary conditions

a smooth transition model between kinetic and hydrodynamic equations this paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain the idea is to use a buffer zone in which both hydrodynamics and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point consequently this model avoids the delicate issue of finding the interface condition in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a simple kinetic scheme is developed to discretize our model and numerical examples are used to validate the method

characterization of some aggregation functions stable for positive linear transformations abstract this paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems the common properties involved in these characterizations are increasing monotonicity and stability for positive linear transformations additional algebraic properties related to associativity allow to completely specify the functions

a kinetic equation with kinetic entropy functions for scalar conservation laws we construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws in particular we prove that it is well posed uniformly in e the microscopic scale we also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions analogous to boltzmann s microscopich function such that they recover krushkov type entropy inequality on the macroscopic scale finally we prove by both bv compactness arguments in the multidimensional case and by compensated compactness arguments in the one dimensional case that the local density of kinetic particles admits a continuum limit as it converges strongly with e 0 to the unique entropy solution of the corresponding conservation law