vanishing of vacuum states and blow up phenomena of the compressible navier stokes equations the navier stokes systems for compressible fluids with density dependent viscosities are considered in the present paper these equations in particular include the ones which are rigorously derived recently as the saint venant system for the motion of shallow water from the navier stokes system for incompressible flows with a moving free surface 14 these compressible systems are degenerate when vacuum state appears we study initial boundary value problems for such systems for both bounded spatial domains or periodic domains the dynamics of weak solutions and vacuum states are investigated rigorously

partial ordering in l underdeterminate sets abstract the purpose of this paper is to improve results on fuzzy partial orderings obtained by zadeh in 9 we overcome the difficulties connected with the axioms of antisymmetry and linearity moreover if the underlying lattice l is a complete residuated lattice we establish a szpilrajn theorem i e any l fuzzy partial ordering has a linear extension in opposition to zadeh s our point of view is that an axiom of antisymmetry without a reference to a concept of equality is meaningless therefore we first introduce the category lus cf 2 which can be considered as a mathematical model of fuzzy equality and subsequently we specify the axioms of l fuzzy partial orderings with respect to the frame given by lus the axioms we use clearly display the usefulness of having a zadeh like complementation and as a consequence the usefulness of a positivistic and nonintuitionistic frame of study an example concerning l rn which we give clearly shows that the lus version of the szpilrajn theorem cannot be reduced to a fuzzification of an already existing theorem but provides us with additional information

on the existence of local strong solutions to chemotaxis shallow water system with large data and vacuum abstract in this paper motivated by the chemotaxis navier stokes system arising from mathematical biology 43 a modified shallow water type chemotactic model is derived for large initial data allowing vacuum the local existence of strong solutions together with the blow up criterion is established

weak and strong solutions for the incompressible navier stokes equations with damping in this paper we show that the cauchy problem of the navier stokes equations with damping u 1u 0 has global weak solutions for any 1 global strong solution for any 7 2 and that the strong solution is unique for any 7 2 5

enriched categories and many valued preorders a question from programming arises if bitstring x compares with bitstring y to some degree and if bitstring y satisfies predicate a to some degree then how should the possibility be mathematically modeled that bitstring x satisfies predicate a to at least some degree related to both and mathematically modeling this question is surprisingly intricate when the underlying conjunctions e g of predicates are non commutative potential applications of this question occur in data mining a field in which pattern matching is important and commonly used this paper uses ideas from enriched categories over monoidal categories to address such issues and enable pattern matching techniques to extend to many valued contexts equipped with non commutative conjunctions first we consider the notion of a set enriched by a po monoid l which turns out to be a set equipped with an l valued preorder second we extend the notion of enriched functors to formulate the appropriate definition of variable basis morphisms between preordered sets over different lattice theoretic bases third we construct the notion of topological systems enriched with many valued preorders and use their extent spaces to motivate and formulate enriched or preordered topological spaces the compatibility or enrichment axioms for such systems and spaces model the programming question stated above using non commutative tensor products en route are determined a number of related notions and results many valued antisymmetry characterizes the l t0 separation axiom many valued preorders are categorically topological and many valued partial orders are monotopological enriched topological spaces form a topological category a large inventory of example classes is provided including programming examples and an extensive discussion of examples based on the l spectra of complete po groupoids and each of these related developments is provided a suitable lattice theoretic and categorical foundation

nonlinear stability of large amplitude viscous shock wave for general viscous gas abstract in the present paper it is shown that the large amplitude viscous shock wave is nonlinearly stable for isentropic navier stokes equations in which the pressure could be general and includes law and the viscosity coefficient is a smooth function of density the strength of shock wave could be arbitrarily large the proof is given by introducing a new variable which can formulate the original system into a new one and the elementary energy method introduced in 21

portfolio optimization problem under concave transaction costs and minimal transaction unit constraints we will propose a branch and bound algorithm for calculating a globally optimal solution of a portfolio construction rebalancing problem under concave transaction costs and minimal transaction unit constraints we will employ the absolute deviation of the rate of return of the portfolio as the measure of risk and solve linear programming subproblems by introducing piecewise linear underestimating function for concave transaction cost functions it will be shown by a series of numerical experiments that the algorithm can solve the problem of practical size in an efficient manner

large scale portfolio optimization this paper describes a practical algorithm for large scale mean variance portfolio optimization the emphasis is on developing an efficient computational approach applicable to the broad range of portfolio models employed by the investment community what distinguishes these from the usual quadratic program is i the form of the covariance matrix arising from the use of factor and scenario models of return and ii the inclusion of transactions limits and costs a third aspect is the question of whether the problem should be solved parametrically in the risk reward trade off parameter or separately for several discrete values of we show how the parametric algorithm can be made extremely efficient by sparsifying the covariance matrix with the introduction of a few additional variables and constraints and by treating the transaction cost schedule as an essentially nonlinear nondifferentiable function then we show how these two seemingly unrelated approaches can be combined to yield good approximate solutions when minimum trading size restrictions buy or sell at least a certain amount or not at all are added in combination these approaches make possible the parametric solution of problems on a scale not heretofore possible on computers where cpu time and storage are the constraining factors

global existence of weak solutions to 3d compressible primitive equations with degenerate viscosity in this paper we investigate the compressible primitive equations cpes with density dependent viscosity for large initial data the cpe model can be derived from the 3d compressible and anisotropic navier stokes equations by hydrostatic approximation motivated by the work of vasseur and yu siam j math anal 48 1489 1511 2016 invent math 206 935 974 2016 in which the global existence of weak solutions to the compressible navier stokes equations with degenerate viscosity was obtained we construct approximate solutions and prove the global existence of weak solutions to the cpe in this paper in our proof we first present the vertical velocity as a function of density and horizontal velocity which plays a role in using the faedo galerkin method to obtain the global existence of the approximate solutions then we obtain the key estimates of lower bound of the density the bresch desjardins entropy on the approximate solutions finally we apply compactness arguments to obtain global existence of weak solutions by vanishing the parameters in our approximate system step by step

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

fundamental study complete and directed complete ω categories let w be a commutative unital quantale complete and directed complete w categories are the core objects in quantitative domain theory this paper based on the theory of f completeness for enriched categories presents a systematic investigation of completeness and directed completeness of w categories

partial quasi metrics in this article we introduce and investigate the concept of a partial quasi metric and some of its applications we show that many important constructions studied in matthews s theory of partial metrics can still be used successfully in this more general setting in particular we consider the bicompletion of the quasi metric space that is associated with a partial quasi metric space and study its applications in groups and bck algebras

on consistency of stochastic dominance and mean semideviation models we analyze relations between two methods frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches new necessary conditions for stochastic dominance are developed these conditions compare values of a certain functional which contains two components the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree if the weight of the semideviation in the composite objective does not exceed the weight of the expected value maximization of such a functional yields solutions which are efficient in terms of stochastic dominance the results are illustrated graphically

singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation abstract a short time existence theorem is proven for the initial boundary value problem for a class of quasilinear symmetric hyperbolic systems containing a constant coefficient spatial operator multiplied by a large parameter solutions u are shown to remain bounded independently of for a time independent of provided that u 0 and u l 0 are bounded independently of and certain structural conditions are satisfied this result is applied to the quasigeostrophic approximation of the shallow water equations and the constant pressure approximation in combustion and solutions for these cases are shown to converge to solutions of limiting equations as

fixed points of adjoint functors enriched in a quantaloid abstract representation theorems are established for fixed points of adjoint functors between categories enriched in a small quantaloid in a very general setting these results set up a common framework for representation theorems of concept lattices in formal concept analysis fca and rough set theory rst which not only extend the realm of formal contexts to multi typed and multi valued ones but also provide a general approach to construct various kinds of representation theorems besides incorporating several well known representation theorems in fca and rst as well as formulating new ones it is shown that concept lattices in rst can always be represented as those in fca through relative pseudo complements of the given contexts especially if the contexts are valued in a non girard quantaloid

global weak solutions to a generic two fluid model this paper deals with mathematical properties of a generic two fluid flow model commonly used in industrial applications more precisely we address the question of whether available mathematical results in the case of a single fluid governed by the compressible barotropic navier stokes equations may be extended to such a two phase model we focus on existence of global weak solutions linear theory and determination of eigenvalues and invariant regions

asymptotics of the 1d compressible navier stokes equations with density dependent viscosity abstract we are concerned with the time asymptotic behavior toward rarefaction waves for strong non vacuum solutions to the cauchy problem of the one dimensional compressible navier stokes equations with degenerate density dependent viscosity the case when the pressure p and the viscosity coefficient for some parameters r is considered for 0 max 1 if the initial data is assumed to be sufficiently regular without vacuum and mass concentrations we show that the cauchy problem of the one dimensional compressible navier stokes equations admits a unique global strong non vacuum solution which tends to the rarefaction waves as time goes to infinity here both the initial perturbation and the strength of the rarefaction waves can be arbitrarily large the proof is established via a delicate energy method and the key ingredient in our analysis is to derive the uniform in time positive lower and upper bounds on the specific volume

third degree stochastic dominance and mean risk analysis in their recent article ogryczak and ruszczynski 1999 proved that those portfolios associated with the efficient frontiers generated by mean lower semi standard deviation model and mean lower semi absolute deviation model are efficient in the sense of second degree stochastic dominance this rather surprising result reveals the importance of lower partial risk models in portfolio analysis in this paper we extend the results of ogryczak and ruszczynski for second degree stochastic dominance to third degree stochastic dominance we show that portfolios on a significant portion of the efficient frontier generated by mean lower semi skewness model are efficient in the sense of third degree stochastic dominance also we prove that the portfolios generated by mean variance skewness model are semi efficient in the sense of third degree stochastic dominance

dynamical behaviors for 1d compressible navier stokes equations with density dependent viscosity abstract the dynamical behaviors of vacuum states for one dimensional compressible navier stokes equations with density dependent viscosity coefficient are considered it is first shown that a unique strong solution to the free boundary value problem exists globally in time the free boundary expands outwards at an algebraic rate in time and the density is strictly positive in any finite time but decays pointwise to zero time asymptotically then it is proved that there exists a unique global weak solution to the initial boundary value problem when the initial data contains discontinuously a piece of continuous vacuum and is regular away from the vacuum the solution is piecewise regular and contains a piece of continuous vacuum before the time t 0 which is compressed at an algebraic rate and vanishes at the time t meanwhile the weak solution becomes either a strong solution or a piecewise strong one and tends to the equilibrium state exponentially

on one dimensional compressible navier stokes equations with degenerate viscosity and constant state at far fields in this paper we are concerned with the cauchy problem for one dimensional compressible isentropic navier stokes equations with density dependent viscosity 0 and pressure p 1 we will establish the global existence and asymptotic behavior of weak solutions for any 0 and 1 under the assumption that the density function keeps a constant state at far fields in particular in the case that 0 12 we obtain the large time behavior of the strong solution obtained by mellet and vasseur when the solution has a lower bound no vacuum

global well posedness and long time dynamics for a higher order quasi geostrophic type equation abstract in this paper we study a higher order viscous quasi geostrophic type equation this equation was derived in 11 as the limit dynamics of a singularly perturbed navier stokes korteweg system with coriolis force when the mach rossby and weber numbers go to zero at the same rate the scope of the present paper is twofold first of all we investigate well posedness of such a model on the whole space r 2 we prove that it is well posed in h s for any s 3 globally in time interestingly enough we show that this equation owns two levels of energy estimates for which one gets existence and uniqueness of weak solutions with different regularities namely h 3 and h 4 regularities this fact can be viewed as a remainder of the so called bd entropy structure of the original system in the second part of the paper we investigate the long time behavior of these solutions we show that they converge to the solution of the corresponding linear parabolic type equation with same initial datum and external force our proof is based on dispersive estimates both for the solutions to the linear and non linear problems

yoneda completeness and flat completeness of ordered fuzzy sets abstract this paper studies yoneda completeness and flat completeness of ordered fuzzy sets valued in the quantale obtained by endowing the unit interval with a continuous triangular norm both of these notions are natural extension of directed completeness in order theory to the fuzzy setting yoneda completeness requires every forward cauchy net converges has a yoneda limit while flat completeness requires every flat weight a counterpart of ideals in partially ordered sets has a supremum it is proved that flat completeness implies yoneda completeness but the converse implication holds only in the case that the related triangular norm is either isomorphic to the ukasiewicz t norm or to the product t norm

effective velocity in compressible navier stokes equations with third order derivatives abstract a formulation of certain barotropic compressible navier stokes equations with third order derivatives as a viscous euler system is proposed by using an effective velocity variable the equations model for instance viscous korteweg or quantum navier stokes flows the formulation in the new variable allows for the derivation of an entropy identity which is known as the bd bresch desjardins entropy equation as a consequence of this estimate a new global in time existence result for the one dimensional quantum navier stokes equations with strictly positive particle densities is proved

on the uniqueness of strong solution to the incompressible navier stokes equations with damping abstract in this paper we show that the cauchy problem of the incompressible navier stokes equations with damping u 1 u 0 has global strong solution for any 3 and the strong solution is unique when 3 5 this improves earlier results

existence of global weak solutions for 3d degenerate compressible navier stokes equations in this paper we prove the existence of global weak solutions for 3d compressible navier stokes equations with degenerate viscosity the method is based on the bresch and desjardins commun math phys 238 211 223 2003 entropy conservation the main contribution of this paper is to derive the mellet and vasseur commun partial differ equ 32 431 452 2007 type inequality for weak solutions even if it is not verified by the first level of approximation this provides existence of global solutions in time for the compressible barotropic navier stokes equations the result holds for any gamma 1 in two dimensional space and for 1 gamma 3 in three dimensional space in both case with large initial data possibly vanishing on the vacuum this solves an open problem proposed by lions mathematical topics in fluid mechanics vol 2 compressible models 1998

a note on a minimax rule for portfolio selection and equilibrium price system this paper concerns a minimax model to investigate the optimal portfolio selection problem without riskless assets and with or without short sale restriction a numerical solution to the problem with short sale restriction is obtained by using the maximum entropy algorithm for the problem without short sale restriction we derive a analytical expression for the optimal solution a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system and an explicit formula for the price system furthermore a numerical example is given to show the validity of the method

low mach number limit of the full navier stokes equations the low mach number limit for classical solutions of the full navier stokes equations is here studied the combined effects of large temperature variations and thermal conduction are taken into account in particular we consider general initial data the equations lead to a singular problem depending on a small scaling parameter whose linearized system is not uniformly well posed yet it is proved that solutions exist and they are uniformly bounded for a time interval which is independent of the mach number ma 0 1 the reynolds number re 1 and the peclet number pe 1 based on uniform estimates in sobolev spaces and using a theorem of g metivier s schochet 30 we next prove that the penalized terms converge strongly to zero this allows us to rigorously justify at least in the whole space case the well known computations given in the introduction of p l lions book 26

global well posedness of the cauchy problem of two dimensional compressible navier stokes equations in weighted spaces abstract in this paper we study the global well posedness of classical solution to 2d cauchy problem of the compressible navier stokes equations with large initial data and vacuum it is proved that if the shear viscosity is a positive constant and the bulk viscosity is the power function of the density that is with 3 then the 2d cauchy problem of the compressible navier stokes equations on the whole space r 2 admits a unique global classical solution u which may contain vacuums in an open set of r 2 note that the initial data can be arbitrarily large to contain vacuum states various weighted estimates of the density and velocity are obtained in this paper and these self contained estimates reflect the fact that the weighted density and weighted velocity propagate along with the flow

minimal concave cost rebalance of a portfolio to the efficient frontier one usually constructs a portfolio on the efficient frontier but it may not be efficient after say three months since the efficient frontier will shift as the elapse of time we then have to rebalance the portfolio if the deviation is no longer acceptable the method to be proposed in this paper is to find a portfolio on the new efficient frontier such that the total transaction cost required for this rebalancing is minimal this problem results in a nonconvex minimization problem if we use mean variance model in this paper we will formulate this problem by using absolute deviation as the measure of risk and solve the resulting linearly constrained concave minimization problem by a branch and bound algorithm successfully applied to portfolio optimization problem under concave transaction costs it will be demonstrated that this method is efficient and that it leads to a significant reduction of transaction costs

existence of global strong solutions in critical spaces for barotropic viscous fluids this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n 2 we address the question of the global existence of strong solutions for initial data close to a constant state having critical besov regularity first this article shows the recent results of charve and danchin arch ration mech anal 198 1 233 271 2010 and chen et al commun pure appl math 63 1173 1224 2010 with a new proof our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity which allows us to cancel out the coupling between the density and the velocity as in haspot well posedness in critical spaces for barotropic viscous fluids 2009 second we improve the results of charve and danchin 2010 and chen et al 2010 by adding as in charve and danchin 2010 some regularity on the initial data in low frequencies in this case we obtain global strong solutions for a class of large initial data which rely on the results of hoff arch rational mech anal 139 303 354 1997 hoff commun pure appl math 55 11 1365 1407 2002 and hoff j math fluid mech 7 3 315 338 2005 and those of charve and danchin 2010 and chen et al 2010 we conclude by generalizing these results for general viscosity coefficients

preordered sets valued in a gl monoid let m l be a gl monoid an m valued preordered set is an l subset endowed with a reflexive and m transitive l relation it is essentially a category enriched in a quantaloid generated by m this paper presents a study of m valued preordered sets with emphasis on symmetrization and the cauchy completion the main result states that symmetrization and the cauchy completion of m valued preordered sets commute up to a natural isomorphism

ekman layers of rotating fluids the case of general initial data in this paper we describe the weak solutions of the navier stokes equations with a large coriolis term as the rossby and the ekman numbers go to zero in a special domain with various boundary conditions this work extends the results in the case of well prepared initial data in 19 30 2000 john wiley sons inc

a multi fluid compressible system as the limit of weak solutions of the isentropic compressible navier stokes equations this paper mainly concerns the mathematical justification of a viscous compressible multi fluid model linked to the baer nunziato model used by engineers see for instance ishii thermo fluid dynamic theory of two phase flow eyrolles paris 1975 under a stratification assumption more precisely we show that some approximate finite energy weak solutions of the isentropic compressible navier stokes equations converge on a short time interval to the strong solution of this viscous compressible multi fluid model provided the initial density sequence is uniformly bounded with corresponding young measures which are linear convex combinations of m dirac measures to the authors knowledge this provides in the multidimensional in space case a first positive answer to an open question see hillairet j math fluid mech 9 343 376 2007 with a stratification assumption the proof is based on the weak solutions constructed by desjardins commun partial differ equ 22 5 6 977 1008 1997 and on the existence and uniqueness of a local strong solution for the multi fluid model established by hillairet assuming initial density to be far from vacuum in a first step adapting the ideas from hoff and santos arch ration mech anal 188 509 543 2008 we prove that the sequence of weak solutions built by desjardins has extra regularity linked to the divergence of the velocity without any relation assumption between and coupled with the uniform bound of the density property this allows us to use appropriate defect measures and their nice properties introduced and proved by hillairet aspects interactifs de la m ecanique des fluides phd thesis ens lyon 2005 in order to prove that the young measure associated to the weak limit is the convex combination of m dirac measures finally under a non degeneracy assumption of this combination stratification assumption this provides a multi fluid system using a weak strong uniqueness argument we prove that this convex combination is the one corresponding to the strong solution of the multi fluid model built by hillairet if initial data are equal we will briefly discuss this assumption to complete the paper we also present a blow up criterion for this multi fluid system following huang et al in serrin type criterion for the three dimensional viscous compressible flows arxiv 2010

asymptotic behavior of a compressible two phase model with well formation interaction abstract in this work we consider a compressible gas liquid model with a well reservoir interaction term that is relevant for coupled wellbore reservoir flow systems involved in e g drilling operations main focus is on deriving estimates that are independent of time under suitable conditions on the well reservoir interaction term we obtain such estimates which allow prediction of the long time behavior of the gas and liquid masses moreover we also obtain a quantification of the convergence rates as a function of time and gain some insight into the role played by the rate characterizing how fast the well reservoir interaction must die out the model is investigated in a free boundary setting where the initial mass is a mixture of both phases i e no single phase zone exists

well posedness in critical spaces for the system of compressible navier stokes in larger spaces this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n geq2 we address the question of well posedness for it large data having critical besov regularity our result improves the analysis of r danchin in cite dw of chen et al in cite c2 and of the author in cite h1 h2 inasmuch as we may take initial density in b nn p 1 with 1 leq p infty our result relies on a new a priori estimate for the velocity where we introduce a new unknown called textit effective velocity to weaken one the coupling between the density and the velocity in particular for the first time we obtain uniqueness without imposing hypothesis on the gradient of the density

global strong solutions to radial symmetric compressible navier stokes equations with free boundary in this paper we consider the two dimensional barotropic compressible navier stokes equations with stress free boundary condition imposed on the free surface as the viscosity coefficients satisfies 2 1 we establish the existence of global strong solution for arbitrarily large spherical symmetric initial data even if the density vanishes across the free boundary in particular we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive and the free boundary propagates along the particle path and expand outwards at an algebraic rate

two level mixed finite element methods for the navier stokes equations with damping abstract in this paper the mixed finite element methods are considered for the navier stokes equations with damping optimal error estimates of the h 1 norm and l 2 norm for the velocity and the l 2 norm for the pressure are obtained moreover two kinds of two level methods based on the oseen correction and newton correction are presented finally two numerical examples are implemented to confirm the analysis

lagrange structure and dynamics for solutions to the spherically symmetric compressible navier stokes equations the compressible navier stokes system cns with density dependent viscosity coefficients is considered in multi dimension the prototype of the system is the viscous saint venat model for the motion of shallow water a spherically symmetric weak solution to the free boundary value problem for cns with stress free boundary condition and arbitrarily large data is shown to exist globally in time with the free boundary separating fluids and vacuum and propagating at finite speed as particle path which is continuous away from the symmetry center detailed regularity and lagrangian structure of this solution have been obtained in particular it is shown that the particle path is uniquely defined starting from any non vacuum region away from the symmetry center along which vacuum states shall not form in any finite time and the initial regularities of the solution is preserved starting from any non vacuum point at a later on time a particle path is also uniquely defined backward in time which either reaches at some initial non vacuum point or stops at a small middle time and connects continuously with vacuum in addition the free boundary is shown to expand outward at an algebraic rate in time and the fluid density decays and tends to zero almost everywhere away from the symmetry center as the time grows up this finally leads to the formation of vacuum state almost everywhere as the time goes to infinity

on the dynamics of navier stokes equations for a shallow water model in this paper we study a free boundary problem of one dimensional compressible navier stokes equations with a density dependent viscosity which include in particular a shallow water model under some suitable assumptions on the initial data we obtain the global existence uniqueness and the large time behavior of weak solutions in particular it is shown that a stationary wave pattern connecting a gas to the vacuum continuously is asymptotically stable for small initial general perturbations

phragmen lindelof alternative results for the shallow water equations for transient compressible viscous flow abstract in this paper the spatial behavior of the viscous shallow water equations in a two dimensional channel domain is studied a differential inequality for suitable energy associated with the solutions of the viscous shallow water equations in a semi infinite channel is derived from which we show the phragmen lindelof alternative results the main tool used is the energy method our results can be viewed as a version of saint venant s principle to the transient compressible viscous flow

the double power monad is the composite power monad in the context of quantaloid enriched categories we rely essentially on the classifying property of presheaf categories to give a conceptual proof of a theorem due to hhle the double power monad and the composite power monad on the category of quantaloid enriched categories are the same via the theory of distributive laws we identify the algebras of this monad to be the completely codistributive complete categories and the homomorphisms between such algebras are the bicontinuous functors with these results we hope to contribute to the further development of a theory of q valued preorders in the sense of pu and zhang

fuzzy galois connections on fuzzy sets abstract in fairly elementary terms this paper presents how the theory of preordered fuzzy sets more precisely quantale valued preorders on quantale valued fuzzy sets is established under the guidance of enriched category theory motivated by several key results from the theory of quantaloid enriched categories this paper develops all needed ingredients purely in order theoretic languages for the readership of fuzzy set theorists with particular attention paid to fuzzy galois connections between preordered fuzzy sets

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

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

superclose and superconvergence of finite element discretizations for the stokes equations with damping a class of conforming mixed finite element methods fems are applied to the stokes equations with damping with the help of the prior estimates for the exact and approximated solutions and the appropriate choice of the parameters a n and r appeared in the problem the superclose and superconvergence results for the velocity in h 1 norm and the pressure in l 2 norm are derived to our best knowledge this is the first superconvergence analysis of conforming mixed fems for this kind nonlinear problem

finite energy method for compressible fluids the navier stokes korteweg model this is the first of a series of papers devoted to the initial value problem for the one dimensional euler system of compressible fluids and augmented versions containing higher order terms in the present paper we are interested in dispersive shock waves and analyze the zero viscosity capillarity limit associated with the navier stokes korteweg system specifically we establish the existence of finite energy solutions as well as their convergence toward entropy solutions to the euler system our method of proof combines energy and effective energy estimates a nonlinear sobolev inequality high integrability properties for the mass density and for the velocity and compactness properties based on entropies 2015 wiley periodicals inc

on the compactness of the reduced gravity two and a half layer equations abstract we consider the reduced gravity two and a half model in oceanic fluid dynamics and prove the stability of weak solutions in periodic domain t 2 the proof is based on the uniform a priori estimates and the method of weak convergence and the limit is carried out with the help of a new higher regularity estimate of the velocity which is derived by constructing a special test function

fuzzy preorder and fuzzy topology this paper presents by means of alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces a systematic investigation of the interrelationship between fuzzy preordered sets topological spaces and fuzzy topological spaces

global existence for the dirichlet problem for the viscous shallow water equations abstract a global existence and uniqueness theorem of strong solutions for the initial boundary value problem with dirichlet boundary conditions is established for small forcing and small initial data an exponentialc0decay rate is also established and the solution is shown to be classical fort 0 the positivity of the fluid heighthfort 0 is also proved

asymptotic behavior of weak solutions to the damped navier stokes equations abstract whether or not weak solutions of classical navier stokes equations decay to zero in l 2 as time tends to infinity was posed by leray in his pioneering paper 12 13 and has been well solved see 15 for instance this paper examines the three dimensional navier stokes equations with damping term u 1 u and proves that the weak solutions decay to zero in l 2 as time tends to infinity for any 1 by developing local in space estimate for weak solutions

blowup of smooth solutions to the compressible navier stokes equation with compact density we present a sufficient condition on the blowup of smooth solutions to the compressible navier stokes equations in arbitrary space dimensions with initial density of compact support as an immediate application it is shown that any smooth solutions to the compressible navier stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support and an upper bound which depends only on the initial data on the blowup time follows from our elementary analysis immediately another implication is that there is no global small decay in time or even bounded in the case that all the viscosity coefficients are positive smooth solutions to the compressible navier stokes equations for polytropic fluids no matter how small the initial data are as long as the initial density is of compact support this is in contrast to the classical theory of global existence of small solutions to the same system with initial data being a small perturbation of a constant state that is not a vacuum the blowup of smooth solutions to the compressible euler system with initial density and velocity of compact support is a simple consequence of our argument 1998 john wiley sons inc

global stability of weak solutions for a multilayer saint venant model with interactions between the layers in this paper we investigate the existence of global weak solutions for the multilayer model introduced by audusse et al which is related to incompressible free surface flows we prove the global stability of weak solutions over the torus we observe that this model admits the so called bd entropy and a gain of integrability on the velocity in the spirit of the work of mellet and vasseur it allows us to obtain enough compactness estimates in order to show the stability of global weak solutions

two grid mfeas for the incompressible stokes type variational inequality with damping abstract in this paper we study two grid mixed finite element algorithms mfeas for the stationary incompressible stokes equations with damping and nonlinear slip boundary conditions we set up the weak formulation and obtain the well posedness then employing the mixed finite element method some optimal error estimates between the exact solution and the approximation solution are derived two kinds of two grid mfeas based on the stokes correction and newton type correction are established some error estimates for two grid mfeas are obtained several numerical results are presented to confirm our theoretical findings

highly rotating viscous compressible fluids in presence of capillarity effects we study here a singular limit problem for a navier stokes korteweg system with coriolis force in the domain mathbb r 2 times 0 1 and for general ill prepared initial data taking the mach and the rossby numbers proportional to a small parameter varepsilon rightarrow 0 we perform the incompressible and high rotation limits simultaneously moreover we consider both the constant and vanishing capillarity regimes in this last case the limit problem is identified as a 2 d incompressible navier stokes equation in the variables orthogonal to the rotation axis if the capillarity is constant instead the limit equation slightly changes keeping however a similar structure due to the presence of an additional surface tension term in the vanishing capillarity regime various rates at which the capillarity coefficient goes to 0 are considered in general this produces an anisotropic scaling in the system the proof of the results is based on suitable applications of the rage theorem combined with microlocal symmetrization arguments

pressureless euler with nonlocal interactions as a singular limit of degenerate navier stokes system abstract we show that weak solutions of degenerate navier stokes equations converge to the strong solutions of the pressureless euler system with linear drag term newtonian repulsion and quadratic confinement the proof is based on the relative entropy method using the artificial velocity formulation for the one dimensional navier stokes system

asymptotic behavior of compressible navier stokes equations with density dependent viscosity and vacuum in this paper we study the one dimensional navier stokes equations connecting to vacuum state with a jump in density when the viscosity depends on the density precisely when the viscosity coefficient is proportional to with 0 where is the density we give the asymptotic behavior and the decay rate of the density function x t furthermore the behavior of the density function x t near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied the analysis is based on some new mathematical techniques and some new useful estimates this fills a final gap on studying navier stokes equations with the viscosity coefficient dependent on the density

mac finite difference scheme for stokes equations with damping on non uniform grids abstract in this paper we consider the numerical methods for stationary stokes equations with damping the mark and cell mac method has been applied to discretize the problem on non uniform grids we establish the lbb condition and the stability for the mac scheme then we obtain the second order super convergence in l2 norm for both velocity and pressure on non uniform grids we also obtain the second order convergence for some terms of h1 norm of the velocity and the other terms of h1 norm are second order convergence on uniform grids numerical experiments using the mac scheme show agreement of the numerical results with theoretical analysis

global existence of strong solution for viscous shallow water system with large initial data on the irrotational part abstract we are interested in studying the cauchy problem for the viscous shallow water system in dimension n 2 we show the existence of global strong solutions with large initial data on the irrotational part of the velocity for the scaling of the equations more precisely our smallness assumption on the initial data is supercritical for the scaling of the equations it allows us to give a first kind of answer to the problem of the existence of global strong solution with large initial energy data in dimension n 2 to do this we introduce the notion of quasi solutions which consists in solving the pressureless viscous shallow water system we can obtain such solutions at least for irrotational data which are subject to regularizing effects both on the velocity and on the density this smoothing effect is purely nonlinear and is crucial in order to build solution of the viscous shallow water system as perturbations of the quasi solutions indeed the pressure term can be considered as a remainder term which becomes small in high frequencies for the scaling of the equations to finish we prove the existence of global strong solution with large initial data when n 2 provided that the mach number is sufficiently large

asymptotic limit for rotational quantum compressible navier stokes equations with multiple scales abstract in this paper we consider the degenerate quantum compressible navier stokes equations giving rise to a variety of mathematical problems in many areas we study the asymptotic limit for the rotational compressible navier stokes equations with quantum term and the ill prepared initial data

global well posedness and decay rates of strong solutions to a non conservative compressible two fluid model in this paper we consider a compressible two fluid model with constant viscosity coefficients and unequal pressure functions p neq p as mentioned in the seminal work by bresch desjardins et al arch rational mech anal 196 599 629 2010 for the compressible two fluid model where p p common pressure is used and capillarity effects are accounted for in terms of a third order derivative of density the case of constant viscosity coefficients cannot be handled in their settings besides their analysis relies on a special choice for the density dependent viscosity refer also to another reference commun math phys 309 737 755 2012 by bresch huang and li for a study of the same model in one dimension but without capillarity effects in this work we obtain the global solution and its optimal decay rate in time with constant viscosity coefficients and some smallness assumptions in particular capillary pressure is taken into account in the sense that delta p p p f neq 0 where the difference function f is assumed to be a strictly decreasing function near the equilibrium relative to the fluid corresponding to p this assumption plays an key role in the analysis and appears to have an essential stabilization effect on the model in question

diagonals between q distributors abstract for a small quantaloid q it is shown that the category of q distributors and diagonals is equivalent to a quotient category of the category of q interior spaces and continuous q distributors kan adjunctions induced by q distributors play a crucial role in establishing this equivalence

the linearized 2d inviscid shallow water equations in a rectangle boundary conditions and well posedness we consider the linearized 2d inviscid shallow water equations in a rectangle a set of boundary conditions is proposed which make these equations well posed several different cases occur depending on the relative values of the reference velocities u 0 v 0 and reference height phi 0 sub or super critical flow at each part of the boundary

existence of global weak solution for a reduced gravity two and a half layer model we investigate the existence of global weak solution to a reduced gravity two and a half layer model in one dimensional bounded spatial domain or periodic domain also we show that any possible vacuum state has to vanish within finite time then the weak solution becomes a unique strong one

quantale valued dissimilarity abstract inspired by the theory of apartness relations of scott we establish a positive theory of dissimilarity valued in an involutive quantale q without the aid of negation it is demonstrated that a set equipped with a q valued dissimilarity is precisely a symmetric category enriched in a subquantaloid of the quantaloid of back diagonals of q interactions between q valued dissimilarities and q valued similarities which are equivalent to q valued equalities in the sense of hohle kubiak are investigated with the help of lax functors in particular it is shown that similarities and dissimilarities are interdefinable if q is a girard quantale with a hermitian and cyclic dualizing element

quantale valued preorders each divisible and unital quantale is associated with two quantaloids categories enriched over these two quantaloids can be regarded respectively as crisp sets endowed with fuzzy preorders and fuzzy sets endowed with fuzzy preorders this paper deals with the relationship between these two kinds of enriched categories this is a special case of the change base issue in enriched category theory two functors the forward globalization functor and the backward globalization functor that map a fuzzy set with a fuzzy preorder to a crisp set with a fuzzy preorder are considered it is shown that both of them preserve cocompleteness with respect to several classes of weights

lp estimates for quantities advected by a compressible flow abstract we consider the evolution of a quantity advected by a compressible flow and subject to diffusion when this quantity is scalar it can be for instance the temperature of the flow or the concentration of some pollutants because of the diffusion term one expects the equations to have a regularizing effect however in their euler form the equations describe the evolution of the quantity multiplied by the density of the flow the parabolic structure is thus degenerate near vacuum when the density vanishes in this paper we show that we can nevertheless derive uniform l p bounds that do not depend on the density in particular the bounds do not degenerate near vacuum furthermore the result holds even when the density is only a measure we investigate both the scalar and the system case in the former case we obtain l bounds in the latter case the quantity being investigated could be the velocity field in compressible navier stokes type of equations and we derive uniform l p bounds for some p depending on the ratio between the two viscosity coefficients the main additional difficulty in that case being to deal with the second viscosity term involving the divergence of the velocity such estimates are to our knowledge new and interesting since they are uniform with respect to the density the proof relies mostly on a method introduced by de giorgi to obtain regularity results for elliptic equations with discontinuous diffusion coefficients

global existence of weak solution for quantum navier stokes poisson equations in this paper we consider the compressible quantum navier stokes poisson equations with a linear density dependent viscosity by the use of a singular pressure close to vacuum we prove the global in time existence of weak solutions in a three dimensional torus for large data in the sense of distribution

well posedness for the viscous rotating shallow water equations with friction terms we consider the cauchy problem for viscous rotating shallow water equations with friction terms the global existence of the solution in some hybrid spaces is shown for the initial data close to a constant equilibrium state away from the vacuum

a non commutative and non idempotent theory of quantale sets in fuzzy set theory non idempotency arises when the conjunction is interpreted by arbitrary t norms there are many instances in mathematics where set theory ought to be non commutative and or non idempotent the purpose of this paper is to combine both ideas and to present a theory of non commutative and non idempotent quantale sets among other things standard concepts like fuzzy preorders and fuzzy equivalence relations will be exhibited as special cases more specifically the category q set is investigated where q is an arbitrary involutive quantale objects quantale sets are pairs consisting of a set and a q valued equality with a suitable symmetry axiom three important properties of q set are shown it is complete cocomplete and has the epi extremal mono factorization property its subcategory s q set of separated quantale sets is reflective in q set and shares the same fundamental properties with q set in particular s q set is also a complete and cocomplete epi extremal mono category the objects of the category q set are interesting categories in their own right two categorical frameworks for objects of q set are exhibited first it is shown that q valued equalities arise from q valued preorders with self adjoint extents by symmetrization which leaves q valued equalities invariant here sets with quantale preorders are shown to be b categories with base b being a specific quantaloid the second approach is based on involutive quantaloids a combination of two well known things quantaloids and ordered categories with involution in this context quantale sets are precisely symmetric b categories w r t appropriately chosen quantaloid b with involution further the cauchy completion preserves the symmetry axiom for a large class of involutive quantales which include quantic frames our non commutative generalization of frames and all left continuous t norms there exist at least two monads on q set the singleton monad and quasi singleton monad which are of special interest for fuzzy set theory the kleisli category associated with the singleton monad is the non commutative and non idempotent analogue of higgs topos while the eilenberg moore category of the quasi singleton monad permits the internalization of lukasiewicz negation as truth arrow finally an application of quantale sets to c algebras is given and the change of base is treated

viscosity effect on the degenerate lake equations abstract this paper concerns the effect of viscosity on the degenerate lake equations anelastic limit when the bottom topography vanishes on the shore we establish the existence and uniqueness of a global weak solutions for various choices of viscosity term in weighted sobolev spaces where the weight is assumed to be a power type weight our solution is constructed by adapting carefully the known works on the incompressible navier stokes equations in unweighted context finally we study in one case the vanishing viscosity limit when the solution of the inviscid lake equations is regular enough generalizing the results by martino et al 2001 to the degenerate case

q closure spaces for a small quantaloid q a q closure space is a small category enriched in q equipped with a closure operator on its presheaf category we investigate q closure spaces systematically with specific attention paid to their morphisms and as preordered fuzzy sets are a special kind of quantaloid enriched categories in particular fuzzy closure spaces on fuzzy sets are introduced as an example by constructing continuous relations that naturally generalize continuous maps it is shown in the generality of the q version that the category of closure spaces and closed continuous relations is equivalent to the category of complete lattices and sup preserving maps

analysis of an inviscid zero mach number system in endpoint besov spaces for finite energy initial data abstract the present paper is the continuation of work 18 devoted to the study of an inviscid zero mach number system in the framework of endpoint besov spaces of type b r s r d r 1 d 2 which can be embedded in the lipschitz class c 0 1 in particular the largest case b 1 1 and the case of holder spaces c 1 are taken into account the local in time well posedness of this system is proved under an additional finite energy hypothesis on the initial data the key to get this result is new a priori estimates for parabolic equations with variable coefficients in endpoint spaces b r s r d which are of independent interest in the special case of space dimension d 2 we are able to give a lower bound for the lifespan such that the solutions tend to be globally defined when the initial inhomogeneity is small there we will show refined a priori estimates in endpoint besov spaces for transport equations

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

towards probabilistic partial metric spaces diagonals between distance distributions abstract the quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories motivated by the categorical interpretation of partial metric spaces we are led to investigate the quantaloid of diagonals between distance distributions which is expected to establish the categorical foundation of probabilistic partial metric spaces observing that the quantale of distance distributions w r t an arbitrary continuous t norm is non divisible we precisely characterize diagonals between distance distributions and prove that one step functions are the only distance distributions on which the set of diagonals coincides with the generated down set

an asymptotic limit of a navier stokes system with capillary effects a combined incompressible and vanishing capillarity limit in the barotropic compressible navier stokes equations for smooth solutions is proved the equations are considered on the two dimensional torus with well prepared initial data the momentum equation contains a rotational term originating from a coriolis force a general korteweg type tensor modeling capillary effects and a density dependent viscosity the limiting model is the viscous quasi geostrophic equation for the rotated velocity potential the proof of the singular limit is based on the modulated energy method with a careful choice of the correction terms

stabilized low order finite elements for stokes equations with damping abstract in this paper we consider the stationary stokes equations with damping low order mixed finite element spaces are used to approximate the velocity and the pressure and a local pressure projection stabilization method is used for the pairs to overcome the lack of the inf sup condition the stability of this method is proved and the optimal order error estimates are derived by some nonlinear analysis techniques at last two numerical examples are implemented to test the stability and effectiveness of the proposed method