quotient mi groups a many identities group mi group for short is a special algebraic structure in which identity like elements called pseudoidentities are specified and collected into a monoidal substructure in this way many algebraic structures such as monoids of fuzzy intervals numbers or convex bodies possessing behavior very similar to that of a group structure may be well described and investigated using a new approach which seems to be superfluous for the classical structures the concept of mi groups was recently introduced by holcapek and st pnicka in the paper mi algebras a new framework for arithmetics of extensional fuzzy numbers to demonstrate how a standard structure can be generalized in terms of mi algebras this paper is a continuation of the development of mi group theory and is focused on the construction of quotient mi groups and a specification of the conditions under which the isomorphism theorems for groups are fulfilled for mi groups

on the vanishing viscosity limit for the 3d navier stokes equations with a slip boundary condition where and below and denote the div and curl operators respectively n is the outward normal and is the unit tangential vector of the investigation of vanishing viscosity limit of solutions of the navier stokes equations both in the two and three spacial dimensional cases is a classical issue there are two related questions arising from here one is how to describe the inviscid limiting behavior of the navier stokes equation and the other is that does the euler equation can be approximated by the navier stokes equations in the case that the solution to the this research is supported in part by zheng ge ru foundation and hong kong rgc earmarked research grants cuhk 4028 04p cuhk 4040 02p and cuhk 4279 00p

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

ranking fuzzy numbers with integral value abstract ranking fuzzy numbers is important in decision making since very often the alternatives are evaluated by fuzzy numbers in a vague environment a comparison between these fuzzy numbers is indeed a comparison between alternatives this paper proposes a method of ranking fuzzy numbers with integral value the method which is independent of the type of membership functions used and the normality of the functions can rank more than two fuzzy numbers simultaneously it is relatively simple in computation especially in ranking triangular and trapezoidal fuzzy numbers further an index of optimism is used to reflect the decision maker s optimistic attitude discussion on comparative advantages is included

a probabilistic approach to rank complex fuzzy numbers abstract techniques for ranking simple fuzzy numbers are abundant in the literature however we lack efficient methods for comparing complex fuzzy numbers that are induced by arithmetic operations in this paper a probabilistic approach is taken membership functions of fuzzy numbers are first converted into probability density functions the mellin transform is then introduced to compute the mean and the variance of a complex fuzzy number the fuzzy number with the higher mean is ranked higher if the means are equal the one with the smaller variance is judged higher rank two numerical examples and a fuzzy multiple attribute decision analysis are illustrated

nonlinear evolution equations and the euler flow abstract a new theorem on abstract nonlinear equations of evolution is proved as an application the existence uniqueness regularity and continuous dependence on the data are proved for the solution of the euler equation for incompressible fluids in a bounded domain in r m

boundary layers associated with incompressible navier stokes equations the noncharacteristic boundary case abstract the goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly noncharacteristic i e there is injection and or suction everywhere at the boundary following earlier work on the boundary layer for linearized navier stokes equations in the case where the boundaries are characteristic no slip at the boundary and non permeable we consider here the case where the boundary is permeable and thus noncharacteristic the form of the boundary layer and convergence results are derived in two cases linearized equation and full nonlinear equations we prove that there exists a boundary layer at the outlet downwind of the form e uz e where u is the speed of injection suction at the boundary z is the distance to the outlet of the channel and e is the kinematic viscosity we improve an earlier result of s n alekseenko 1994 siberian math j 35 no 2 209 230 where the convergence in l 2 of the solutions of the navier stokes equations to that of the euler equations at vanishing viscosity was established in the two dimensional case we are able to derive the physically relevant uniform in space l norm estimates of the boundary layer the uniform in space estimate is derived by properly developing our previous idea of better control on the tangential derivative and the use of an anisotropic sobolev imbedding to the best of our knowledge this is the first rigorously proved result concerning boundary layers for the full nonlinear navier stokes equations for incompressible fluids

criteria for evaluating fuzzy ranking methods abstract in this paper four criteria for evaluating fuzzy ranking methods are investigated fuzzy preference representation rationality of fuzzy ordering distinguishability and robustness based on these criteria two existing ranking methods baas and kwakernaak s and nakamura s are evaluated and a new improved ranking method is suggested

the beale kato majda criterion for the 3d magneto hydrodynamics equations we study the blow up criterion of smooth solutions to the 3d mhd equations by means of the littlewood paley decomposition we prove a beale kato majda type blow up criterion of smooth solutions via the vorticity of velocity only namely sup j in mathbb z int 0 t delta j nabla times u infty dt where j is the frequency localization operator in the littlewood paley decomposition

uniform regularity estimates of solutions to three dimensional incompressible magnetic benard equations with navier slip type boundary conditions in half space abstract in this paper we are concerned with the uniform estimates of solutions to three dimensional 3d incompressible magnetic benard equations with navier slip type boundary conditions being imposed on both velocity and magnetic field in half space where the physical boundary is assumed to be insulation under the assumption that the viscosity and resistivity coefficients are same which are parameterized by a small parameter of e the uniform estimates of solutions to the viscous magnetic benard system of equations are established in the conormal sobolev space which is independent of e as a direct consequence the inviscid type limit between the solutions to viscous magnetic benard system and the ideal magnetic benard system is proved rigorously

a characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere we describe a characterization of convex polyhedra in h 3 in terms of their dihedral angles developed by rivin we also describe some geometric and combinatorial consequences of that theory one of these consequences is a combinatorial characterization of convex polyhedra in e 3 all of whose vertices lie on the unit sphere that resolves a problem posed by jakob steiner in 1832

on the roughness induced effective boundary conditions for an incompressible viscous flow abstract we consider the laminar viscous channel flow with the lateral surface of the channel containing surface irregularities it is supposed that a uniform pressure gradient is maintained in the longitudinal direction of the channel after studying the corresponding boundary layers we obtain rigorously the navier friction condition it is valid when the size and amplitude of the imperfections tend to zero furthermore the coefficient in the law is determined through an auxiliary boundary layer type problem and the tangential drag force and the effective mass flow are determined up to order o e3 2 the value of the effective coefficient is shown to be independent with respect to the position of the mean surface in the range of o e

a regularity criterion for the three dimensional mhd equations in terms of one directional derivative of the pressure in this work we will establish a sufficient condition for the regularity criterion to the 3d mhd equations in terms of one directional derivative of the pressure more precisely we prove that if x 3 x t l 2 1 r 0 t m 2 3 r r 3 for 0 r 1 then the solution u b is regular we obtain some improvement of the related results in berselli and galdi 2002 cao and wu 2010 jia and zhou 2012 lin and du 2013 and yamazaki 2013

a new approach for ranking fuzzy numbers by distance method abstract many ranking methods have been proposed so far however there is yet no method that can always give a satisfactory solution to every situation some are counterintuitive not discriminating some use only the local information of fuzzy values some produce different rankings for the same situation for overcoming the above problems we propose a new method for ranking fuzzy numbers by distance method our method is based on calculating the centroid point where the distance means from original point to the centroid point x 0 y 0 and the x 0 index is the same as murakami et al s x 0 however the y 0 index is integrated from the inverse functions of an lr type fuzzy number thus we use ranking function r a x 2 y 2 distance index as the order quantities in a vague environment our method can rank more than two fuzzy numbers simultaneously and the fuzzy numbers need not be normal furthermore we also propose the coefficient of variation cv index to improve lee and li s method comput math appl 15 1988 887 896 lee and li rank fuzzy numbers based on two different criteria namely the fuzzy mean and the fuzzy spread of the fuzzy numbers and they pointed out that human intuition would favor a fuzzy number with the following characteristics higher mean value and at the same time lower spread however when higher mean value and at the same time higher spread or lower mean value and at the same time lower spread exists it is not easy to compare its orderings clearly our cv index is defined as cv standard error mean which can overcome lee and li s problem efficiently in this way our proposed method can also be easily calculated by the mathematica package to solve problems of ranking fuzzy numbers at last we present three numerical examples to illustrate our proposed method and compare with other ranking methods

hausdorff measure of the singular set in the incompressible magnetohydrodynamic equations we derive a local energy inequality for weak solutions of the three dimensional magnetohydrodynamic equations combining biot savart law interpolation inequalities and the local energy inequality we prove a partial regularity theorem for suitable weak solutions furthermore we obtain an improved estimate for the logarithmic hausdorff dimension of the singular set of suitable weak solutions

on the regularity of flows with ladyzhenskaya shear dependent viscosity and slip or non slip boundary conditions navier stokes equations with shear dependent viscosity under the classical nonslip boundary condition were introduced and studied in the 1960s by o a ladyzhenskaya and in the case of gradient dependent viscosity by j l lions a particular case is the well known smagorinsky turbulence model this is nowadays a central subject of investigation on the other hand boundary conditions of slip type seems to be more realistic in some situations in particular in numerical applications they are a main research subject the existence of weak solutions u to the above problems with slip or nonslip type boundary conditions is well known in many cases however regularity up to the boundary still presents many open questions in what follows we present some regularity results in the stationary case for weak solutions to this kind of problem see theorem 3 1 and theorem 3 2 the evolution problem is studied in a forthcoming paper 6 a cornerstone in our proof is the classical nirenberg translation method see 38

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

ranking fuzzy numbers based on decomposition principle and signed distance by using the decomposition principle and the crisp ranking system on r we construct a new ranking system for fuzzy numbers which is very realistic and also matching our intuition as in r

finite element discretization of the navier stokes equations with a free capillary surface the instationary navier stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions a stable finite element discretization is presented the key idea is the treatment of the curvature terms by a variational formulation in the context of a discontinuous in time space time element discretization stability in weak energy norms can be proved numerical examples in 2 and 3 space dimensions are given

a note on the regularity criterion for 3d mhd equations in b 1 space abstract in this note we consider sufficient conditions for the regularity of leray hoph hopf solutions of the 3d incompressible magnetohydrodynamic equations via the velocity and magnetic fields in terms of b 1 spaces we prove that if u b belongs to the space l 2 0 t b 1 r 3 then the solution u b is regular this extends recent results contained in gala 2011 3

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

zero viscosity limit for analytic solutions of the navier stokes equation on a half space i existence for euler and prandtl equations this is the first of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in this paper we prove short time existence theorems for the euler and prandtl equations with analytic initial data in either two or three spatial dimensions the main technical tool in this analysis is the abstract cauchy kowalewski theorem for the euler equations the projection method is used in the primitive variables to which the cauchy kowalewski theorem is directly applicable for the prandtl equations cauchy kowalewski is applicable once the diffusion operator in the vertical direction is inverted

global regularity to the 3d mhd equations with large initial data in bounded domains this paper considers the global regularity to the 3d incompressible mhd equations with large initial data in bounded domains let u and b denote the viscosity coefficient magnetic diffusivity velocity field and magnetic field respectively we construct new systems for u b and u b to overcome the difficulties caused by the large initial data it is shown that u b h1 is globally bounded as long as u0 b0 h1 1 or u0 b0 h1 1 is sufficiently small which indicates that the navier stokes equations can be regularized by the magnetic field

partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations in this paper we study the local behavior of the solutions to the three dimensional magnetohydrodynamic equations we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions it is shown that in some neighborhood of x0 t0 the gradients of the velocity field u and the magnetic field b are locally uniformly bounded in l norm as long as that either the scaled local l2 norm of the gradient or the scaled local total energy of the velocity field is small and the scaled local total energy of the magnetic field is uniformly bounded these estimates indicate that the velocity field plays a more dominant role than that of the magnetic field in the regularity theory as an immediately corollary we can derive an estimates of hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid various partial regularity results are obtained as consequences of our blow up estimates

algebraic properties and topological properties of the quotient space of fuzzy numbers based on mares equivalence relation abstract in this paper we obtain some algebraic properties and topological properties of the quotient space of fuzzy numbers with respect to the equivalence relation defined by mares every fuzzy number has only one mares core and equivalent fuzzy numbers have the same mares core in addition equivalence classes of fuzzy numbers can be only expressed as the sum of its mares core and the set of symmetric fuzzy numbers which shows the notable difference between the equivalence classes of fuzzy numbers and the cosets of the normal subgroup in a group based on these results we introduce a new concept of convergence under which the quotient space is complete as an application of the main results it is shown that if we identify every fuzzy number with the corresponding equivalence class there would be more differentiable fuzzy functions than what is found in the literature

vanishing viscosity limit for a coupled navier stokes allen cahn system abstract in this paper we study the vanishing viscosity limit for a coupled navier stokes allen cahn system in a bounded domain we first show the local existence of smooth solutions of the euler allen cahn equations by modified galerkin method then using the boundary layer function to deal with the mismatch of the boundary conditions between navier stokes and euler equations and assuming that the energy dissipation for navier stokes equation in the boundary layer goes to zero as the viscosity tends to zero we prove that the solutions of the navier stokes allen cahn system converge to that of the euler allen cahn system in a proper small time interval in addition for strong solutions of the navier stokes allen cahn system in 2d the convergence rate is c 1 2

vanishing viscosity limit for the 3d magnetohydrodynamic system with a slip boundary condition abstract this work investigates the solvability regularity and vanishing viscosity limit of the 3d viscous magnetohydrodynamic system in a class of bounded domains with a slip boundary condition

regularity criterion for 3d mhd fluid passing through the porous medium in terms of gradient pressure abstract the aim of the paper is to establish regularity criteria for the weak solution of fluid passing through the porous media in r 3 our results show that if p l with 2 3 3 1 then the weak solution is regular and unique if p l with 2 3 2 3 2 then the weak solution is regular and unique

an improved regularity criterion for the 3d hall mhd equations via the vorticity abstract in this paper we consider the three dimensional incompressible hall magnetohydrodynamic equations and establish an improved regularity criterion of local in time classical solutions involving only the vorticity field consequently this improves the previous result

on incompressible viscous fluid flows with slip boundary conditions we consider stationary and nonstationary problems of viscous incompressible fluid flows with slip boundary conditions in a rotating bounded domain we show a geometrical representation of the slip conditions where principal curvatures of its boundary surfaces are characteristic coefficients when the domain is axisymmetric it is proved that a steady flow exists if external force f in equations of motion is orthogonal to rigid rotational flows and that a nonstationary flow converges to a steady flow depending on its initial flow as time tends to infinity if f is independent of time and orthogonal to rigid rotational flows and if the l2 norm of f is sufficiently small

regularity criteria for a lagrangian averaged magnetohydrodynamic α model abstract in this paper we study the n dimensional lagrangian averaged magnetohydrodynamic lamhd model with 5 n 7 throughout the whole space various regularity criteria are established for both the cases with and those without viscosity

solutions for semilinear parabolic equations in lp and regularity of weak solutions of the navier stokes system abstract we construct a unique local regular solution in l q 0 t l p for a class of semilinear parabolic equations which includes the semilinear heat equation u t u u u 0 and the navier stokes system here p and q are so chosen that the norm of l q 0 t l p is dimensionless or scaling invariant the main relation between p and q for the semilinear heat equation is 1 q 1 p 1 q n 2 provided that initial data are in l r with r n 2 1 where n is the space dimension applying our regular solutions to the navier stokes system we show that the k 2 dimensional hausdorff measure of possible time singularities of a turbulent solution is zero if the turbulent solution is in l q 0 t l p where k 2 q nq p p n 1 q we show moreover that a turbulent solution is regular if it is in c 0 t l n

regularity criteria and small data global existence to the generalized viscous hall magnetohydrodynamics in this paper we establish the regularity criteria of solutions to the three space dimensions generalized viscous hall magnetohydrodynamics moreover we also prove that there exist classical solutions globally in time to the generalized viscous hall mhd if the initial data is small enough or the fractional laplacian dissipation powers and are suitably large these results are some improvements of very recent work chae and lee 2014 established by chae and lee

a new regularity criterion for weak solutions to the viscous mhd equations in terms of the vorticity field abstract in this paper we consider regularity criterion for solutions to the 3d viscous incompressible mhd equations in morrey campanato spaces it is proved that if the vorticity field u belongs to m 2 3 r for 0 r 1 on 0 t then the solution remains smooth on 0 t

remarks on singularities dimension and energy dissipation for ideal hydrodynamics and mhd for weak solutions of the incompressible euler equations there is energy conservation if the velocity is in the besov space b 3 s with s greater than 1 3 b 3 s consists of functions that are lip s i e holder continuous with exponent s measured in the l p norm here this result is applied to a velocity field that is lip 0 except on a set of co dimension on which it is lip agr 1 with uniformity that will be made precise below we show that the frisch parisi multifractal formalism is valid at least in one direction for such a function and that there is energy conservation if analogous conservation results are derived for the equations of incompressible ideal mhd i e zero viscosity and resistivity for both energy and helicity in addition a necessary condition is derived for singularity development in ideal mhd generalizing the beale kato majda condition for ideal hydrodynamics

global well posedness for the 3 d incompressible inhomogeneous mhd system in the critical besov spaces abstract in this paper we study the cauchy problem for the incompressible inhomogeneous magnetohydrodynamic mhd system in r 3 we obtain the global existence of a unique solution for this system without any small conditions imposed on the third component of the initial velocity field and magnetic field in the critical besov spaces our methods mainly rely upon the fourier frequency localization and bony s paraproduct decomposition

regularity criteria in terms of the pressure for the three dimensional mhd equations in this paper we consider the cauchy problem for the 3d incompressible mhd equations a regularity criterion by providing sufficient condition in terms of the pressure is established more precisely we show that if p l 0 t l r 3 with 3 2 7 4 and 12 5 4 then any weak solutions u b of the 3d mhd equations is regular on 0 t

ranking and defuzzification methods based on area compensation abstract we present some interesting properties related to the area compensation procedure to compare fuzzy numbers it has been proved that this method produces more than a fuzzy interval order it induces a ranking of fuzzy numbers some further results are given about the transitivity property and about computational aspects extensions to non normal fuzzy numbers and fuzzy quantities are also proposed

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

a new regularity criterion for the 3d incompressible mhd equations in terms of one component of the gradient of pressure abstract in this paper we study the global regularity issue for the 3d incompressible mhd equations it is proved that if the pressure p satisfies 3 p l 0 t l r 3 with 2 3 2 3 and 1 then the corresponding weak solution u b is regular on 0 t

zero viscosity limit of the linearized navier stokes equations for a compressible viscous fluid in the half plane the zero viscosity limit for an initial boundary value problem of the linearized navier stokes equations of a compressible viscous fluid in the half plane is studied by means of the asymptotic analysis with multiple scales we first construct an approximate solution of the linearized problem of the navier stokes equations as the combination of inner and boundary expansions next by carefully using the technique on energy methods we show the pointwise estimates of the error term of the approximate solution which readily yield the uniform stability result for the linearized navier stokes solution in the zero viscosity limit 1999 john wiley sons inc

on the vanishing viscosity limit of 3d navier stokes equations under slip boundary conditions in general domains we consider the vanishing viscosity limit for the navier stokes equations with certain slip without friction boundary conditions in a bounded domain with non flat boundary in particular we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary the proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity

effective boundary conditions for laminar flows over periodic rough boundaries effective boundary conditions or wall laws are proposed for a laminar flow over a rough wall with periodic roughness elements these effective conditions are posed on a regularized boundary which allows the details of the wall to be avoided and dramatically reduces the computational cost the effective conditions stem from an asymptotic expansion of the solution which is presented here both first and second order conditions are discussed and tested numerically on bidimensional cases

zero viscosity limit for analytic solutions of the navier stokes equation on a half space ii construction of the navier stokes solution this is the second of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in either 2d or 3d under the assumption of analytic initial data we construct solutions of navier stokes for a short time which is independent of the viscosity the navier stokes solution is constructed through a composite asymptotic expansion involving the solutions of the euler and prandtl equations which were constructed in the first paper plus an error term this shows that the navier stokes solution goes to an euler solution outside a boundary layer and to a solution of the prandtl equations within the boundary layer the error term is written as a sum of first order euler and prandtl corrections plus a further error term the equation for the error term is weakly nonlinear its linear part is the time dependent stokes equation this error equation is solved by inversion of the stokes equation through expressing the solution as a regular euler like part plus a boundary layer prandtl like part the main technical tool in this analysis is the abstract cauchy kowalewski theorem

on weighted possibilistic mean and variance of fuzzy numbers dubois and prade defined an interval valued expectation of fuzzy numbers viewing them as consonant random sets carlsson and fuller defined an interval valued mean value of fuzzy numbers viewing them as possibility distributions in this paper we shall introduce the notation of weighted interval valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval valued probabilistic mean we shall also introduce the notations of crisp weighted possibilistic mean value variance and covariance of fuzzy numbers which are consistent with the extension principle furthermore we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

global regularity of the two dimensional incompressible generalized magnetohydrodynamics system abstract in this paper we consider the global regularity of the two dimensional generalized incompressible magnetohydrodynamics system with velocity dissipation exponent 1 4 and magnetic diffusion exponent 1 based on the improved integrability in terms of vorticity this result is a further improvement of very recent works jiu and zhao 2014 and yamazaki 2013 which require 1 3 and 1 therefore our result is more closer to the resolution of the well known global regularity issue on the 2d magnetohydrodynamics system 0 1

on possibilistic mean value and variance of fuzzy numbers dubois and prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions in this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval valued possibilistic mean and investigate its relationship to the interval valued probabilistic mean we also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions which are consistent with the extension principle we also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

asymptotic limits of the isentropic compressible viscous magnetohydrodynamic equations with navier slip boundary conditions abstract in this paper two kinds of asymptotic limits to the isentropic compressible viscous magnetohydrodynamic equations in a three dimensional bounded domain with navier slip boundary conditions are discussed one is the incompressible limit with ill prepared initial data and the other is the combined inviscid and incompressible limit with well prepared initial data in the first case we show that the weak solutions of the compressible viscous magnetohydrodynamic equations converge weakly to the weak solutions of the incompressible viscous magnetohydrodynamic equations provided the index of the fluid friction coefficient 1 1 as the mach number goes to 0 moreover the convergence of the velocity in l 2 0 l 2 is indeed strong under some geometrical assumptions on the domain and 1 1 2 in the second case we show that the weak solution of the compressible viscous magnetohydrodynamic equations converges to the local strong solution of the ideal incompressible magnetohydrodynamic equations furthermore the convergence rates are also obtained

realizability and inscribability for simplicial polytopes via nonlinear optimization we show that nonlinear optimization techniques can successfully be applied to realize and to inscribe matroid polytopes and simplicial spheres in order to show non realizability of simplicial spheres we extend the method of finding biquadratic final polynomials for matroid polytopes to partial matroid polytopes combining these two methods we obtain a complete classification of neighborly polytopes of dimension 4 6 and 7 with 11 vertices of neighborly 5 polytopes with 10 vertices as well as a complete classification of simplicial 3 spheres with 10 vertices into polytopal and non polytopal spheres surprisingly many of the realizable polytopes are also inscribable

on the uniqueness of weak solutions for the 3d viscous magneto hydrodynamic equations abstract a uniqueness result of weak solutions for the 3d viscous magneto hydrodynamic equations is proved by means of the fourier localization technique and bony s paraproduct decomposition

remarks on the regularity criteria of generalized mhd and navier stokes systems we study the regularity criteria of the three dimensional generalized magnetohydrodynamics mhd and navier stokes systems in particular we show that the regularity criteria of the generalized mhd system may be reduced to depend only on two diagonal entries of the jacobian matrix of the velocity vector field or one vorticity component and one entry of the jacobian matrix of the velocity vector field

a regularity criterion for the 3d magneto micropolar fluid equations in triebel lizorkin spaces abstract we consider the regularity criterion for the 3d magneto micropolar fluid equations in triebel lizorkin spaces it is proved that if u l p 0 t f q 2 q 3 0 with 2 p 3 q 2 3 2 q then the solution remains smooth in 0 t as a corollary we obtain the classical beal kato majda criterion that is the condition u l 1 0 t b 0 ensures the smoothness of the solution

limiting case for the regularity criterion to the 3 d magneto hydrodynamics equations abstract we prove that any weak solution u b of three dimensional incompressible magneto hydrodynamics equations is regular if u l 0 t l 3 r 3 and b l 0 t vmo 1 r 3 the proof is based on the blow up analysis and backward uniqueness for the parabolic operator developed by escauriaza seregin sverak

remarks on partial regularity for suitable weak solutions of the incompressible magnetohydrodynamic equations abstract in this paper we are concerned with the partial regularity for suitable weak solutions of the tri dimensional magnetohydrodynamic equations with the help of the de giorgi iteration method we obtain the results proved by he and xin c he z xin partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations j funct anal 227 2005 113 152 namely the one dimensional parabolic hausdorff measure of the possible singular points of the velocity field and the magnetic field is zero

global regularity for the 212d incompressible hall mhd system with partial dissipation abstract in this paper we investigate the cauchy problem for the 2 1 2 dimensional incompressible hall magnetohydrodynamic equations with partial dissipation by using energy estimate we obtain the local existence of strong solution and the global in time existence of the strong solution

geometric measure type regularity criteria for the 3d magnetohydrodynamical system abstract several formulations of a local geometric measure type condition are imposed on super level sets of mild solutions to the homogeneous incompressible 3d magnetohydrodynamical system with bounded initial data to prevent finite time singularity formation supporting this results regarding the existence uniqueness and real analyticity of mild solutions are established as is a sharp lower bound on the radius of analyticity

initial boundary value problem to 2d boussinesq equations for mhd convection with stratification effects abstract this paper is concerned with the initial boundary value problem to 2d magnetohydrodynamics boussinesq system with the temperature dependent viscosity thermal diffusivity and electrical conductivity first we establish the global weak solutions under the minimal initial assumption then by imposing higher regularity assumption on the initial data we obtain the global strong solution with uniqueness moreover the exponential decay rates of weak solutions and strong solution are obtained respectively

boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations abstract we present some new regularity criteria for suitable weak solutions of magnetohydrodynamic equations near boundary in dimension three we prove that suitable weak solutions are holder continuous near boundary provided that either the scaled l x t p q norm of the velocity with 3 p 2 q 2 2 q or the scaled l x t p q norm of the vorticity with 3 p 2 q 3 2 q are sufficiently small near the boundary

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

remarks on the regularity criteria of three dimensional magnetohydrodynamics system in terms of two velocity field components we study the three dimensional magnetohydrodynamics system and obtain its regularity criteria in terms of only two velocity vector field components eliminating the condition on the third component completely the proof consists of a new decomposition of the four nonlinear terms of the system and estimating a component of the magnetic vector field in terms of the same component of the velocity vector field this result may be seen as a component reduction result of many previous works c he and z xin on the regularity of weak solutions to the magnetohydrodynamic equations j differ equ 213 2 234 254 2005 y zhou remarks on regularities for the 3d mhd equations discrete contin dyn syst 12 5 881 886 2005

strong solutions to the incompressible magnetohydrodynamic equations with vacuum we consider the incompressible magnetohydrodynamic mhd equations with the coefficients depending on the density and temperature we prove the existence of unique local strong solutions for all initial data satisfying a natural compatibility condition the initial density need not be positive and may vanish in an open set

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

a new criterion of choice between generalized triangular fuzzy numbers in this paper we consider a new criterion of choice between generalized or rounded triangular fuzzy numbers based on the concept of the weighted possibilistic mean introduced by fullr and majlender first we introduce a preference relation which establishes a partial order on the family of generalized triangular fuzzy numbers second we present a weak preference relation which leads to a total order on this family then we consider the special case of triangular fuzzy numbers and rephrase the preceding results in terms of selected parameters characterizing a triangular fuzzy number finally we compare our results with a number of new approaches recently discussed in the literature

gradual numbers and their application to fuzzy interval analysis in this paper we introduce a new way of looking at fuzzy intervals instead of considering them as fuzzy sets we see them as crisp sets of entities we call gradual real numbers they are a gradual extension of real numbers not of intervals such a concept is apparently missing in fuzzy set theory gradual numbers basically have the same algebraic properties as real numbers but they are functions a fuzzy interval is then viewed as a pair of fuzzy thresholds which are monotonic gradual real numbers this view enables interval analysis to be directly extended to fuzzy intervals without resorting to alpha cuts in agreement with zadeh s extension principle several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end points of intervals are changed into left and right fuzzy bounds our approach is illustrated on two known problems computing fuzzy weighted averages and determining fuzzy floats and latest starting times in activity network scheduling

on the regularity of generalized mhd equations abstract this paper studies the regularity of generalized magneto hydrodynamics equation on the condition 0 3 2 it will show if u l p q on 0 t with 2 p 3 q 2 3 2 q then the solution can be extended past t