fuzzy risk analysis based on similarity measures of generalized fuzzy numbers in this paper we present a new method for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers firstly we present a method called the simple center of gravity method scgm to calculate the center of gravity cog points of generalized fuzzy numbers then we use the scgm to propose a new method to measure the degree of similarity between generalized fuzzy numbers the proposed similarity measure uses the scgm to calculate the cog points of trapezoidal or triangular generalized fuzzy numbers and then to calculate the degree of similarity between generalized fuzzy numbers we also prove some properties of the proposed similarity measure and use an example to compare the proposed method with the existing similarity measures the proposed similarity measure can overcome the drawbacks of the existing methods we also apply the proposed similarity measure to develop a new method to deal with fuzzy risk analysis problems the proposed fuzzy risk analysis method is more flexible and more intelligent than the existing methods due to the fact that it considers the degrees of confidence of decisionmakers opinions

some existence results for a periodic problem with non smooth potential abstract in this paper two existence results for a class of second order periodic boundary value problems with non smooth potential are obtained we extend the castro lazer thews reduction method to non smooth functionals the obtained result is then exploited to prove the existence of a nontrivial solution furthermore we prove the existence of multiple solutions by using a multiplicity result based on local linking

positive solutions of generalized nonlinear logistic equations via sub super solutions abstract let be a smooth bounded domain in r n n 1 let m n be two nonnegative functions defined in and let r n r n be a continuous and strictly monotone mapping we consider the existence and nonexistence of positive solutions for nonlinear problems involving the laplacian of the form div u m x f u n x g u in u 0 on where 0 is a real parameter and f g 0 0 are continuous functions modeled by f t t q and g t t r with 0 q r the subdiffusive equidiffusive and superdiffusive cases are all treated and some qualitative properties of the solutions are also given as a byproduct we obtain results in the case of a roughly speaking sublinear nonlinearity f and n 0 we point out that some of our results are new even for the usual p laplacian our main tool is the sub supersolutions method combined with some estimates on related nonlinear problems

solvability of strongly nonlinear boundary value problems for second order differential inclusions abstract in this paper we study a problem for a second order differential inclusion with dirichlet neumann and mixed boundary conditions the equation is driven by a nonlinear not necessarily homogeneous differential operator satisfying certain conditions and containing as a particular case the p laplacian operator we prove the existence of solutions both for the case in which the multivalued nonlinearity has convex values and for the case in which it has not convex values the presence of a maximal monotone operator in the equation make the results applicable to gradient systems with non smooth time invariant convex potential and differential variational inequalities

strongly nonlinear multivalued boundary value problems in this paper we study nonlinear second order differential inclusions involving the differential operator depending on both unknown function x and its derivative x a multivalued maximal monotone operator and nonlinear multivalued boundary conditions our framework is general and can be applied to the classical boundary value problems namely the dirichlet the neumann and the periodic problems using notions and techniques from the nonlinear operator theory and from multivalued analysis we obtain solutions for both the convex and nonconvex problems finally we present the cases of special interest which fit into our framework illustrating the generality of our results

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

local regularity criteria of the 3d navier stokes and related equations abstract in this paper we are concerned with the local regularity of suitable weak solutions to the 3d navier stokes equations and its generalized case with fractional power of the laplacian 3 4 1 in the first part we derive some regularity criteria in terms of the deformation tensor d u for the classical navier stokes equations in the second part for the fractional case we obtain some regularity conditions for suitable weak solutions including the velocity u the gradient of the velocity u the rotation tensor u and the deformation tensor d u this generalizes the results obtained by gustafson et al 2007

fuzzy logarithmic least squares ranking method in analytic hierarchy process abstract we xu and zhai 1992 have discussed the extensions of analytic hierarchy process in fuzzy environment and presented a procedure for constructing the fuzzy judgment matrix this paper continues the discussion and goes further into the problem about extracting the fuzzy weights from the fuzzy judgment matrix by logarithmic least squares method which is a main ranking method in analytic hierarchy process first we define the metric of the fuzzy judgment space and develop the expression form of logarithmic least squares method in fuzzy environment next we derive the associated normal equations from the problem of fuzzy logarithmic least squares and prove that the solutions of fuzzy logarithmic least squares model are equivalent to the solutions of its normal equations finally for every t 0 1 we can get its explicit solutions by solving the normal equations the technique proposed in this paper is rather simple to realize and can be used for dealing with actual problems

backorder fuzzy inventory model under function principle in this paper the fuzzy inventory model is discussed especially in the case of permitting backorder under the fuzzy environment of fuzzy demand fuzzy order cost fuzzy inventory cost and fuzzy backorder cost we use the function principle instead of the extension principle to calculate the total fuzzy inventory cost we also apply the median rule to find the optimal economic order quantity eoq and shortage quantity

generalized mhd equations abstract solutions of the d dimensional generalized mhd gmhd equations t u u u p b b u t b u b b u b are studied in this paper we pay special attention to the impact of the parameters and on the regularity of solutions our investigation is divided into three major cases 1 0 and 0 2 0 and 0 and 3 0 and 0 when 0 and 0 the gmhd equations with any 0 and 0 possess a global weak solution corresponding to any l2 initial data furthermore weak solutions associated with 1 2 d 4 and 1 2 d 4 are actually global classical solutions when their initial data are sufficiently smooth as a special consequence smooth solutions of the 3d gmhd equations with 5 4 and 5 4 do not develop finite time singularities the study of the gmhd equations with 0 and 0 is motivated by their potential applications in magnetic reconnection a local existence result of classical solutions and several global regularity conditions are established for this case these conditions are imposed on either the vorticity u or the current density j b but not both and are weaker than some of current existing ones when 0 and 0 the gmhd equations reduce to the ideal mhd equations it is shown here that the ideal mhd equations admit a unique local solution when the prescribed initial data is in a holder space cr with r 1

positive solutions for nonlinear problems involving the one dimensional ϕ laplacian abstract let a b r m l 1 and 0 be a real parameter let l be the differential operator given by l u u r x u where r r is an odd increasing homeomorphism and 0 r l 1 we study the existence of positive solutions for problems of the form l u m x f u in u 0 on where f 0 0 is a continuous function which is roughly speaking sublinear with respect to our approach combines the sub and supersolution method with some estimates on related nonlinear problems we point out that our results are new even in the cases r 0 and or m 0

blowup criterion for viscous baratropic flows with vacuum states we prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth strong solutions for the 3 dimensional 3d barotropic compressible navier stokes equations more precisely if a solution of the 3d barotropic compressible navier stokes equations is initially regular and loses its regularity at some later time then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches our result is the same as ponce s criterion for 3 dimensional incompressible euler equations ponce in commun math phys 98 349 353 1985 in addition initial vacuum states are allowed in our cases

a new proof of the caffarelli kohn nirenberg theorem here we give a self contained new proof of the partial regularity theorems for solutions of incompressible navier stokes equations in three spatial dimensions these results were originally due to scheffer and caffarelli kohn and nirenberg our proof is much more direct and simpler 1998 john wiley sons inc

positive solutions for singular second order neumann boundary value problems via a cone fixed point theorem in this paper we consider the existence of positive solutions for the singular second order neumann boundary value problem x k 2x f t g t x 0

periodic solutions for nonlinear differential equations with maximal monotone terms we examine nonlinear periodic problems for scalar and vector differential equations involving a maximal monotone operator which is not necessarily defined everywhere in the scalar case the nonlinear differential operator depends on both x and x linearly in x while in the vector case the differential operator depends only on x and is a generalization of the p laplacian our approach is based on the theory of operators of monotone type and on the leray schauder principle

multiple nontrivial solutions for nonlinear periodic problems with the p laplacian abstract we consider a nonlinear periodic problem driven by the scalar p laplacian with a nonsmooth potential hemivariational inequality using the degree theory for multivalued perturbations of s operators and the spectrum of a class of weighted eigenvalue problems for the scalar p laplacian we prove the existence of at least three distinct nontrivial solutions two of which have constant sign

bilinear estimates in bmo and the navier stokes equations we prove that the bmo norm of the velocity and the vorticity controls the blow up phenomena of smooth solutions to the navier stokes equations our result is applied to the criterion on uniqueness and regularity of weak solutions in the marginal class

nonlinear boundary value problems for second order differential inclusions abstract in this paper we study a class of nonlinear value boundary problems for second order differential inclusions with nonlinear perturbations which satisfy the generalized hartman condition weaker than that considered in some papers using techniques from multivalued analysis theory of monotone operators and fixed points we prove the existence of solutions in both convex and nonconvex cases our framework can be incorporated with dirichlet neumann and mixed boundary problems

existence of positive and of multiple solutions for nonlinear periodic problems abstract in this paper we consider a scalar periodic problem driven by the ordinary p laplacian differential operator and having a nonsmooth potential using a variational method based on nonsmooth critical point theory first we prove the existence of a strictly positive solution then by strengthening our hypotheses on the nonsmooth potential we prove the existence of a second periodic solution

periodic solutions for second order differential inclusions with the scalar p laplacian we study periodic problems driven by the scalar p laplacian with a multivalued right hand side nonlinearity we prove two existence theorems in the first we assume nonuniform nonresonance conditions between two successive eigenvalues of the negative p laplacian with periodic boundary conditions in the second we employ certain landesman lazer type conditions our approach is based on degree theory

interior regularity criteria for suitable weak solutions of the navier stokes equations we present new interior regularity criteria for suitable weak solutions of the 3 d navier stokes equations a suitable weak solution is regular near an interior point z if either the scaled l p q x t norm of the velocity with 3 p 2 q 2 1 q or the l p q x t norm of the vorticity with 3 p 2 q 3 1 q or the l p q x t norm of the gradient of the vorticity with 3 p 2 q 4 1 q 1 p is sufficiently small near z

extremal solutions for the difference φ laplacian problem with nonlinear functional boundary conditions abstract in this paper we study the existence and approximation of the extremal solutions for the laplacian problem lying between a pair of a lower solution and an upper solution such that we consider general boundary functional conditions that include classical ones as separated or periodic

fuzzy sets and their operations ii among the basic operations which can be performed on fuzzy sets are the operations of union intersection complement algebraic product and algebraic sum in addition to these operations new operations called bounded sum and bounded difference were defined by l a zadeh to investigate the fuzzy reasoning which provides a way of dealing with the reasoning problems which are too complex for precise solution this paper investigates the algebraic properties of fuzzy sets under these nex operations of bounded sum and bounded difference and the properties of fuzzy sets in the case where these new operations are combined with the well known operations of union intersection algebraic product and algebraic sum

remarks on a paper by j t beale t kato and a majda we prove that the maximum norm of the deformation tensor controls the possible breakdown of smooth solutions for the 3 dimensional euler equations more precisely the loss of regularity in a local smooth solution of the euler equations implies the growth without bound of the deformation tensor as the critical time approaches equivalently if the deformation tensor remains bounded the existence of a smooth solution is guaranteed

strongly nonlinear second order differential inclusions with generalized boundary conditions abstract in this paper we study second order differential inclusions in r n with a maximal monotone term and generalized boundary conditions the nonlinear differential operator need not be necessary homogeneous and incorporates as a special case the one dimensional p laplacian the generalized boundary conditions incorporate as special cases well known problems such as the dirichlet picard neumann and periodic problems as application to the proven results we obtain existence theorems for both convex and nonconvex problems when the maximal monotone term a is defined everywhere and when not case of variational inequalities

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

evaluating r d projects as investments by using an overall ranking from four new fuzzy similarity measure based topsis variants research and development r d project ranking as investments is a well known problem that is made difficult by incomplete and imprecise information about future project profitability this paper shows how profitability results of r d project evaluation with the fuzzy pay off method can be ranked with four new variants of fuzzy topsis each using a different fuzzy similarity measure an overall project ranking that incorporates the four new variants rankings with three different ideal solutions totaling 12 subrankings is presented the implementation of the created methods is illustrated with a numerical example

multiple positive solutions to second order neumann boundary value problems in this paper the existence of multiple positive solutions to the second order neumann bvps u mu f t u u 0 u 1 0andu mu f t u u 0 u 1 0are proved by a fixed point theorem in cone due to krasnoselskii

existence and uniqueness results for some nonlinear boundary value problems u a s u b s0 dirichlet 2 u9 a s u9 b s 0 neumann 3 u a s u b and u9 a s u9 b periodic 4 w x here f r a r is an odd increasing homeomorphism k a b a r and w x 2 py2 f a b r a r equation 1 with f s s s s where p 1 and k t s n y 1 rt arises in the study of radial solutions for the p laplacian equation on an annular domain in n dimensions py2 n div u u q f x u u s 0 a x b x g r 5 w x and has been studied extensively see for instance 1 4 6 in this paper we shall establish existence results for 1 with each of the above boundary conditions 2 3 and 4 under various growth conditions on f in particular our results give the existence of radial solutions

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

operations of fuzzy numbers with step form membership function using function principle abstract the function principle was introduced in 1984 by chen to keep the original type of membership function and simplify the arithmetic operations of fuzzy numbers this paper shows how to treat the operations of fuzzy numbers with step form by using function principle

partial regularity of suitable weak solutions to the fractional navier stokes equations in this paper we study the partial regularity of fractional navier stokes equations in mathbb r 3 times 0 infty with 3 4 s 1 we show that the suitable weak solution is regular away from a relatively closed singular set whose 5 4s dimentional hausdorff measure is zero the result is a generalization of the partial regularity for the classical navier stokes system in caffarelli et al commun pure appl math 35 771 831 1982

periodic problems for strongly nonlinear second order differential inclusions in this paper we study periodic problems for second order differential inclusions in rn with a maximal monotone term the nonlinear differential operator is not necessarily homogeneous does not obey any growth condition and incorporates as a special case the one dimensional p laplacian using techniques from multivalued analysis and the theory of operators of monotone type we prove the existence of solutions for both the convex and nonconvex problems when the maximal monotone term a is defined everywhere and when it is not defined everywhere case of variational inequalities

multiplicity theorems for periodic systems with a p laplacian like operator abstract in this paper we study the existence of multiple solutions for nonlinear periodic systems with a p laplacian like operator using an abstract local linking result a two solution theorem is obtained in both resonant and nonresonant cases

a unified proof on the partial regularity for suitable weak solutions of non stationary and stationary navier stokes equations abstract the partial regularity of the suitable weak solutions to the navier stokes equations in r n with n 2 3 4 and the stationary navier stokes equations in r n for n 2 3 4 5 6 are investigated in this paper using some elementary observation of these equations together with de giorgi iteration method we present a unified proof on the results of caffarelli kohn and nirenberg 1 struwe 17 dong and du 5 and dong and strain 7 particularly we obtain the partial regularity of the suitable weak solutions to the 4d non stationary navier stokes equations which improves the previous result of 5 where dong and du studied the partial regularity of smooth solutions of the 4d navier stokes equations at the first blow up time

existence and comparison results for difference φ laplacian boundary value problems with lower and upper solutions in reverse order abstract this paper is devoted to the study of the existence and comparison results for nonlinear difference laplacian problems with mixed dirichlet neumann and periodic boundary value conditions we deduce existence of extremal solutions of periodic and neumann boundary value problems lying between a pair of lower and upper solutions given in reverse order we prove the optimality of some assumptions in