w2 p estimates for fully nonlinear elliptic equations with oblique boundary conditions abstract we study fully nonlinear elliptic equations with oblique boundary conditions we obtain a global w 2 p estimate n 0 p for viscosity solutions of such problems when the boundary of the domain is in c 2 for every 0 1

fuzzy least squares linear regression analysis using shape preserving operations abstract in this paper we introduce a new class of fuzzy linear regression model with fuzzy input fuzzy output data using shape preserving arithmetic operations on l r fuzzy numbers for least squares fitting a mixed nonlinear programming approach is used to derive the satisfying solution this answers one of diamond s questions inform sci 46 1988 141

nonlinear oblique boundary value problems for nonlinear elliptic equations on considere le probleme aux valeurs limites a derivee oblique non lineaire pour des equations uniformement elliptiques quasi lineaires et totalement non lineaires d ordre 2 les operateurs elliptiques satisfont des conditions de structure naturelle on donne des theoremes d existence pour les solutions

uniqueness of the critical point of the solutions to some semilinear elliptic boundary value problems in we consider some two dimensional semilinear elliptic boundary value problems over a bounded convex domain in r2 and show the uniqueness of the critical point of the solutions

possibilistic linear systems and their application to the linear regression model abstract it is the purpose of this paper to illustrate possibilistic linear systems based on possibility measure and to formulate a linear regression analysis by possibilistic linear models linear regression by a possibilistic model is called possibilistic linear regression this is a new interpretation of fuzzy linear regression and also includes a new method by which interval analysis can be done in fuzzy numbers

linear oblique derivative problems for the uniformly elliptic hamilton jacobi bellman equation on demontre la resolubilite et l unicite des problemes aux valeurs limites generaux et de dirichlet

higher dimensional ginzburg landau equations under weak anchoring boundary conditions abstract for n 3 and 0 1 let r n be a bounded simply connected smooth domain and u r n r 2 solve the ginzburg landau equation under the weak anchoring boundary condition u 1 2 1 u 2 u in u u g 0 on where the anchoring strength parameter k for some k 0 and 0 1 and g c 2 s 1 motivated by the connection with the landau de gennes model of nematic liquid crystals under weak anchoring conditions we study the asymptotic behavior of u as goes to zero under the condition that the total modified ginzburg landau energy satisfies f u m log for some m 0

global solutions of shock reflection by large angle wedges for potential flow when a plane shock hits a wedge head on it experiences a reflectiondiffraction process and then a self similar reflected shock moves outward as the original shock moves forward in time experimental computational and asymptotic analysis has shown that various patterns of shock reflection may occur including regular and mach reflection however most of the fundamental issues for shock reflection have not been understood including the global structure stability and transition of the different patterns of shock reflection therefore it is essential to establish the global existence and structural stability of solutions of shock reflection in order to understand fully the phenomena of shock reflection on the other hand there has been no rigorous mathematical result on the global existence and structural stability of shock reflection including the case of potential flow which is widely used in aerodynamics such problems involve several challenging difficulties in the analysis of nonlinear partial differential equations such as mixed equations of elliptic hyperbolic type free boundary problems and corner singularity where an elliptic degenerate curve meets a free boundary in this paper we develop a rigorous mathematical approach to overcome these difficulties i nvolved and establish a global theory of existence and stability for shock reflection by large angle wedges for potential flow the techniques and ideas developed here will be useful for other nonlinear problems involving similar difficulties

fuzzy linear regression and its applications to forecasting in uncertain environment abstract linear regression has been used for many years in developing mathematical models for application in marketing management and sales forecasting in this paper two different sales forecasting techniques are discussed the first technique involves non fuzzy abstract methods of linear regression and econometrics a study of the international market sales of cameras done in 1968 by john scott armstrong utilized these non fuzzy forecasting techniques the second sales forecasting technique uses fuzzy linear regression introduced by h tanaka s uejima and k asai in 1980 in this paper a study of the computer and peripheral equipment sales in the united states is discussed using fuzzy linear regression moreover fuzzy linear regression is applied to forecasting in an uncertain environment finally some possible improvements and suggestions for further study are mentioned

existence and uniqueness analysis of a detached shock problem for the potential flow abstract we study a problem for two dimensional steady potential and isentropic euler equations in a bounded domain where an artificial detached shock interacts with a wedge using the stream function we obtain a free boundary problem for the subsonic state and the detached artificial shock curve and we prove that such configuration admits a unique solution in certain weighted holder spaces the proof is based on various holder and schauder estimates for second order elliptic equations and fixed point theorems moreover we pose an energy principle and remark that the physical attached shock is the minimizer of the energy functional

asymptotics of solutions of a quasilinear system involving curl this paper concerns the asymptotic behavior of the solutions of a singularly perturbed quasilinear system involving a small parameter and a quadratic form gm curl h mcurl h curl h this system arises in the mathematical theory of nucleation of instability of the meissner states of anisotropic superconductors and the location of the maximum points of the quadratic form suggests the location where instability begins to nucleate the existence and regularity of the solutions of this system for fixed have been established by pan a quasilinear system involving the operator curl calculus var partial differ equ 36 317 2009 in this paper we find an optimal bound of the boundary data for the solvability for all small and find the asymptotic behavior of the solutions as goes to zero in particular it is proved that the maximum points of the quadratic form approach a point on the domain boundary where the tangential component of the boundary datum is the maximal in the special case where

oblique boundary value problems for augmented hessian equations ii abstract in this paper we continue our investigations into the global theory of oblique boundary value problems for augmented hessian equations we construct a global barrier function in terms of an admissible function in a uniform way when the matrix function in the augmented hessian is only assumed regular this enables us to derive global second derivative estimates in terms of boundary estimates which are then obtained by strengthening the concavity or monotonicity conditions in our previous work on the strictly regular case finally we give some applications to existence theorems which embrace standard hessian equations as special cases

pointwise estimates for oblique derivative problems in nonsmooth domains abstract there is a long history of studying boundary value problems for elliptic and parabolic differential equations when the equation is posed in a domain with sufficiently smooth boundary in this paper we prove some pointwise estimates and regularity results for solutions when a directional derivative is prescribed on the boundary which satisfies an interior cone condition we consider very weak hypotheses on the data of the problem in particular we consider an optimal relation between the interior cone and the direction of the prescribed directional derivative and we assume very little smoothness of the coefficients in the equation and the boundary condition

existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross sections we establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross sections including a slowly varying de laval nozzle the transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance uniform subsonic downstream flow at the exit at infinity and the slip boundary condition on the nozzle boundary our results indicate that if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow there exists a solution that consists of a c1 subsonic flow in the unbounded downstream region converging to a uniform velocity state at infinity and a c1 multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow and the shock is orthogonal to the nozzle boundary at every point of their intersection in order to construct such a transonic flow we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase in which the equation is elliptic and the free boundary is a transonic shock the free boundary conditions are determined by the rankine hugoniot conditions along the shock we further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain we also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

on existence of solutions for a class of fully nonlinear noncoercive problems 0 arises in the three dimensional water wave theory see m shinbrot lo and also in the engineering problem of hydraulic fracturing of oil wells see j r canon and g h meyer 2 7 mathematically the model problem 1 is of interest since it represents one of the simplest noncoercive elliptic problems i e the lopatinski shapiro condition fails see 4 for which there is no general theory the field of fully nonlinear elliptic equations has recently attracted a great deal of attention see e g a recent paper of g m lieberman and n s trudinger 6 and the references therein to other work of the same authors as well as that of l evans n krylov p l lions and others it appears that the case of second order boundary operators is not well studied particularly for noncoercive problems we present an existence result for l which extends the one in 3 where we had considered the equation

local c 0 α estimates for viscosity solutions of neumann type boundary value problems abstract in this article we prove the local c 0 regularity and provide c 0 estimates for viscosity solutions of fully nonlinear possibly degenerate elliptic equations associated to linear or nonlinear neumann type boundary conditions the interest of these results comes from the fact that they are indeed regularity results and not only a priori estimates from the generality of the equations and boundary conditions we are able to handle and the possible degeneracy of the equations we are able to take into account in the case of linear boundary conditions

two dimensional nonlinear boundary value problems for elliptic equations on considere la regularite limite des solutions du probleme aux valeurs limites non lineaire f x u du d 2 u 0 dans g x u du 0 sur pour des domaines a 2 dimensions f est uniformement elliptique et g depend de du on demontre des estimations de continuite pour des derivees premieres et secondes de u sous des hypotheses faibles pour la regularite de f g et

the nonlinear oblique derivative problem for quasilinear elliptic equations on considere des problemes aux valeurs limites pour une equation elliptique quasilineaire d ordre 2 qu 0 dans ou est un domaine borne de r n n 2 et q est donne sur c 2 par qu x a ij x u x du x d ij u x a x u x du x

the neumann problem of special lagrangian equations with supercritical phase abstract in this paper we establish the global c 2 estimates of the neumann problem of special lagrangian equations with supercritical phase and the existence theorem by the method of continuity

on the second boundary value problem for lagrangian mean curvature flow abstract we consider a fully nonlinear parabolic equation with nonlinear neumann type boundary condition and show the long time existence and convergence of the flow finally we apply this study to the boundary value problem for minimal lagrangian graphs

the uniqueness of transonic shocks in supersonic flow past a 2 d wedge abstract we have proved the uniqueness of transonic shocks in steady supersonic flows past a slightly perturbed two dimensional infinite wedge under appropriate conditions on the downstream subsonic flows we formulate it to a mathematical problem of the uniqueness of solutions of nonlinear partial differential equations of hyperbolic elliptic mixed type with a free boundary by working on several elliptic equations of physical quantities separately we obtain a priori estimates of them and then prove the uniqueness without assumptions on high regularity moreover uniform estimates on the ellipticity and the positive lower bound of the speed are achieved under a geometrical condition on the wedge the mathematical ideas and techniques developed here will also be useful for other related problems involving similar analytical difficulties

a mathematical programming approach to fuzzy linear regression analysis most of previous studies on fuzzy regression analysis have a common characteristic of increasing spreads for the estimated fuzzy responses as the independent variable increases its magnitude which is not suitable for general cases in this paper fuzzy linear regression models with fuzzy crisp output fuzzy crisp input are considered and an estimated method along with a mathematical programming based approach is proposed the advantages of the proposed approach are simplicity in programming and computation and minimum difference of total spread between observed and estimated values

transonic shock in a nozzle i 2d case in this paper we establish the existence and uniqueness of a transonic shock for the steady flow through a general two dimensional nozzle with variable sections the flow is governed by the inviscid potential equation and is supersonic upstream has no flow boundary conditions on the nozzle walls and an appropriate boundary condition at the exit of the exhaust section the transonic shock is a free boundary dividing two regions of c 1 1 0 flow in the nozzle the potential equation is hyperbolic upstream where the flow is supersonic and elliptic in the downstream subsonic region in particular our results show that there exists a solution to the corresponding free boundary problem such that the equation is always subsonic in the downstream region of the nozzle when the pressure in the exit of the exhaustion section is appropriately larger than that in the entry this problem is motivated by the conjecture of courant and friedrichs on the transonic phenomena in a nozzle 10 furthermore the stability of the transonic shock is also proven when the upstream supersonic flow is a small steady perturbation for the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation the main ingredients of our analysis are a generalized hodograph transformation and multiplier methods for elliptic equation with mixed boundary conditions and comer singularities

free boundary and mixed boundary value problems for quasilinear elliptic equations tangential oblique derivative and degenerate dirichlet boundary problems abstract we present holder estimates and holder gradient estimates for a class of free boundary problems with tangential oblique derivative boundary conditions provided the oblique vector does not vanish at any point on the boundary we also establish the existence result for a general class of quasilinear degenerate problems of this type including nonlinear wave systems and the unsteady transonic small disturbance equation

a proof of existence of perturbed steady transonic shocks via a free boundary problem we prove the existence of a solution of a free boundary problem for the transonic small disturbance equation the free boundary is the position of a transonic shock dividing two regions of smooth flow assuming inviscid irrotational flow as modeled by the transonic small disturbance equation the equation is hyperbolic upstream where the flow is supersonic and elliptic in the downstream subsonic region to study the stability of a uniform planar transonic shock we consider perturbation by a steady c1 upstream disturbance if the upstream disturbance is small in a c1 sense then there is a steady solution in which the downstream flow and the transonic shock are holder continuous perturbations of the uniform configuration this result provides a new use of inviscid perturbation techniques to demonstrate in two dimensions the stability of transonic shock waves of the type that appear for example over the wing of an airplane along an airfoil or as bow shocks in a flow with a supersonic free stream velocity 2000 john wiley sons inc

the conormal derivative problem for elliptic equations of variational type on considere des solutions du probleme qu 0 dans nu 0 sur ou est un domaine borne dans r n et q et n sont definis par qu x div a x u x du x b x u x du x x nu x a x u x du x x x x

regularity for fully nonlinear elliptic equations with oblique boundary conditions in this paper we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions in particular we derive the pointwise c c 1 and c 2 regularity as byproducts we also prove the a b p maximum principle harnack inequality uniqueness and solvability of the equations

on special points on load displacement paths in the prebuckling domain of thin shells points on load displacement paths of thin shells subjected to proportional loading at which the second and or the third derivative of the displacement components with respect to the load parameter vanishes are termed special points such points represent global characteristics of the state of deformation of the shell in the sense that for the respective values of the load parameter the mentioned rate s of all displacement components at all points of the shell must vanish it will be shown that special points on load displacement paths correspond to special points of one order lower on the det kt diagram where det kt is the determinant of the tangent stiffness matrix within the framework of the finite element method and is a dimensionless load parameter points of inflection on load displacement diagrams for example correspond to extreme values on the det kt diagram the main reason for the occupation with special points on load displacement paths is that points of inflection and flat points on these paths correspond to special points on eigenvalue curves in the context of accompanying linear stability analyses of geometrically non linear prebuckling analyses of thin shells by the finite element method investigated in a companion paper

the viscosity method for the homogenization of soft inclusions in this paper we consider periodic soft inclusions te with periodicity e where the solution ue satisfies semi linear elliptic equations of non divergence in omega epsilon omega setminus overline t epsilon with neumann data on partial t mathfrak a the difficulty lies in the non divergence structure of the operator where the standard energy method which is based on the divergence theorem cannot be applied the main object is to develop a viscosity method to find the homogenized equation satisfied by the limit of ue referred to as u as e approaches to zero we introduce the concept of a compatibility condition between the equation and the neumann condition on the boundary for the existence of uniformly bounded periodic first correctors the concept of a second corrector is then developed to show that the limit u is the viscosity solution of a homogenized equation

fuzzy seasonality forecasting abstract in this paper a fuzzy forecasting technique for seasonality in the time series data is presented using the following procedure first with the fuzzy regression analysis the fuzzy trend of a time series is analyzed then the fuzzy seasonality is defined by realizing the membership grades of the seasons to the fuzzy regression model both making fuzzy forecast and crisp forecast are investigated seasonal fuzziness and trends are analyzed the method is applied to the sales forecasting problem of a food distribution company

possibilistic linear regression analysis for fuzzy data abstract fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined recently it has become important to deal with fuzzy data in connection with expert knowledge three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data since our formulations can be reduced to linear programming problems the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters this approach can be regarded as a fuzzy interval analysis in a fuzzy environment

gradient estimates for semi linear elliptic equations with prescribed contact angle problem abstract in this paper we find a new auxiliary function and use the maximum principle to give a new proof for the gradient of a solution for semi linear elliptic equations with capillarity type problem

multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type we are concerned with the existence and stability of multidimensional transonic shocks for the euler equations for steady potential compressible fluids the euler equations consisting of the conservation law of mass and the bernoulli law for the velocity can be written as the following second order nonlinear equation of mixed elliptic hyperbolic type for the velocity potential r r 1 1 div d d 0 where the density function q is

multiobjective fuzzy linear regression analysis for fuzzy input output data abstract fuzzy linear regression models where both input data and output data are fuzzy numbers are introduced by using three indices for equalities between fuzzy numbers by considering the conflict between the fuzzy threshold for the three indices and the fuzziness of the fuzzy linear regression model three types of multiobjective programming problems for obtaining fuzzy linear regression models are formulated corresponding to the three indices then a linear programming based interactive decision making method to derive the satisficing solution of the decision maker for the formulated multiobjective programming problems is developed a numerical example demonstrates the appropriateness and efficiency of the proposed method

linear second order elliptic equations with venttsel boundary conditions we prove the existence of solutions of quasilinear second order elliptic equations with quasilinear venttsel boundary conditions in both classical and weak sense under natural structure conditions

solvability of quasilinear elliptic equations with nonlinear boundary conditions ii abstract it is shown that solvability of the second order quasilinear elliptic equation qu 0 in with first order nonlinear boundary condition nu 0 on can be inferred from appropriate estimates on solutions of the problem qu in nu 0 on as varies over a suitable function class this result improves previous work of the author where estimates were required on solutions of qu in nu on as varies over some function space the value of this improvement is demonstrated by some examples

steady transonic shocks and free boundary problems in infinite cylinders for the euler equations we establish the existence and stability of multidimensional transonic shocks hyperbolic elliptic shocks for the euler equations for steady compressible potential fluids in infinite cylinders the euler equations consisting of the conservation law of mass and the bernoulli law for velocity can be written as a second order nonlinear equation of mixed elliptic hyperbolic type for the velocity potential the transonic shock problem in an infinite cylinder can be formulated into the following free boundary problem the free boundary is the location of the multidimensional transonic shock which divides two regions of c1 flow in the infinite cylinder and the equation is hyperbolic in the upstream region where the c1 perturbed flow is supersonic we develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem in unbounded domains our results indicate that there exists a solution of the free boundary problem such that the equation is always elliptic in the unbounded downstream region the uniform velocity state at infinity in the downstream direction is uniquely determined by the given hyperbolic phase and the free boundary is c1 provided that the hyperbolic phase is close in c1 to a uniform flow we further prove that if the steady perturbation of the hyperbolic phase is c2 the free boundary is c2 and stable under the steady perturbation 2003 wiley periodicals inc

local estimates for subsolutions and supersolutions of oblique derivative problems for general second order elliptic equations we consider solutions and subsolutions and supersolutions of the boundary value problem au x u du diju u x u du 0 in 2 s x diu y x u g x on3fi for a lipschitz domain s a positive definite matrix valued function u j and a vector field s which points uniformly into q without making any continuity assumptions on the known functions we prove harnack and holder estimates for u near 3i2 in addition we bound the l norm of u near 3i2 in terms of an appropriate lp norm and the known functions our approach is based on that for the corresponding interior estimates of trudinger this paper is concerned with analogs for solutions of oblique boundary value problems of the results in 10 our results will extend previous work of lieberman and trudinger 5 and of nadirashvili 9 specifically we consider second order differential operators q of the form

the neumann problem for hessian equations in this paper we prove the existence of a classical solution to a neumann boundary value problem for hessian equations in uniformly convex domain the method depends upon the establishment of a priori derivative estimates up to second order so we give an affirmative answer to a conjecture of n trudinger in 1987

insight of a fuzzy regression model fuzzy regression a nonparametric method can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise and variables are interacting in an uncertain qualitative and fuzzy way thus it may have considerably practical applications in many management and engineering problems but there is still lack of proper interpretation about fuzzy regression in this paper we provide an insight into regression intervals so that regression interval analysis data type analysis and variable selections can be analytically performed numerical examples are provided for illustration

evaluation of fuzzy linear regression models by comparing membership functions fuzzy linear regression models can provide an estimated fuzzy number that has a fuzzy membership function if a point that has the highest membership value from the estimated fuzzy number is not within the support of the observed fuzzy membership function a decision maker can have high risk from the estimate in this study a modification of fuzzy linear regression analysis based on a criterion of minimizing the difference of the fuzzy membership values between the observed and estimated fuzzy numbers is proposed two numerical examples are used to evaluate the fuzzy regression models

three dimensional steady subsonic euler flows in bounded nozzles abstract the existence and uniqueness of three dimensional steady subsonic euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit if in addition the normal component of the voriticity and the variation of bernoulli s function at the entrance are both zero then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number as the magnitude of the normal component of the momentum approaches the critical number the associated flows converge to a subsonic sonic flow furthermore when the normal component of vorticity and the variation of bernoulli function are both small the existence and uniqueness of subsonic euler flows with non zero vorticity are established the proof of these results is based on a new formulation for the euler system a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions detailed study for a linear div curl system and delicate estimate for the transport equations

fuzzy linear regression analysis for fuzzy input output data using shape preserving operations abstract in this paper we have presented a new method to evaluate fuzzy linear regression models based on tanaka s approach where both input data and output data are fuzzy numbers using t w based fuzzy arithmetic operations this method simplifies the computation of fuzzy arithmetic operations general linear program is applied to derive the solutions we also prove scale independent property of our models and discuss the effects of outliers

gradient bounds for solutions of nonuniformly elliptic oblique derivative problems introduction in the theory of quasilinear elliptic equations there are three archetypical forms which seem to embody the various possible behaviors of solutions laplace s equation or more generally a uniformly elliptic equation the minimal surface equation and a sort of false minimal surface equation sii diudiu d u 0 for each of these equations the behavior of solutions to the dirichlet problem is wellunderstood see for example 3 5 10 11 additionally uniformly elliptic conormal problems were studied in 5 chapter lo and minimal surface type conormal problems xvere studied in l 13 61 the class of equations considered in 6 was much broader than those in l 131 but did not include the false minimal surface equation finally uniformly elliptic oblique derivative problems were studied in 7 91 while minimal surface type oblique derivative problems are the subject of 4 here we examine the oblique derivative problem on a smooth domain q c 2

a fuzzy approach for multiresponse optimization an off line quality engineering problem abstract multiresponse optimization techniques are used to identify settings of process parameters that make the product s performance close to target values in the presence of multiple quality characteristics in this study a fuzzy multiresponse optimization procedure is proposed to search an appropriate combination of process parameter settings based on multiple quality characteristics or responses fuzzy regression models are first used to model the relations between process parameters and responses the possibility distributions of the prediction responses are then obtained the problem is reduced to a multiobjective optimization problem with fuzzy objectives a strategy of optimizing the most possible response values and minimizing the deviations from the most possible values is proposed we consider not only the most possible value but also the imprecision of the prediction responses through a die casting example we show how to use our approach to reach an appropriate machine setting which simultaneously optimize both casting quality and die life

global regularity of solutions of nonlinear second order elliptic and parabolic differential equations on considere des solutions du probleme de dirichlet pour une equation elliptique totalement non lineaire dans un domaine borne lisse et du probleme parabolique analogue

on bounding properties of eigenvalues from linear initial fe stability analyses of thin elastic shells with respect to stability limits from geometrically non linear prebuckling analyses there is consensus in the literature that the eigenvalues of smallest absolute value from linear initial stability analyses of thin elastic shells by the finite element method fem do not posses bounding properties with respect to corresponding stability limites from geometrically non linear stability analyses a linear initial stability analysis by the fem representes the first step of an accompanying linear stability analysis by this method in this paper two modes of such stability analyses of thin elastic shells will be presented it will be proved that for mode 1 in contrast to mode 2 bounding properties of eigenvalues of smallest absolute value with respect to corresponding stability limits from geometrically non linear stability analyses in fact do exist moreover bounding properties of such eigenvalues from mode 1 relative to corresponding eigenvalues from mode 2 will be shown to exist the existence of these properties is important from the standpoint of engineering practice

properties of certain fuzzy linear regression methods abstract fuzzy linear regression was originally introduced by tanaka uejima and asai ieee trans systems man cybern 12 1982 903 907 in subsequent years several different approaches to fuzzy linear regression have been proposed the purpose of this paper is to review and examine some of these formulations to discuss their strengths and weaknesses relative to each other and to suggest possible improvements in addition we compare and contrast these methods to the method of ordinary least squares regression

a global subsonic solution to an interacting transonic shock for the self similar nonlinear wave equation abstract we present the existence of the subsonic solution to a two dimensional riemann problem governed by a self similar nonlinear wave equation where the boundary of the subsonic region consists of a transonic shock and the sonic circle thus the governing equation becomes a free boundary problem on the transonic shock and degenerates on the sonic circle by utilizing the barrier methods and iterative methods we show the well posedness of the transonic shock in the entire subsonic region and thus establish the global solution this result does not rely on any smallness of riemann data

on the second boundary value problem for monge ampere type equations and geometric optics in this paper we prove the existence of classical solutions to second boundary value problems for generated prescribed jacobian equations as recently developed by the second author thereby obtaining extensions of classical solvability of optimal transportation problems to problems arising in near field geometric optics our results depend in particular on a priori second derivative estimates recently established by the authors under weak co dimension one convexity hypotheses on the associated matrix functions with respect to the gradient variables a3w we also avoid domain deformations by using the convexity theory of generating functions to construct unique initial solutions for our homotopy family thereby enabling application of the degree theory for nonlinear oblique boundary value problems

weingarten hypersurfaces with prescribed gradient image we prove the existence of globally smooth convex solutions u of a class of curvature equations subject to the boundary condition du omega omega where omega and omega are smooth uniformly convex domains in mathbb r n the results generalize some of our previous work on the two dimensional case and on hessian equations in all dimensions

on optimal regularity of free boundary problems and a conjecture of de giorgi we present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free boundary as an application we give a full positive answer to a conjecture of de giorgi on the analyticity of local minimizers of the mumford shah functional 2004 wiley periodicals inc

exact steady periodic water waves with vorticity we consider the classical water wave problem described by the euler equations with a free surface under the influence of gravity over a flat bottom we construct two dimensional inviscid periodic traveling waves with vorticity they are symmetric waves whose profiles are monotone between each crest and trough we use bifurcation and degree theory to construct a global connected set of such solutions c 2004 wiley periodicals inc

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

regularity of solutions of nonlinear elliptic boundary value problems on utilise des estimations de type schauder pour ameliorer la regularite supposee des solutions de problemes aux limites non lineaires elliptiques

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

a fuzzy seasonal arima model for forecasting this paper proposes a fuzzy seasonal arima fsarima forecasting model which combines the advantages of the seasonal time series arima sarima model and the fuzzy regression model it is used to forecast two seasonal time series data of the total production value of the taiwan machinery industry and the soft drink time series the intention of this paper is to provide business which are affected by diversified management with a new method to conduct short term forecasting this model includes both interval models with interval parameters and the possible distribution of future value based on the results of practical application it can be shown that this model makes good forecasts and is realistic furthermore this model makes it possible for decision makers to forecast the best and worst estimates based on fewer observations than the sarima model

periodic traveling gravity water waves with discontinuous vorticity we use elliptic theory to prove the existence of steady two dimensional periodic waterwaves of large amplitude in a flowwith an arbitrary bounded but discontinuous vorticity this is achieved by developing a local and global bifurcation construction of weak solutions of the elliptic partial differential equations that are relevant to this hydrodynamical context

the neumann problem for equations of monge ampere type we prove the existence of a classical solution to a neumann type problem for nonlinear elliptic equations of monge ampere type the methods depend upon the establishment of a priori derivative estimates up to order two and yield a sharp result for the equation of prescribed gauss curvature we also present applications to asymptotic problems which approach the non unique case and maximum principles for linear equations of aleksandrov bakelman type

gradient estimates for singular fully nonlinear elliptic equations abstract we study a class of singular fully nonlinear elliptic equations under suitable natural conditions with the model equation being u b d u d u c d u 2 f for lipschitz functions b 0 c and f where d denotes distance to the boundary of the domain and is a suitable extension of the interior unit normal we show that such equations have a unique globally c 1 solution without any a priori prescription of boundary data