some properties of convolution operators in the class pα β abstract making use of several families of convolution operators we introduce and study a certain general class p 0 u we also investigate the relationships between the class p and the hardy space h of bounded analytic functions in u finally we consider some interesting applications of the results presented here to a class of generalized hypergeometric functions

some properties of α convex and α quasiconvex functions with respect to n symmetric points the main object of the present paper is to investigate convex and quasiconvex functions with respect to n symmetric points some interesting properties such as inclusion relationships integral representations convolution conditions are obtained

eigencurves for two parameter sturm liouville equations this paper concerns two parameter sturm liouville problems of the form p x y q x y lambda r x mu y quad a leqslant x leqslant b with self adjoint boundary conditions at a and b the set of lambda mu in bf r 2 for which there exists a nontrivial y satisfying the differential equation and the boundary conditions turns out to be a countable union of graphs of analytic functions our focus is on these graphs which are termed eigencurves in the literature although eigencurves have been used in a variety of ways for about a century they seem comparatively underdeveloped in their own right our plan is to give motivation for the topic elementary properties of eigencurves illustrations on a simple example first studied by richardson in 1918 and since then by several authors and some natural questions which may whet the reader s appetite some of these questions lead to new types of inverse sturm liouville problems

a certain one parameter additive family of operators defined on analytic functions abstract y komatu proved several interesting results for a certain one parameter additive family of operators defined on analytic functions regular in the unit disk and presented two conjectures for univalent functions in the unit disk it is the purpose of this paper to prove a number of results relevant to komatu s conjectures for certain classes of univalent functions with negative coefficients in the unit disk

left definite sturm liouville problems abstract left definite regular self adjoint sturm liouville problems with either separated or coupled boundary conditions are studied we give an elementary proof of the existence of eigenvalues for these problems for any fixed equation we establish a sequence of inequalities among the eigenvalues for different boundary conditions and estimate the range of each eigenvalue as a function on the space of boundary conditions some of our results here yield an algorithm for numerically computing the eigenvalues of a left definite problem with an arbitrary coupled boundary condition our inequalities imply that the well known asymptotic formula for the eigenvalues in the separated case also holds in the coupled case moreover we study the continuous and differentiable dependence of the eigenvalues of the general left definite problem on all the parameters in its differential equation and boundary condition

the intersection of the spectra of two sturm liouville equations this paper studies the intersection of the spectra for two sturm liouville equations with general separated bcs and real coupled bcs under certain conditions we proved that a two dimensioned vectorial slps with separated bcs only has finitely many double eigenvalues and obtain a bound m q depending on q x and its eigenvalues which are larger than m q are all simple finally with the help of the obtained results we conclude that the number of the same eigenvalue is finite for two one dimensioned slps with general separated bcs or real coupled bcs

some functional inequalities and inclusion relationships associated with certain families of integral operators by making use of certain familiar integral operators the authors introduce and investigate several new subclasses of starlike convex close to convex and quasi convex functions among other results presented here the authors establish a number of inclusion relationships associated with some of these integral operators some of the results established in this paper would provide extensions of those given in earlier works

asymptotics of eigencurves for second order ordinary differential equations i abstract the regular two parameter sturm liouville equation py qy f r y is studied for l1 coefficients with p r 0 for each fixed number n of internal zeros of the eigenfunctions y n is analytic in necessary and sufficient conditions which are in fact independent of n are given for lim n gl to exist as or asymptotic expansions for n are derived in cases of existence and non existence of lim n

energy decay rate of wave equations with indefinite damping abstract we consider the one dimensional wave equation with an indefinite sign damping and a zero order potential term using a shooting method we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of coefficients in addition if the damping coefficient is more positive than negative we prove that the energy of system decays uniformly exponentially to zero this sharp result generalizes a previous work of freitas and zuazua 1996

a class of rough multiple objective programming and its application to solid transportation problem this paper establishes a rough multiple objective programming model for a solid transportation problem furthermore a general model for rough multiple objective programming problem is presented properties of the feasible and efficient solutions of rough multiple objective programming problems are investigated in addition compromise solutions are obtained by using the interactive fuzzy satisfying method to solve the rough multiple objective solid transportation problem the rough simulation based genetic algorithm is proposed in which the rough simulation is embedded into the genetic algorithm finally an application of the solid transportation problem at xiluodu hydropower station is provided as an illustration

some inclusion relationships and integral preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators the object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions by making use of these novel integral operators we introduce and investigate several new subclasses of starlike convex close to convex and quasi convex meromorphic functions in particular we establish some inclusion relationships associated with the aforementioned integral operators several interesting integral preserving properties are also considered

stability analysis of the zero solution for two class evolution equations abstract by constructing some suitable lyapunov type functionals and applying the theory of the definite quadratic form we obtain the stability of the zero solution of two classes of evolution equations with delays including reaction diffusion equations and damped wave equations our criteria depend on the derivatives of delays consequently when the delays are constants these criteria are independent of the magnitudes of the delays so the delays are harmless for the stability of the zero solution

the hardy space of analytic functions associated with certain one parameter families of integral operators abstract recently h m srivastava and s owa j math anal appl 118 1986 80 87 proved a number of results relevant to komatu s conjectures cf y komatu bull fac sci engrg chuo univ ser i math 22 1979 1 22 for a certain one parameter additive family of operators defined on analytic functions regular in the open unit disk the object of the present paper is to investigate several one parameter families of integral operators and to prove certain inclusion theorems involving the hardy space h p of analytic functions and the class of functions whose derivative has a positive real part an application involving a generalized hypergeometric function is also considered

nonlinear multiparameter eigenvalue problems linearised and nonlinearised solutions abstract the paper focuses on a nonlinear multiparameter eigenvalue problem called p this problem involves n spectral parameters and also depends on n 2 numerical parameters where n 2 is an integer if these numerical parameters vanish p degenerates into n linear one parameter eigenvalue problems called p i 0 i 1 n in connection with p one can consider another n nonlinear one parameter eigenvalue problems called p i the problems p i have eigenvalues with as well as without linear counterparts the paper suggests to consider p i as nonunperturbed instead of p i 0 using properties of eigenvalues of p i one manages to prove existence of eigentuples of p among the eigentuples found in this way there are eigetuples with as well as without linear counterparts results of the paper are found with a nonclassical approach applications of the found results to nonlinear optics are shown

root vectors for geometrically simple two parameter eigenvalues a class of multiparameter eigenvalue problems involving generally non self adjoint and unbounded operators is studied bases for lower order root subspaces at geometrically simple eigenvalues of fredholm type of arbitrary finite index are computed in terms of the underlying multiparameter system

multiparameter definiteness conditions a previous attempt to systematize various conditions from multiparameter spectral theory is extended to weaker forms of definiteness the latter not only occur in the established literature but are also under active investigation at present several algebraic and geometrical formulations exist and questions concerning their equivalence are approached in a unified fashion where possible

oscillation theory for indefinite sturm liouville problems with eigenparameter dependent boundary conditions in previous papers we have studied oscillation properties of sturm liouville problems py qy ry with dependent boundary conditions under various definiteness conditions here we present a new unified approach which also covers cases previously untreated e g of semidefinite weight and also the fully indefinite problem

rough multiple objective programming abstract in this paper we focused on characterizing and solving the multiple objective programming problems which have some imprecision of a vague nature in their formulation the rough set theory is only used in modeling the vague data in such problems and our contribution in data mining process is confined only in the post processing stage these new problems are called rough multiple objective programming rmop problems and classified into three classes according to the place of the roughness in the problem also new concepts and theorems are introduced on the lines of their crisp counterparts e g rough complete solution rough efficient set rough weak efficient set rough pareto front weighted sum problem etc to avoid the prolongation of this paper only the 1st class where the decision set is a rough set and all the objectives are crisp functions is investigated and discussed in details furthermore a flowchart for solving the 1st class rmop problems is presented

classification of eigentuples for uniformly elliptic multiparameter problems abstract let tm vmn be self adjoint operators in hilbert spaces hm the t3 having compact resolvents and lower bounds m 0 and the vmn satisfying uniform ellipticity 1 m n k when m 0 for each m these conditions are called uniform left definiteness and guarantee that all eigenvalues for the simultaneous equations wm xm 0 xm 0 wm tm n 1k nvmn belong to r k and are semi simple in an appropriate sense when some m 0 these conclusions may fail and we use an embedding technique to discuss for example algebraic multiplicities of eigenvalues transitions between real and non real eigenvalues and bounds for the numbers of eigenvalues of various types

characterizing solutions of rough programming problems abstract in this paper we define a new kind of mathematical programming problems this kind in which the decision set is a rough set is called a rough programming problem a rough optimal solution and a rough saddle point will be characterized some illustrative examples are presented

stability results for the wave equation with indefinite damping abstract the one dimensional wave equation with damping of indefinite sign in a bounded interval with dirichlet boundary conditions is considered it is proved that solutions decay uniformly exponentially to zero provided the damping potential is in thebv class has positive average is small enough and satisfies a finite number of further constraints guaranteeing that the derivative of the real part of the eigenvalues is negative when the damping vanishes this sharp result completes a previous one by the first author showing that an indefinite sign damping always produces unstable solutions if it is large enough and it answers by the afirmative to a conjecture concerning small damping terms the method of proof relies on the developments by s cox and the second author on the high frequency asymptotic expansion of the spectrum for damped wave equations and on the characterization of the decay rate in terms of the spectral abscissa

on certain subclasses of close to convex and quasi convex functions with respect to k symmetric points abstract in the present paper the authors introduce two new subclasses s s k of close to convex functions and c s k of quasi convex functions the integral representations for functions belonging to these classes are provided the convolution conditions growth theorems distortion theorems and covering theorems for these classes are also provided the results obtained generalize some known results and some other new results are obtained

two bayesian approaches to rough sets abstract bayesian inference and probabilistic rough sets prss provide two methods for data analysis both of them use probabilities to express uncertainties and knowledge in data and to make inference about data many proposals have been made to combine bayesian inference and rough sets the main objective of this paper is to present a unified framework that enables us a to review and classify bayesian approaches to rough sets b to give proper perspectives of existing studies and c to examine basic ingredients and fundamental issues of bayesian approaches to rough sets by reviewing existing studies we identify two classes of bayesian approaches to prssand three fundamental issues one class is interpreted as bayesian classification rough sets which is built from decision theoretic rough set dtrs models proposed by yao wong and lingras the other class is interpreted as bayesian confirmation rough sets which is built from parameterized rough set models proposed by greco matarazzo and slowinski although the two classes share many similarities in terms of making use of bayes theorem and a pair of thresholds to produce three regions their semantic interpretations and hence intended applications are different the three fundamental issues are the computation and interpretation of thresholds the estimation of required conditional probabilities and the application of derived three regions dtrs models provide an interpretation and a method for computing a pair of thresholds according to bayesian decision theory naive bayesian rough set models give a practical technique for estimating probability based on bayes theorem and inference finally a theory of three way decisions offers a tool for building ternary classifiers the main contribution of the paper lies in weaving together existing results into a coherent study of bayesian approaches to rough sets rather than introducing new specific results

hill s equation with a large potential we obtain asymptotic expansions for large values of the parameter lambda of the stability boundaries the stability band widths the floquet multipliers and the solutions of hill s equation left frac d 2 dx 2 lambda 2 q x t right u eu the potential q x is assumed to be periodic and to have a unique global minimum within each period at which q 0 the results for the stability band widths show that they decay exponentially with lambda as lambda increases these results generalize those for symmetric potentials due to harrell and that for the mathieu equation due to meixner and schafke

exponential decay of energy of evolution equations with locally distributed damping consider an evolution equation with energy dissipation frac partial partial t y x t ay x t by x t on a bounded x domain omega where by signifies a dissipative perturbation to an otherwise energy conserving system this dissipation may be due to medium impurities viscous effects or artificially imposed dampers and stabilizers it is distributed over only part of the domain omega the question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined because of the locally distributed nature of energy dissipation the problem lacks coercivity and is not directly solvable by energy identities thus to get conditions sufficient for uniform exponential decay a different approach needs to be taken provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorbon the separated eigenmodes or clustered eigenmodes ofa the main theorems are general enough to treat the wave and bea

asymptotic expansion of the variational eigencurve for two parameter simple pendulum type equations abstract we consider the nonlinear two parameter simple pendulum type equation u t u p sin u t u t 0 t i t t u t 0 where p 1 is a constant and 0 are parameters for a given 0 there exists a solution triple u r 2 c 2 i which is obtained by a variational method such that u 0 as we establish the precise asymptotic formula for the variational eigencurve as whose growth order is sublinear

a numerical method for the solution of two parameter eigenvalue problems abstract we consider a two parameter weakly coupled eigenvalue problem for matrix equations under known assumptions 4 such a problem can be reduced to a system of one parameter problems in a tensor product space after which it can be treated by known numerical methods the method is illustrated by a numerical example of the simple two parameter problem and the example of binding and browne 5 it turns out that the method is especially suitable for problems of smaller orders

eigencurves of non definite sturm liouville problems for the p laplacian abstract the eigencurves are studied for a weighted quasi linear sturm liouville type problem of the form p y p 1 r q s sgn y y p 1 on 0 1 with sturmian type boundary conditions p being the p laplacian topics include holder classes c k and asymptotics including existence of oblique asymptotes an example illustrates precision of our holder exponents when p 2

singular left definite sturm liouville problems abstract we study singular left definite sturm liouville problems with an indefinite weight function the existence of eigenvalues is established based on the existence of eigenvalues of corresponding right definite problems furthermore for each singular left definite problem with limit circle non oscillatory endpoints we construct a regular left definite problem with the same eigenvalues and use it to obtain properties of eigenvalues and eigenfunctions inequalities among eigenvalues recently established for regular left definite problems are extended to the singular case

timoshenko systems with indefinite damping abstract we consider the timoshenko system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign present only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 0 l a x d x 0 and a a l 2 for small enough the decay rate will be described explicitly in the arguments we shall also give a new proof of exponential stability for the constant case a a moreover we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth sdg property i e the type of the induced semigroup coincides with the spectral bound for its generator

boundary problems of the second order with an indefinite weight function on considere des problemes aux limites de la forme au wu ou est un domaine borne de r n u w 1 2 soit a q soit a d p x d dx dx q x pour n 1 on suppose que w est une fonction de signe indefinie dans tandis que a a un spectre negatif

notes on jung kim srivastava integral operator abstract the object of the present paper is to investigate some properties of certain integral operator q introduced and studied recently by jung kim and srivastava j math anal appl 176 1993 138 147

the inertia of a hermitian pencil abstract let a and b be hermitian matrices and p a b where r 2 using parametric dependence of the eigenvalues we study the inertia of p under variation of and under small hermitian perturbations in particular we give semicontinuous dependence results for the set of where inertia of p is discontinuous

multiparameter sturm liouville problems with eigenparameter dependent boundary conditions abstract a system of ordinary differential equations y j q j y j k 1 n k r jk y j j 1 n 0 1 with real valued and continuous coefficient functions q j r jk is studied on 0 1 subject to boundary conditions y j 0 y j 0 cot j and b j y j 1 d j y j 1 e t j c j y j 1 a j y j 1 0 2 for j 1 n here e t e 1 e 2 e n is an arbitrary n n matrix of real numbers and j a j d j b j c j 0 a point 1 n t c n satisfying 0 1 and 0 2 is called an eigenvalue of the system results are given on the existence and location of the eigenvalues and completeness and oscillation of the eigenfunctions

spectral properties of two parameter eigenvalue problems ii we study the self adjoint eigenvalue problem w x 0 in hilbert space for one equation in two parameters here is bounded below with compact resolvent for each 1 2 we give necessary and sufficient conditions for the existence of so that holds with w 0 and we investigate the geometry of the set z 0 of such we also discuss higher order solution sets z i where the ith eigenvalue of w vanishes deriving various asymptotic results in a unified fashion

dual variational approaches to multiparameter eigenvalue problems abstract we study the abstract multiparameter problem t m x m k n 1 n v mn x m 0 x m h m m 1 k for selfadjoint operators t m and v mn on separable hilbert spaces h m we develop dual variational approaches related to the polar duality between certain convex sets the primal approach has been the basis of several investigations particularly in the so called right definite case here we use the dual approach to derive existence and comparison results for the left definite case

existence conditions for eigenvalue problems generated by compact multiparameter operators let t v 1 v k denote compact symmetric linear operators on a separable hilbert space h and write w t 1 v 1 k v k 1 k k we study conditions on the cone related to solubility of the multiparameter eigenvalue problem with w i nonpositive definite the main result is as follows theorem if 0 v then is soluble for any t if 0 v then there exists t such that is insoluble we also deduce analogous results for problems involving self adjoint operators with compact resolvent

existence conditions for higher order eigensets of multiparameter operators we consider classes of self adjoint operators for which the nonpositive part of the spectrum consists of eigenvalues 0 1 repeated according to multiplicity the sets of where i is negative and zero are labelled n i and z i respectively and p i k n i z i we study conditions on the v j sufficient to ensure nonemptiness of at least one of n i z i and p i for all t or for all positive definite t as well as conditions which are necessary in the sense that failure permits emptiness for at least one t as an example of our results we show in the sturm liouville case with l coefficients and separated end conditions that nonemptiness of z i for all t i e for all p 0 all q and all boundary data is equivalent to the i independent condition that the ft j do not vanish simultaneously on a set of positive measure

layer structures for the solutions to the perturbed simple pendulum problems we consider the perturbed simple pendulum equation u t f u t sinu t t i t t u t 0 t i u t 0 where 0 and r are parameters the typical example of f is f u u p 1u p 1 the purpose of this paper is to study the shape of the solutions when 1 more precisely by using a variational approach we show that there exist two types of solutions one is almost flat inside i and another is like a step function with two steps

schrodinger operator with a strong varying interaction on a curve in r2 in this paper we study a two dimensional quantum system governed by the hamiltonian corresponding to the formal expression where 0 is a continuous compactly supported function and is a curve in r2 we derive the asymptotics of eigenvalues for and analyze consequences of introducing varying delta potential

eigencurves for two parameter self adjoint ordinary differential equations of even order abstract the eigenvalue problem ly x x r x y x is considered for a self adjoint 2nth order operator l which is bounded below with compact resolvent on l2 a b and for real functions f r with certain restrictions it is shown that the eigencurves are piecewise analytic with no line segments unless s f r is constant a e when the curves are lines and possesses left right hand asymptotes iff s attains its minimum maximum value a e on some interval the asymptote equations are given explicitly in terms of the eigenvalues of certain simpler boundary value problems the second order case is discussed in detail

instability results for the damped wave equation in unbounded domains abstract we extend some previous results for the damped wave equation in bounded domains in r d to the unbounded case in particular we show that if the damping term is of the form a with bounded a taking on negative values on a set of positive measure then there will always exist unbounded solutions for sufficiently large positive in order to prove these results we generalize some existing results on the asymptotic behaviour of eigencurves of one parameter families of schrodinger operators to the unbounded case which we believe to be of interest in their own right

two parameter eigenvalue problems for matrices abstract the linked pair of two parameter eigenvalue problems t m 1 v m 1 2 v m 2 x m 0 x m 0 x m h m is considered for hermitian matrices t m v m1 v m2 acting on on the finite dimensional hilbert spaces h m m 1 2 we dispense with customary definiteness conditions although for m 1 2 we assume the existence of a linear combination of v m1 v m2 which is definite an embedding technique is used to study eigenvalues r 2 of specified variational index the transition between real and nonreal eigenvalues and algebraic multiplicity

asymptotics of the number of zeros and of the eigenvalues of general weighted sturm liouville problems soit n le nombre de zeros d une solution de l equation de sturm liouville ponderee generale p x y r x q x y 0 sur 0 b ou 0 b p q r 0 b r et 1 p q r l 0 b on donne une demonstration directe de l estimation asymptotique de n