caratheodory toeplitz and nehari problems for matrix valued almost periodic functions in this paper the positive and strictly contractive extension problems for almost periodic matrix functions are treated we present nece ssary and sufficient conditions for the existence of extensions in terms of toeplit z and hankel operators on besicovitch spaces and lebesgue spaces furthermore when a solution exists a special extension the band extension is constructed which enjoys a maximum entropy property a linear fractional parameterization of the set of all extensions is also provided the techniques used xn the proofs include factorizations of matrix valued almost periodic functions and a general algebraic scheme called the band method

existence of positive solutions for a system of generalized lidstone problems in this paper we study the existence of positive solutions for the system of generalized lidstone problems for ordinary differential equations 1 mu 2 m f 1 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 1 nv 2 n f 2 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 a 0u 2 i 0 b 0u 2 i 1 0 a 1u 2 i 1 b 1u 2 i 1 1 0 i 0 1 m 1 a 0v 2 j 0 b 0v 2 j 1 0 a 1v 2 j 1 b 1v 2 j 1 1 0 j 0 1 n 1 here f 1 f 2 c 0 1 xr m n r r 0 our hypotheses imposed on the nonlinearities f 1 and f 2 are formulated in terms of nonnegative matrices we use fixed point index theory to establish our main results based on a priori estimates of positive solutions

on the existence and nonexistence of positive solutions for nonlinear sturm liouville boundary value problems abstract in this paper the existence and nonexistence results of positive solutions are obtained for sturm liouville boundary value problem p x u q x u f x u x 0 1 a u 0 b p 0 u 0 0 c u 1 d p 1 u 1 0 where p c 1 0 1 q c 0 1 p x 0 q x 0 for x 0 1 f c 0 1 r a b c d 0 are constants and satisfy a b c d 0 the discussion is based on the positivity estimation for the green s function of associated linear boundary value problem and the fixed point index theory in cones

positive solutions of two point boundary value problems for second order differential equations with the nonlinearity dependent on the derivative abstract the existence of positive solutions is established for two point boundary value problems for second order differential equations with the nonlinearity dependent on the derivative l x h x f x x 0 x 1 r 1 1 0 1 0 0 r 2 2 1 2 1 0 where l x p x x q x x conditions are given in terms of the relative behaviors of the quotient f u v u v for u v near 0 and

algebras of almost periodic functions with bohr fourier spectrum in a semigroup hermite property and its applications abstract it is proved that the unital banach algebra of almost periodic functions of several variables with bohr fourier spectrum in a given additive semigroup is an hermite ring the same property holds for the wiener algebra of functions that in addition have absolutely convergent bohr fourier series as applications of the hermite property of these algebras we study factorizations of wiener hopf type of rectangular matrix functions and the toeplitz corona problem in the context of almost periodic functions of several variables

positive solutions of sub superlinear sturm liouville problems in this paper we introduce the notion of a strict lower upper solution to nonlinear sturm liouville boundary value problems based on the maximum principles we establish a result of leray schauder degree on the ordered intervals induced by the pairs of strict lower and upper solutions applying the result and the fixed point index theory in cones we obtain the global existence results of positive solutions for sub superlinear sturm liouville problems

sufficient conditions for the projective freeness of banach algebras let r be a unital semi simple commutative complex banach algebra and let m r denote its maximal ideal space equipped with the gelfand topology sufficient topological conditions are given on m r for r to be a projective free ring that is a ring in which every finitely generated projective r module is free several examples are included notably the hardy algebra h x of bounded holomorphic functions on a riemann surface of finite type and also some algebras of stable transfer functions arising in control theory

a measure theoretic axiomatization of fuzzy sets abstract using measurement theory this paper examines three empirical structures that underlie the representation of fuzzy sets the fuzzy membership structure the fuzzy component structure and the fuzzy system structure these qualitative structures justify the use of the standard min max system to represent fuzzy sets the results of this study facilitate the development of a sound measurement theoretic axiomatization of fuzzy systems

a model for the measurement of membership and the consequences of its empirical implementation representation and uniqueness theorems are presented for the fundamental measurement of the membership of a fuzzy set when the domain of discourse is order dense the conclusion that membership is on an interval scale is justified by the inapplicability of extensive measurement to fuzziness and the lack of a natural origin for membership some descriptive statistics are also presented from an empirical study currently in progress to construct membership functions they suggest that subjects differ in their perception of fuzziness and that the models in the literature for certain linguistic operators such as not very and antonym are not sufficiently general to account for the range of individual perceptions of vague attributes a more general mathematical model is proposed the question of the meaningfulness of statements about membership functions is also discussed in the light of the assertion that membership can be fundamentally measured at best on an interval scale some of the difficulties which arise in fuzzy set theory due to this property are illustrated and a solution is suggested involving the use of a function which is derived from membership but is on an absolute scale

existence of solutions to nonlinear hammerstein integral equations and applications abstract in this paper we study the existence and multiplicity of solutions of the operator equation k f u u in the real hilbert space l 2 g under certain conditions on the linear operator k we establish the conditions on f which are able to guarantee that the operator equation has at least one solution a unique solution and infinitely many solutions respectively the monotone operator principle and the critical point theory are employed to discuss this problem respectively in argument quadratic root operator k 1 2 and its properties play an important role as an application we investigate the existence and multiplicity of solutions to fourth order boundary value problems for ordinary differential equations with two parameters and give some new existence results of solutions

positive periodic solutions for nonlinear difference equations with periodic coefficients abstract we prove the existence of positive solutions of second order nonlinear difference equations on a finite discrete segment with periodic boundary conditions obtained results yield positive periodic solutions of the equation on the whole discrete axis provided that the coefficients are periodic

a global bifurcation phenomenon for second order singular boundary value problems we establish an existence result of unbounded continuum of solutions from the trivial branch for a second order singular boundary value problem as an application we prove several existence and multiplicity results of positive solutions for certain singular boundary value problems

the measurement of membership by subjective ratio estimation when we perform algebraic operations on membership degrees we must be sure that they are compatible with the kind of scale on which these degrees are measured for example we will not add in a weighted average membership degrees that are measured on an ordinal scale an important question is therefore how to determine on which kind of scale we measure the membership there are several techniques for measuring membership in this paper we present some of them based on stevens technique of ratio estimation and we characterize them thereby providing a sound way to determine the level of measurement we also discuss the problem of the representation of the union or intersection by a t conorm or t norm

existence and multiplicity of solutions to 2mth order ordinary differential equations abstract in this paper the existence and multiplicity of solutions are obtained for the 2mth order ordinary differential equation two point boundary value problems 1 m u 2 m t i 1 m 1 m i a i u 2 m i t f t u t for all t 0 1 subject to dirichlet neumann mixed and periodic boundary value conditions respectively where f is continuous a i r for all i 1 2 m since these four boundary value problems have some common properties and they can be transformed into the integral equation of form u i 1 m a i t i u t m f u we firstly deal with this nonlinear integral equation by using the strongly monotone operator principle and the critical point theory we establish some conditions on f which are able to guarantee that the integral equation has a unique solution at least one nonzero solution and infinitely many solutions furthermore we apply the abstract results on the integral equation to the above four 2mth order two point boundary problems and successfully resolve the existence and multiplicity of their solutions

multiplicity of solutions to two point boundary value problems for second order impulsive differential equations abstract in this paper we obtain some sufficient condition for the existence of at least three solutions to two point boundary value problems for second order impulsive differential equations by using leray schauder degree theory we assume the existence of two pairs of strict lower and upper solutions and the nonlinear term f satisfies a nagumo s growth condition with respect to the first order derivative

on sign changing solutions for nonlinear operator equations abstract in this paper the existence of sign changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory the main theorems are some new three solution theorems which are different from the famous amann s and leggett williams three solution theorems as well as the results in f li g han generalization for amann s and leggett williams three solution theorems and applications j math anal appl 298 2004 638 654 these three solutions are all nonzero one of them is positive another is negative and the third one is a sign changing solution furthermore the theoretical results are successfully applied to both integral and differential equations

solutions of periodic boundary value problems for second order nonlinear differential equations via variational methods abstract by introducing a variational framework for a class of second order nonlinear differential equations with non separated periodic boundary value conditions some results on the existence of non trivial positive and negative solutions of the problems are obtained some results by atici guseinov graef kong etc obtained by topological degree methods are extended the resonant case of the problems where the nonlinearities are unbounded and satisfy ahmad lazer paul type conditions is also considered

unitary colligations reproducing kernel hilbert spaces and nevanlinna pick interpolation in several variables abstract recently j agler studied the class s d of scalar valued analytic functions of d complex variables f for which f t 1 t d has norm at most 1 for any collection of d commuting contractions t 1 t d on a hilbert space h among other results he obtained a characterization of such functions in terms of a positivity property and in terms of a representation as the transfer function of a certain type of d variable linear system as well as a nevanlinna pick interpolation theorem for this class of functions in this note we examine the system theory aspects and uniqueness of the transfer function representation and give a simpler proof of the nevanlinna pick interpolation theorem for the class s d and obtain a d variable version of the toeplitz corona theorem by using ideas of arov and grossman introduced for 1 variable problems as a bonus we obtain a collection of linear fractional maps which parametrize the set of all s d solutions of an interpolation problem

positive solutions of two point boundary value problems for systems of nonlinear second order singular and impulsive differential equations abstract this paper is devoted to the study of multiple and single positive solutions of two point boundary value problems for nonlinear second order singular and impulsive differential systems by constructing a cone k 1 k 2 which is the cartesian product of two cones in the space c 0 1 and computing the fixed point index in the k 1 k 2 we establish the conditions for the existence of at least one or at least two positive solutions to two point boundary value problems for systems of nonlinear second order singular and impulsive differential equations

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

fuzzy sets probability and measurement abstract in recent years the problem of uncertainty modeling has received much attention from scholars in artificial intelligence and decision theory various formal settings including but not restricted to fuzzy sets and possibility measures have been proposed based on different intuitions and dealing with various kinds of uncertain data the two main research directions are upper and lower probabilities which convey the idea of imprecisely estimated probability measures and distorted probabilities for the descriptive assessment of partial belief possibility measures and thereby fuzzy sets stand at the crossroads of these new approaches traditional views interpretive settings and canonical experiments for the measurement of probability such as frequentist approaches betting theories comparative uncertainty relations are currently extended to the generalized uncertainty measures these works shed new light on various interpretations of fuzzy sets and clarify their links with probability theory conversely zadeh s logical point of view on fuzzy sets suggests a set theoretic perspective on uncertainty measures that brings together numerical quantification and logic

ordinal decomposability and fuzzy connectives the benefit of computing with linguistic terms is now generally accepted fuzzy set theory provides us the conceptual tool for the interpretation and evaluation of linguistic concepts and expressions it constitutes a quantification of the compatibility degree of objects with the associated linguistic concept through a membership function when we make computation using fuzzy membership values such as in the evaluation of fuzzy rules confidence the implicit assumptions are that the membership values have quantitative semantics the extensive scale assumption and that the numeric values are commensurate among the different fuzzy sets generated by the different concepts involved the common scale assumption in most situations these assumptions are difficult to justify and may lead to various anomalies the membership values are more suitably interpreted only as ordinal scales where the numeric representations reflect compatibility orderings in this paper we examine the concept of fuzzy intersection and union from the perspective of decomposability and ordinal conjoint structure in measurement theory we determine conditions under which a weak order induced by a fuzzy set or otherwise can be decomposed into other weak orders we show particular cases of ordinal decomposability which correspond naturally to our concept of fuzzy intersection and union this perspective of fuzzy connectives help us resolve some of the difficulties related to the above assumptions

on linear and nonlinear fourth order eigenvalue problems with indefinite weight abstract we determine the principal eigenvalues of the linear indefinite weight problem u x r g x u x x 0 1 u 0 u 1 u 0 u 1 0 moreover we investigate the existence of positive solutions for the corresponding nonlinear indefinite weight problem where g 0 1 r is a continuous function which attains both positive and negative values f c r r and r is a parameter

positive solutions of second order two delay differential systems with twin parameter abstract the paper is concerned with the existence of positive solutions for a second order two delay differential systems with twin parameter firstly we present some sufficient conditions with the twin parameter belonging to an open rectangular region eigenvalue region to ensure the existence of positive solutions for the differential systems with singularity secondly we deal with the superlinear semipositone problem of the differential systems and establish the existence of positive solutions for the systems the proofs are based on a fixed point theorem in cones

existence of positive solutions forboundary value problems of second order functional difference equations abstract we prove the existence of positive solutions for boundary value problems of second orderfunctional difference equations the result here is the generalization of a corresponding result for ordinary difference equations

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

the corona theorem and the existence of canonical factorization of triangular ap matrix functions abstract using the corona theorem canonical factorizability criteria for triangular almost periodic matrix valued functions of the form formula are obtained this allows the authors to obtain effective criteria for the existence of canonical factorization as well as to construct explicit factorizations for new classes of almost periodic matrix functions in a companion paper

positive solutions of nonlinear singular two point boundary value problems for second order impulsive differential equations in this paper we study the positive solutions of nonlinear singular two point boundary value problems for second order impulsive differential equations the existence of one or two positive solutions are established by using the fixed point index theorem in cone

existence of solutions to a class of nonlinear second order two point boundary value problems in this paper the existence and multiplicity results of solutions are obtained for the second order two point boundary value problem u t f t u t for all t 0 1 subject to u 0 u 1 0 where f is continuous the monotone operator theory and critical point theory are employed to discuss this problem respectively in argument quadratic root operator and its properties play an important role

equivalence and compositions of fuzzy rationality measures an axiomatic basis for fuzzy rationality measures has already been introduced by the authors in a previous paper 5 formalizing the fact that there exist degrees of consistency when preferences over a fixed set of alternatives are expressed in terms of fuzzy binary preference relations this paper deals with some practical consequences on the one hand similarities and compositions of fuzzy rationality measures are considered showing natural ways of deriving new measures on the other if basic stability properties are introduced in order to assure that small intensity measurement errors never lead to big changes in the associate rationality value it is shown that crisp i e binary rationality measures present serious difficulties when applied to fuzzy preference relations

multiple sign changing solutions to the sturm liouville boundary value problem with resonance abstract in this paper we study the sturm liouville boundary value problem p x u q x u f x u x 0 1 subject to u 0 u 0 u 1 u 1 0 by constructing a new sobolev space h 1 0 1 we discuss the existence of multiple solutions especially the existence of multiple sign changing solutions to this problem when the nonlinear f is resonant both at 0 and by combining the methods of the morse theory the topological degree and the fixed point index we establish a multiple solutions theorem which guarantees that the problem has at least six nontrivial solutions if this problem has only finitely many solutions then of these solutions there are two positive solutions two negative solutions and two sign changing solutions

on a family of connectives for fuzzy sets abstract in this paper we find the general solution of the functional equation s t x y t x n y x where s is a t conorm t is a t norm and n is a strong negation on the unit interval in particular the result yields a family of connectives for fuzzy sets

global bifurcation and multiple results for sturm liouville problems we consider the nonlinear sturm liouville boundary value problem lu t email protected t f u t 0

existence of nontrivial solutions for discrete nonlinear two point boundary value problems in this paper by using strongly monotone operator principle and critical point theory the existence of nontrivial solutions for discrete nonlinear two point boundary value problems is established two illustrative examples are given in the last part of the paper

a measurement theoretic axiomatization of trapezoidal membership functions in many applications of fuzzy set theory the membership of an object is not defined directly one of its attributes like height age weight etc is first mapped to a real number often by means of a physical instrument and a parametric function then maps this real number to a membership degree in some fuzzy set like tall old heavy etc a very common parametric function is the trapezoidal one this paper presents some conditions guaranteeing the existence of such a trapezoidal membership function representing the knowledge of an expert further experimental research is needed for testing whether these conditions are satisfied by human agents

existence of positive solutions of a fourth order boundary value problem abstract we consider the fourth order boundary value problem u f t u u 0 t 1 u 0 u 1 u 0 u 1 0 where f t u p au b p u p near 0 0 and f t u p cu dp u p near we give conditions on the constants a b c d that guarantee the existence of positive solutions the proof of our main result is based upon global bifurcation techniques

on the number of solutions of two classes of sturm liouville boundary value problems abstract we employ global bifurcation theory of p h rabinowitz together with sturm comparison theorem to establish multiplicity results for some classes of sturm liouville boundary value problems

positive solutions of second order boundary value problems with sign changing nonlinear terms abstract in this paper the existence results of positive solutions are obtained for second order boundary value problem u f t u t 0 1 u 0 u 1 0 where f c 0 1 r whose sign may change the proof is based on the fixed point index theory in cones

an empirical test of some measurement theoretic axioms for fuzzy sets in the previous years some authors have been elaborating on the measurement theoretic foundations of fuzzy set theory a well known problem in this approach is the difficult applicability of the deterministically formulated axioms on data obtained from an expert or social science data in general in this paper a statistical method is proposed which can be used for the testing of measurement axioms in a pairwise comparison design consequently we apply this method for the testing of two of these axioms i e transitivity and order of operations used in the context of fuzzy set theory the results clearly indicate that subjects act in agreement with transitivity but for order of operations there is no such vivid evidence which may have repercussions for some of the earlier theoretical work

measurement theoretic justification of connectives in fuzzy set theory abstract the problem of representing intersection and union in fuzzy set theory is considered there are various proposals in the literature to model these concepts the possibility of using continuous triangular norms and conorms including min and max are taken up in a measurement theoretic setting the conditions are laid out to arrive at cardinal scales on which addition and multiplication are meaningful and critically discussed these conditions must either be accepted on normative grounds or must be empirically verified before the modeling process in order to see which operations are meaningful it is emphasized that the archimedean axiom and the existence of natural bounds are crucial in arriving at ratio and absolute scale representations

unbounded solutions of the singular boundary value problems for second order differential equations on the half line this paper presents some results on the existence of multiple unbounded solutions for the boundary value problems for second order differential equations on half line and on the uniqueness of unbounded solution

nontrivial solutions of singular sublinear sturm liouville problems abstract the singular superlinear sturm liouville problems l x h x f x 0 x 1 r 1 1 0 1 0 0 r 2 2 1 2 1 0 are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators where l x p x x q x x and h x is allowed to be singular at both x 0 and x 1 in particular f is not necessary to be nonnegative the existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory

positive solutions of a second order integral boundary value problem in this paper we study the existence of positive solutions of a second order integral boundary value problems for ordinary differential equations our results presented here unify generalize and substantially improve the existing results in the literature moreover it is worthwhile to point out that our method will dispense with constructing a new green function

projective free algebras of continuous functions on compact abelian groups abstract it is proved that the wiener algebra of functions on a connected compact abelian group whose bohr fourier spectra are contained in a fixed subsemigroup of the additive dual group is projective free the semigroup is assumed to contain zero and have the property that it does not contain both a nonzero element and its opposite the projective free property is proved also for the algebra of continuous functions with the same condition on their bohr fourier spectra as an application the connected components of the set of factorable matrices are described the proofs are based on a key result on homotopies of continuous maps on the maximal ideal spaces of the algebras under consideration

toeplitz operators of finite interval type and the table method abstract we solve a riemann hilbert problem with almost periodic coefficient g associated to a toeplitz operator t g in a class which is closely connected to finite interval convolution equations based on a generalization of the so called table method the explicit determination of solutions to that problem allows one to establish necessary and sufficient conditions for the invertibility of the corresponding toeplitz operator and to determine an appropriate factorization of g providing explicit formulas for the inverse of t g some unexpected properties of the fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same problem

existence of positive solutions of lidstone boundary value problems abstract we show that there exists at least one positive solution for lidstone boundary value problem 1 n u 2 n t f t u t u t u 2 n 1 t 0 t 1 u 2 i 0 u 2 i 1 0 i 0 1 n 1 under some suitable conditions our proof is based upon global bifurcation techniques

factorization of matrix functions with subgroup supported fourier coefficients abstract it is proved that if a wiener class matrix function on a connected compact abelian group admits a factorization with respect to a connected compact abelian supergroup then it admits a factorization with respect to the original group in particular all factorization indices are characters of the original group an illustrative example is considered

existence of solutions of semilinear systems with gradient dependence via eigenvalue criteria abstract in this paper new criteria are established for the existence of positive radial solutions of a semilinear elliptic system depending on the gradient these criteria are determined by some relationships between the upper and lower bounds on suitable strips of r n of the nonlinearities of the system and the principal characteristic values of some associated linear hammerstein integral operators moreover using smoothing tools the totality of the involved cone is established

positive solutions and eigenvalue regions of two delay singular systems with a twin parameter abstract the paper is concerned with a two delay singular differential system with a twin parameter applying fixed point index theory we show the relationship between the asymptotic behaviors of nonlinearities at zero and infinity and the open regions eigenvalue regions of parameters which are correlated with delays such that the system has zero one and two positive solution s

generalization for amann s and leggett williams three solution theorems and applications abstract in this paper some new three solution theorems are obtained moreover the famous amann s and leggett williams three solution theorems in nonlinear functional analysis can be seen as their special cases namely these two famous theorems are united so they are both improved and that some new three solution theorems are applied to ordinary differential equations and some new existence results are obtained

general lidstone problems multiplicity and symmetry of solutions abstract for the 2mth order lidstone boundary value problem y 2 m t f y t y t y 2 i t y 2 m 1 t t 0 1 y 2 i 0 y 2 i 1 0 0 i m 1 where 1 mf r m 0 thinsp is continuous growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions this generalizes earlier papers which have applied avery s generalization of the leggett williams theorem to lidstone problems we then prove the analogous result for difference equations

constructive proof for existence of nonlinear two point boundary value problems owing to the importance of differential equations in physics the existence of solutions for differential equations has been paid much attention in this paper the existence of solution are obtained for the nonlinear second order two point boundary value problem in the reproducing kernel space under certain assumptions on right hand side we propose constructive proof for the existence result and a method is presented to obtain the exact solution expressed by the form of series this paper is a extension of previous paper wei jiang minggen cui the exact solution and stability analysis for integral equation of third or first kind with singular kernel appl math comput 202 2 2008 666 674 which extends a method of solving linear problems to present method for solving nonlinear problems

multiple positive solutions of nonlinear two point boundary value problems we improve the results obtained by erbe hu and wang in a recent paper we show that there exist at least two positive solutions of two point boundary value problems under conditions weaker than those used by erbe hu and wang

a three point boundary value problem for nonlinear fourth order differential equations abstract in this paper the authors consider the nonlinear fourth order ordinary differential equation e u t g t f u 0 with the boundary conditions b u 0 u 1 u 0 u p u 1 0 some results on the existence and nonexistence of positive solutions to problem e b are obtained results on the existence of infinitely many positive solutions are also presented examples are included to demonstrate that the results are sharp

type i and type ii fuzzy system modeling abstract two system modeling approaches are proposed with a unification of fuzzy methodologies type i and type ii knowledge representation are reviewed together with their proposed approximate reasoning schemes type i representation and inference are based on boolean normal forms type i models are myopic because in these models either the disjunctive or the conjunctive boolean normal forms are selected rather arbitrarily for knowledge representation and inference and then they are fuzzified whereas in type ii models representation and inference are based on fuzzy disjunctive and conjunctive normal forms which are derived from the fuzzy truth tables

the corona theorem and the canonical factorization of triangular ap matrix functions effective criteria and explicit formulas abstract using results of the companion paper the authors obtain effective criteria for the existence of canonical factorization for new classes of triangular almost periodic matrix functions of the form formula the important role in the proof of necessity in these criteria is played by a result on the stability of canonical ap factorizability obtained in the present paper by finding corona solutions for a pair of binomial almost periodic functions it is possible to calculate explicitly the factors of a canonical factorization for a class of considered matrix functions with trinomial f

the existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method abstract in this paper we study the existence and multiplicity of classical solutions for a second order impulsive differential equation with periodic boundary conditions by using a variational method and critical point theory we give some new criteria to guarantee that the impulsive problem has at least one solution two solutions and infinitely many solutions when the parameter pair c lies in different intervals respectively some examples are given in this paper to illustrate the main results

positive solutions of m point boundary value problems the second order m point boundary value problem x h x f x 0 0 x 1 0 0 1 i 1m 2ai i is considered under some conditions concerning the first eigenvalue of the relevant linear operator where i 0 1 with 0 1 2 m 2 1 ai 0 with i 1m 2ai 1 h x is allowed to be singular at x 0 and x 1 the existence of positive solutions and multiple positive solutions is obtained by means of fixed point index theory similarly conclusions hold for some other m point boundary value conditions

multiplicity results for second order m point boundary value problem by using fixed point theorems some new results for multiplicity of positive solutions for a class of second order m point boundary value problem are obtained the associated green s function of the problem is also given

interval valued preference structures different languages that are offered to model vague preferences are reviewed and an interval valued language is proposed to resolve a particular difficulty encountered with other languages it is shown that interval valued languages are well defined for de morgan triples constructed by continuous triangular norms conorms and a strong negation function a new transitivity condition for vague preferences is suggested and its relationships to known transitivity conditions are established a complete characterization of intervalvalued preference structures is also provided

eigenvalue criteria for existence of multiple positive solutions to boundary value problems of second order delay differential equations abstract criteria are established for existence of multiple positive solutions to the boundary value problems expressed by second order delay differential equations of the form p t y t q t y t f t y t y t a t 0 1 y t y t t t 0 y t y t t t 1 1 a where 0 a 1 4 are suitably small p c 1 0 1 p 0 q c 0 1 and q 0

positive solutions of a 2nth order boundary value problem involving all derivatives via the order reduction method this paper is mainly concerned with the existence multiplicity and uniqueness of positive solutions for the 2nth order boundary value problem 1 nu 2 n f t u u 1 i 2 u i 1 n 1u 2 n 1 u 2 i 0 u 2 i 1 1 0 i 0 1 n 1 where n 2 and f c 0 1 xr 2 n r r 0 we first use the method of order reduction to transform the above problem into an equivalent initial value problem for a first order integro differential equation and then use the fixed point index theory to prove the existence multiplicity and uniqueness of positive solutions for the resulting problem based on a priori estimates achieved by developing spectral properties of associated parameterized linear integral operators finally as a byproduct our main results are applied for establishing the existence multiplicity and uniqueness of symmetric positive solutions for the lidstone problem involving all derivatives

existence of three positive solutions for some second order boundary value problems in this paper a new fixed point theorem of functional type in a cone is established with using the new fixed point theorem and imposing growth conditions on the nonlinearity the existence of three positive solutions for the boundary value problemx t f t x t x t 0 0 0 is continuous finally an example is given to illustrate the importance of results obtained

multiplicity results for second order two point boundary value problems with superlinear or sublinear nonlinearities we consider boundary value problems for nonlinear second order differential equations of the form u a t f u 0 t epsilon 0 1 u 0 u 1 0 where a epsilon c 0 1 0 infinity and f r r is continuous and satisfies f s s 0 for s not equal 0 we establish existence and multiplicity results for nodal solutions to the problems if either f 0 0 f infinity infinity or f 0 infinity f 0 0 where f s s approaches f 0 and f infinity as s approaches 0 and infinity respectively we use bifurcation techniques to prove our main results c 2004 elsevier inc all rights reserved