stochastic reaction diffusion equations on networks with dynamic time delayed boundary conditions abstract we consider a reaction diffusion equation on a network subjected to dynamic boundary conditions with time delayed behavior also allowing for multiplicative gaussian noise perturbations exploiting semigroup theory we rewrite the aforementioned stochastic problem as an abstract stochastic partial differential equation taking values in a suitable product hilbert space for which we prove the existence and uniqueness of a mild solution eventually a stochastic optimal control application is studied

existence theorems for a second order three point boundary value problem abstract letf 0 1 r 2 r be continuous ande c 0 1 let i 0 1 ai r all of theai s having the same sign i 1 2 m 2 0 x t f t x t x t e t t 0 1 e x 0 0 x 1 i 1 m 2 a i x i bc m we discuss existence theorems for the problem e bcm under some sign condition offabout the origin our analysis is based on a nonlinear alternative of leray schauder

optimal constants in a nonlocal boundary value problem we give improved results on the existence of positive solutions for a nonlinear differential equation with nonlocal boundary conditions that arise as a model of a thermostat we obtain some optimal criteria for the existence of one positive solution which involve the principal eigenvalue of a related linear operator we also determine optimal values of some other constants that are useful in obtaining existence of multiple positive solutions

operators and comparisons of hesitant fuzzy linguistic term sets the theory of hesitant fuzzy linguistic term sets hfltss is very useful in objectively dealing with situations in which people are hesitant in providing linguistic assessments the purpose of this paper is to develop comparison methods and study the aggregation theory for hfltss we first define operations on hfltss and give possibility degree formulas for comparing hfltss we then define two aggregation operators for hfltss a hesitant fuzzy lwa operator and a hesitant fuzzy lowa operator in actual application we use these operators and the comparison methods to deal with multicriteria decision making problems with different situations in which importance weights of criteria or experts are known or unknown

the poincare series of the module of derivations of affine monomial curves abstract let a be a graded k algebra and m be a finitely generated a module the poincare series p m a z is the formal power series i dim k tor i a k m z i we study the poincare series of der k k s the module of derivations of a numerical semigroup ring k s and we relate it to the poincare series of k over k s and to the type of s we then use this in order to determine the poincare series of der k k s or at least its rationality for some classes of examples we finally give an example of a non rational p der k k s k s z

solvability of a three point nonlinear boundary value problem for a second order ordinary differential equation in case f x u u ps x p x u pjx u with pk 0 l 4 r locally integrable the boundary value problem l lt 1 2 was studied by kiguradze and lomtatidze i the purpose of this paper is to obtain existence and uniqueness theorems for the boundary value problem 1 1 t 1 2 under natural conditions on f using degree theoretic arguments we note that if u is a solution of 1 1 1 2 then there exists at least one 5 e q l such that u c 0 accordingly the boundary value problem

differential operators on monomial curves abstract let k be an algebraically closed field of characteristic 0 let n 0 be a numerical semigroup and let a k be the corresponding semigroup algebra we give an explicit description of the ring d d a of k linear differential operators on a the associated graded ring grd a and the module of derivations derk a we also classify all graded d modules which are finitely generated torsion free a modules of rank 1 considered as modules over the sub ring a d a

existence and nonexistence results for positive solutions of an integral boundary value problem abstract this paper deals with the existence and nonexistence of positive solutions for the integral boundary value problem a u b u g t f t u cos 0 u 0 sin 0 u 0 0 1 u d cos 1 u 1 sin 1 u 1 0 1 u d we provide sufficient conditions for the existence of either none or one or more positive solutions of the above problem the main tool used in the proofs of existence results is a fixed point theorem in a cone due to krasnoselskii and zabreiko the results presented substantially unify and extend the existing results in the literature

set measure directed multi source information fusion our concern here is with the multi source fusion problem two important aspects of this problem are the representation of information provided by the sources and the formulation of the instructions on how to fuse the information provided which we refer to as the fusion imperative we investigate the use of a monotonic set measure as a means of representing the fusion imperative we look at the fusion of various different types of information precise data uncertain information such as probabilistic and possibilistic we also consider the case of imprecise uncertain information such as that represented by a dempster shafer belief structure

a fuzzy measure similarity between sets of linguistic summaries in this paper we consider the problem of evaluating the similarity of two sets of linguistic summaries of sensor data huge amounts of available data cause a dramatic need for summarization in continuous monitoring it is useful to compare one time interval of data with another for example to detect anomalies or to predict the onset of a change from a normal state assuming that summaries capture the essence of the data it is sufficient to compare only those summaries i e they are descriptive features for recognition in previous work we developed a similarity measure between two individual summaries and proved that the associated dissimilarity is a metric additionally we proposed some basic methods to combine these similarities into an aggregate value here we develop a novel parameter free method which is based on fuzzy measures and integrals to fuse individual similarities that will produce a closeness measurement between sets of summaries we provide a case study from the eldercare domain where the goal is to compare different nighttime patterns for change detection the reasons for studying linguistic summaries for eldercare are twofold first linguistic summaries are the natural communication tool for health care providers in a decision support system and second due to the extremely large volume of raw data these summaries create compact features for an automated reasoning for detection and prediction of health changes as part of the decision support system

lie rinehart cohomology and integrable connections on modules of rank one abstract let k be an algebraically closed field of characteristic 0 let r be a commutative k algebra and let m be a torsion free r module of rank one with a connection we consider the lie rinehart cohomology with values in end r m with its induced connection and give an interpretation of this cohomology in terms of the integrable connections on m when r is an isolated singularity of dimension d 2 we relate the lie rinehart cohomology to the topological cohomology of the link of the singularity and when r is a quasi homogenous hypersurface of dimension two we give a complete computation of the cohomology

differential operators on an affine curve let x denote an irreducible affine algebraic curve over an algebraically closed field k of characteristic zero denote by 3 x the sheaf of differential operators on x and 2 x f x 3 x the ring of global differential operators on x the following is established theorem 3 x is a finitely generated k algebra and a noetherian ring furthermore 2 x has a unique minimal non zero ideal j and 3 x j is a finite dimensional k algebra let x denoted the normalisation of x and n x x the projection map the main technique is to compare 2 x with 3 x

linguistic summarization using if then rules and interval type 2 fuzzy sets linguistic summarization ls is a data mining or knowledge discovery approach to extract patterns from databases many authors have used this technique to generate summaries like most senior workers have high salary which can be used to better understand and communicate about data however few of them have used it to generate if then rules like if x is large and y is medium then z is small which not only facilitate understanding and communication of data but can also be used in decision making in this paper an ls approach to generate if then rules for causal databases is proposed both type 1 and interval type 2 fuzzy sets are considered five quality measures the degrees of truth sufficient coverage reliability outlier and simplicity are defined among them the degree of reliability is especially valuable for finding the most reliable and representative rules and the degree of outlier can be used to identify outlier rules and data for close up investigation an improved parallel coordinates approach for visualizing the if then rules is also proposed experiments on two datasets demonstrate our ls and rule visualization approaches finally the relationships between our ls approach and the wang mendel wm method perceptual reasoning and granular computing are pointed out

linguistic summarization of time series using a fuzzy quantifier driven aggregation we propose new types of linguistic summaries of time series data that extend those proposed in our previous papers the proposed summaries of time series refer to the summaries of trends identified here with straight line segments of a piecewise linear approximation of time series we first show how to construct such an approximation then we employ a set of features attributes to characterize the trends such as the slope of the line segment the goodness of approximation and the length of the trend the derivation of a linguistic summary of a time series is then related to a linguistic quantifier driven aggregation of trends for this purpose we employ the classic zadeh s calculus of linguistically quantified propositions but extending our previous works with different t norms in addition to the basic minimum we show an application to the analysis of time series data on daily quotations of an investment fund over an eight year period present some interesting linguistic summaries obtained and show results for different t norms the results are very promising

on numerical studies of multi point boundary value problem and its fold bifurcation based upon shooting method we set up a numerical method for approximating solutions and fold bifurcation solutions of second order multi point boundary value problems we prove the equivalence of the regularity of solutions and simple fold bifurcation solutions between the numerical method and the multi point boundary value problems many numerical experiments are carried out to illustrate the theoretical analysis from which we explore that the fold bifurcation phenomenon are generic in multi point boundary value problems although there is no theoretical analysis in the literature so far

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

a distance metric for a space of linguistic summaries producing linguistic summaries of large databases or temporal sequences of measurements is an endeavor that is receiving increasing attention these summaries can be used in a continuous monitoring situation like eldercare where it is important to ascertain if the current summaries represent an abnormal condition it is therefore necessary to compute the distance between summaries as a basis for such a determination in this paper we propose a dissimilarity measure between summaries based on fuzzy protoforms and prove that this measure is a metric we take into account not only the linguistic meaning of the summaries but also two quality evaluations namely the truth values and the degrees of focus we present examples of how the distance metric behaves and show that it corresponds with intuition

rings of differential operators on invariant rings of tori let k be an algebraically closed field of characteristic zero and g a torus acting diagonally on k for a subset 8 of s 1 2 s set up u e k u o if j e 8 then g acts on d up the ring of regular functions on up and we study the ring d d up g of all differential operators on the invariantvring more generally suppose that is a set of subsets of s such that each invariant ring d u g b e has the same quotient field we prove thatn g d d up g is noetherian and finitely generated as a k algebra now g acts on each d d up and there is a natural map 0 n d d ub n d d up g d ya g obtained by restriction of the differential operators we find necessary and sufficient conditions for 0 to be suuective and describe the kernel of the algebras n g d up g and n g a d up g carry a natural filtration given by the order of the differential operators we show that the associated graded rings are finitely generated commutative algebras and are gorensetin rings we also determine the centers of n ga d up5 g and n ga d d u g introduction throughout this paper k will be an algebraically closed field of characteristic zero if k is a commutative k algebra we denote by do k the set of k linear maps k k and if 1 a k linear map f k k belongs to dp k provided the map f r defined by f r s f rs rf s for s e k belongs to dp l k for all r e k the set d k upaodp k forms a subring of endk k called the ring of differential operators on k we consider k as a left d k module where f r f r for all f e d k r e k the ring of differential operators on the invariant ring of a finite group acting on a polynomial ring has been studied in ka l1 and l2 we carry out a similar study for the invariant ring of a torus we assume that the torus g acts on ks as a group of diagonal matrices if jb is a subset of s 1 2 s then g acts on ua u e ksluj o if j e jb also g acts on p u via gf u f g 1u for g e g f e g u 3 u e u 3 more generally suppose that for some set of subsets a of s we have y ue ua where each invariant ring p u c has the same quotient field f then each d p u 6 is a received by the editors june 18 1986 and in revised form december 11 1986 1980 mclthemcltiss subject clclssificcltion 1985 revision primary 16a33 secondary 13n05 14l30 p 1987 american mathematical s clety 0002 9947 87 1 00 25 per page

gradual inference rules in approximate reasoning abstract gradual inference rules of the form the more x is f the more y is g or of similar forms with the less instead of the more which express a progressive change of the degree to which the entity y satisfies the gradual property g when the degree to which the entity x satisfies the gradual property f is modified are often encountered in commonsense reasoning a representation of such rules by means of fuzzy sets is proposed and discussed this representation turns out to be based on a special implication function already considered in multiple valued logic patterns of reasoning involving gradual inference rules are formalized their links with interpolation mechanisms are pointed out

optimal existence criteria for symmetric positive solutions to a three point boundary value problem abstract in this paper we shall consider the following second order three point boundary value problem u t a t f t u t 0 0 t 1 u 0 u 1 u where 0 1 0 1 2 a l 1 0 1 is nonnegative and symmetric on 0 1 f 0 1 0 0 satisfies caratheodory conditions and f u is symmetric on 0 1 for all u 0 by using fixed point index theorems we get some optimal existence criteria for the existence of one or two symmetric solutions which involve the principal eigenvalue of a related linear operator

a fuzzy measure approach to systems reliability modeling our objective here is to study the role that fuzzy measures can play in systems reliability modeling we first introduce some basic ideas from fuzzy measure theory and then introduce some specialized ideas about fuzzy measures cardinality index and attitudinal character which will later be useful in comparing systems reliability basic ideas of reliability modeling and the role of the system structure function are discussed the system s signatures associated with a structure function are introduced and we show their relationship to expected time to system failure we show how we can model a systems structure function using a fuzzy measure s a description of the role of a measures cardinality index and attitudinal character in providing tools for comparing systems reliability is provided we describe how to obtain a structure model of a complex system using aggregation operators and the measure representation of individual components

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

existence of nontrivial solutions for a nonlinear sturm liouville problem with integral boundary conditions abstract this paper deals with the existence of nontrivial solutions for a nonlinear singular sturm liouville problem with integral boundary conditions

solvability of an m point boundary value problem for second order ordinary differential equations let 0 1 r2 r be a function satisfying caratheodory s conditions and e t l1 0 1 let i 0 1 ai r all of the ai s having the same sign i 1 2 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a solution for the m point boundary value problem x t t x t x t e t t 0 1 e formula conditions for the existence of a solution for the above boundary value problem are given using the leray schauder continuation theorem

on an m point boundary value problem for second order ordinary differential equations where q e 0 1 is given we obtain conditions for the existence and uniqueness of a solution for the boundary value problem 2 using the leray schauder continuation theorem 2 we give an example of a three point boundary value problem where the existence condition is not satisfied and no solution exists gupta 3 recently studied the boundary value problem 2 when q 1 our results on the three point boundary value problem 2 extend the results of gupta 3 to the case of general cy see also 4 51 we use the classical spaces c o 11 c o 11 lk o 11 and l o l of continuous k times continuously differentiable measurable real valued functions whose kth power of the absolute value is lebesgue integrable on 0 11 or measurable functions that are essentially bounded

eigenvalues of semi positone hammerstein integral equations and applications to boundary value problems eigenvalue intervals and the existence of finitely many positive eigenfunctions for semi positone hammerstein integral equations are obtained the positive characteristic values and their upper and lower bounds of the corresponding linear hammerstein integral operators are studied applications of the results are given to third order differential equations with three point boundary conditions

hypermatching similarity matching with extreme values an approach is developed for object similarity to support a focus on the role of extreme values in object matching which is termed hypermatching importance weights are first introduced to the matching and variations formulated for objects that do not share all the same attributes extreme attribute values are considered by introducing amplification of attribute importance and several significant cases examined the objects can both possess the same or different extreme valued attributes another case is where one object may have an extreme attribute which the other object does not have then the analysis of the effect of multiple extreme attributes is presented finally for attributes with 0 1 values features similarity matching is considered and a closed form solution for the similarity is developed this provides the basis for the yager petry index which is then compared with the jaccard similarity index

existence of multiple positive solutions for multipoint boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for a one dimensional p laplacian p u a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 a i u i where p s s p 2 s p 1 0 1 2 m 2 1 a i 0 for i 1 2 m 3 and a m 2 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

positive solutions of a nonlinear m point boundary value problem let ai 0 for i 1 m 3 and am 2 0 let i satisfy 0 1 2 m 2 1 and m 2i 1 ai i 1 we study the existence of positive solutions to the boundary value problem where a c 0 1 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed point theorem in cones

on the existence of positive solution for a kind of multi point boundary value problem at resonance abstract this paper concerns the existence of positive solution for a class of second order m point boundary value problems under different resonant conditions by using the leggett williams norm type theorem due to o regan and zima we obtain the existence of positive solution an example is given to demonstrate the main results