positive solutions of some singular m point boundary value problems at non resonance this paper investigates the existence of positive solutions for second order singular m point boundary value problems at non resonance a necessary and sufficient condition for the existence of c 0 1 as well as c 1 0 1 positive solutions is given by constructing lower and upper solutions and with the maximal theorem our nonlinearity f t x may be singular at x t 0 and or t 1

note on fuzzy regression abstract regression analysis has been widely used in several areas for many years fuzzy linear regression was introduced in 1980 by h tanaka s uejima and k asai in this paper the general form of regression equations is developed for fuzzy numbers it is showed that the problem of fuzzy regression can be formulated as a mathematical programming problem the special case of linear regression yields a linear programming problem different measures of vagueness are introduced to define the best estimate two simple numerical examples illustrate the methodology and allow a partial comparison among the different measures of vagueness

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

the hybrid fuzzy least squares regression approach to modeling manufacturing processes uncertainty in manufacturing processes is caused both by randomness as in material properties and by fuzziness as in the inexact knowledge previous research has seldom considered these two types of uncertainty when modeling manufacturing processes in this paper a hybrid fuzzy least squares regression hflsr approach to modeling manufacturing processes which does take into consideration these two types of uncertainty is proposed and described and a new form of weighted fuzzy arithmetic is introduced to develop the hybrid fuzzy least squares regression method the proposed hflsr approach not only features the capability of dealing with the two types of uncertainty but also addresses the consideration of replication of responses in experiments to investigate the effectiveness of the proposed approach to process modeling it was applied to the modeling solder paste dispensing process modeling results were compared with those based on statistical regression and fuzzy linear regression it was found that the accuracy of prediction based on the hflsr is slightly better than that based on statistical regression and much better than that based on the peters fuzzy regression

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

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

bicriteria variable selection in a fuzzy regression equation abstract by considering two criteria of minimum total sum of vagueness and minimum total sum of squares in estimation this article proposes a variable selection method for a fuzzy regression equation with crisp input and fuzzy output a branch and bound algorithm is designed and the least resistance principle is adopted to determine the set of compromised solutions numerical examples are provided for illustration

positive solutions for semi positone three point boundary value problems using a fixed point theorem of generalized cone expansion and compression we present in this paper criteria which guarantee the existence of at least two positive solutions for semi positone three point boundary value problems with parameter l 0 belonging to a certain interval

extrapolating internet users in taiwan by risk assessment abstract in a competitive environment most products usually have different stages of life cycle by different sales thus satisfying consumers requirements could make the product competitive from the experiences of experts the analytic hierarchy process has been used to analyze the expected range for a specified plc stage to enable a decision maker to derive proper marketing strategies however in decision theory the belfavior of a decision maker is always affected by her risk perception and risk propensity to result in different decision making in order to cope with this problem a fuzzy forecasting system to the risk perception and risk propensity is derived to extrapolate the internet users for a specified plc stage because of uncertainty and unknown system structure in the future

horseshoes in two degree of freedom hamiltonian systems with saddle centers we consider a class of two degree of freedom hamiltonian systems which have saddle centers with homoclinic orbits and do not take the form of small perturbations of integrable systems using a melnikov type global perturbation technique we present a condition under which orbits transversely homoclinic to periodic orbits exist and horseshoes are created on surfaces of energy level near the saddle centers we apply the theory to systems with potentials and give concrete examples in particular we can detect the presence of horseshoes in a class of systems to which previous results did not apply

positive solutions of the three point boundary value problem for second order differential equations with an advanced argument abstract in this paper by using the fixed point index method we establish the existence of at least one or at least two positive solutions to the three point boundary value problem for a second order differential equation with an advanced argument u t a t f u h t 0 t 0 1 u 0 0 u u 1 where 0 1 0 and 1 0 as an application we also give an example to demonstrate our result

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

comet and hill type periodic orbits in restricted n 1 body problems abstract we consider the planar restricted n 1 body problem where the interaction potential between the particle and the primaries is taken to be a finite sum of terms of the form distance with 0 the primaries are assumed to be in a relative equilibrium that is they form a uniformly rotating rigid configuration we show two results first if the infinitesimal particle is far from the primaries and the long range dominant term r of the potential is such that 0 and 2 then there exist two one parameter families of large nearly circular periodic solutions these solutions called comet solutions are elliptic and kam stable for 2 and unstable for 2 second if the infinitesimal particle is close to one of the primaries and the short range dominant term r of the potential near that primary is such that 0 and 2 then there exist two one parameter families of nearly circular periodic solutions called hill solutions that encircle the nearby primary for 2 these orbits are unstable the methodology applied involves appropriate symplectic scalings poincare s continuation method and averaging theory the kam stability of the comet periodic orbits is decided by verifying arnol d s non degeneracy conditions

existence and uniqueness results for discrete second order periodic boundary value problems abstract we prove existence and uniqueness results for solutions of second order nonlinear difference equations on a finite discrete segment with periodic boundary conditions the results are based on the notion of upper and lower solutions

positive periodic solutions of first order singular systems abstract we establish a complete structure for the existence of positive periodic solutions of first order non autonomous singular system u i t a i t u i t b i t f i u t i 1 n the methods employed are fixed point index theorems leray schauder degree and lower and upper solutions method

multiple positive solutions of multi point boundary value problem for second order impulsive differential equations this paper is devoted to study the existence of multiple positive solutions for the second order multi point boundary value problem with impulse effects the arguments are based upon fixed point theorems in a cone an example is worked out to demonstrate the main results

multiple positive solutions of quasi linear boundary value problems for finite difference equations abstract in this paper we consider a discrete second order quasi linear boundary value problem which nonlinear term f is involved with the first order difference by using a generalization of the leggett williams fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of at least three positive solutions

neuro fuzzy and genetic algorithm in multiple response optimization abstract optimization of a multiple output system whose function is only approximately known and is represented in tabular form is modeled and optimized by the combined use of a neuro fuzzy network and optimization techniques which do not require the explicit representation of the function neuro fuzzy network is useful for learning the approximate original tabular system however the results obtained by the neuro fuzzy network are represented implicitly in the network the manfis neuro fuzzy network which is an extension of the anfis network is used to model the multiple output system and a genetic algorithm is used to optimize the resulting multiple objective decision making problem a chemical process whose function is represented approximately in tabular form is solved to illustrate the approach

positive solutions of three point boundary value problems for second order impulsive differential equations with advanced arguments in this paper we discuss three point boundary value problems for second order impulsive differential equations with advanced arguments we establish sufficient conditions under which such problems have positive solutions to obtain the results we use the fixed point index

least squares model fitting to fuzzy vector data abstract we consider model fitting problems in which the mathematical model of an observed event is a system of equations involving model parameters and observables and in which the data are fuzzy vectors such problems naturally arise in applications when data are scarce and information is vague about distributions of variances that are contained in the observations then it may only be possible to obtain estimates of membership functions of the data a model can be fitted to such data by maximizing the membership values of the adjusted observations we achieve this by minimizing the sum of squares of the deviations of the membership values from one the optimization problem simplifies significantly if the membership functions of the fuzzy vectors belong to a class of conical functions which are defined in terms of an elliptic norm properties of these functions are discussed and a membership propagation formula derived which component wise obeys the extension principle the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares one obtains as a solution a fuzzy model parameter vector and a number of indicators which describe the quality of the fit viz the grade of compatibility between data and model their discord and dilators of model and data membership functions these new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem

positive solutions to a system of second order nonlocal boundary value problems abstract in this paper we study the existence of positive solutions to a system of second order nonlocal boundary value problems by using fixed point index theory in a cone our hypotheses imposed on nonlinearities are those which characterize systems of nonlocal boundary value problems and our boundary value conditions are expressed in terms of possibly nonlinear functions of riemann stieltjes integrals thus generalizing and unifying the boundary value conditions in the literature therefore our results cannot be routinely deduced from the ones for single nonlocal problem in the literature

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

possibilistic linear programming for managing interest rate risk abstract in this study we consider the linear programming problem with the objective of the investment discounted value where the interest rate is imprecise and has a triangular possibilistic distribution an crisp auxiliary bi objective linear programming model is proposed to resolve this possibilistic nature furthermore we develop an extended zimmermann approach called augmented max min approach for solving this auxiliary bi objective linear programming problem and other multiple objective linear programming problems finally a numerical bank balance sheet problem where interest rates price of futures contract loan demand deposit supply and ratio of desired loan to deposit are assumed to be fuzzy is solved for illustrating the new approach

second order nonlinear singular sturm liouville problems with integral boundary conditions this paper is concerned with the second order singular sturm liouville integral boundary value problems u t lh t f t u t 00 h is allowed to be singular at t 0 1 and f t x may be singular at x 0 by using the fixed point theory in cones an explicit interval for l is derived such that for any l in this interval the existence of at least one positive solution to the boundary value problem is guaranteed our results extend and improve many known results including singular and non singular cases

positive solutions for second order four point boundary value problems with alternating coefficient abstract in this paper we investigate the existence of positive solutions for a class of nonlinear second order four point boundary value problems with alternating coefficient our approach relies on the krasnosel skii fixed point theorem the result of this paper is new and extent the previously known result

multiplicity results for some second order four point boundary value problems abstract in this paper by using a fixed point theorem of functional type in a cone some new results for the multiplicity of positive solutions of second order four point boundary value problems are obtained the emphasis is put on the nonlinear term involved with the first order derivative

on the effect of linear data transformations in possibilistic fuzzy linear regression abstract in this paper the effect of linear data transformations is analysed in possibilistic fuzzy regression models in classical linear regression the measure of the goodness of fit is invariant with respect to these transformations but these fuzzy models depend on them

fuzzy linear regression models with least square errors to estimate the parameters of fuzzy linear regression models with fuzzy output and crisp inputs we develop a mathematical programming model in this paper the method is constructed on the basis of minimizing the square of the total difference between observed and estimated spread values or in other words minimizing the least square errors the advantage of the proposed approach is its simplicity in programming and computation as well as its performance to compare the performance of the proposed approach with the other methods two examples are presented

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

positive solutions of fourth order four point boundary value problems with p laplacian operator in this paper we consider the existence of positive solutions for the singular fourth order p laplacian equation p u t f t u t 0 t 1 with the four point boundary conditions u 0 0 u 1 au u 0 0 u 1 bu where p t t p 2t p 1 0 1 f c 0 1 0 0 may be singular at t 0 and or 1 and u 0 by using the upper and lower solution method and fixed point theorems the existence of positive solutions to the above the boundary value problem is obtained

multiplicity of positive solutions for second order three point boundary value problems we study the multiplicity of positive solutions for the second order three point boundary value problem u h t f u 0 t 0 1 u 0 0 u u 1 where 0 1 0 1 the methods employed are fixed point index theorems and leray schauder degree and upper and lower solutions

evaluation of fuzzy regression models by fuzzy neural network in this paper a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients parameters of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs is presented here a neural network is considered as a part of a large field called neural computing or soft computing moreover in order to find the approximate parameters a simple algorithm from the cost function of the fuzzy neural network is proposed finally we illustrate our approach by some numerical examples

existence of positive solution for singular semi positone k n k conjugate m point boundary value problem this paper is about a class of singular semi positone k n k conjugate m point boundary value problems by using the fixed point index theory we get a sufficient condition for the existence of positive solution to this problem

new fixed point theorems for mixed monotone operators and local existence uniqueness of positive solutions for nonlinear boundary value problems abstract in this article we present a new fixed point theorem for a class of general mixed monotone operators which extends the existing corresponding results moreover we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators based on them the local existence uniqueness of positive solutions for nonlinear boundary value problems which include neumann boundary value problems three point boundary value problems and elliptic boundary value problems for lane emden fowler equations is proved the theorems for nonlinear boundary value problems obtained here are very general

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

positive solutions to semi positone second order three point problems on time scales using a fixed point theorem of generalized cone expansion and compression we establish the existence of at least two positive solutions for the nonlinear semi positone three point boundary value problem on time scales u d t email protected t u t 0 u a 0 au h u t here email protected a t t where t is a time scale a 0 email protected a r t t a h a 0 belongs to a certain interval these results are new for difference equations as well as for general time scales an example is provided for differential difference and q difference equations

successive iteration and positive solution for nonlinear second order three point boundary value problems in this paper we study the existence of positive solution for two classes of nonlinear second order three point boundary value problems using some monotone iterative schemes in both cases such schemes start off with known constant functions and therefore are useful to computation purpose

higher level fuzzy numbers arising from fuzzy regression consider a fuzzy random variable y with expectation symbol b x where b is an unknown fuzzy number and an unknown real number for n observations yi xi there is a model yi b xi ei i 1 2 n where ei are fuzzy valued errors independently and identically distributed in some sense the aim is to obtain estimates of b when all fuzzy numbers are triangular and the ei are uniformly distributed maximum likelihood estimators emerge naturally as a special form of higher level fuzzy number thus mle can be interpreted as an estimation procedure which transforms randomness into higher levels of fuzziness

a new approach to some possibilistic linear programming problems abstract in practice the unit costs profits of new products or new projects the lending and borrowing interest rates and cash flows are always imprecise we provide an auxiliary multiple objective linear programming model to solve a linear programming problem with imprecise objective and or constraint coefficients our strategy is to maximize the most possible value of the imprecise profit at the same time we would like to minimize the risk of obtaining lower profit and maximize the possibility of obtaining higher profit this strategy is equivalent to the practical considerations of financial problems in this paper a numeric investment problem is solved for illustrating the new approach

discrete third order three point boundary value problem we are concerned with the discrete boundary value problemlx t email protected 3x t f t x t 1 t 1

multiple positive solutions to a three point boundary value problem with p laplacian abstract sufficient conditions are obtained that guarantee the existence of at least two positive solutions for the equation g u t a t f u 0 subject to boundary conditions by a simple application of a new fixed point theorem due to avery and henderson

identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters abstract we have already discussed several models of the possibilities linear regression analysis under the assumption that probabilitioes parameters in the models are non interactive i e the possibilistic distribution of parameters is defined by minimum operators in this paper quadratic membership functions as defined by a celmi s are considered to propose an identification method of interactive fuzzy parameters in possibilistic linear systems our method can be reduced to linear programming so that it is very easy to obtain the posssibilistic distribution of parameters

evaluation of fuzzy linear regression models abstract fuzzy linear regression provides means for tackling regression problems lacking a significant amount of data for determining regression models and with vague relationships between the dependent variable and independent variables in the paper a two stage construction of a linear regression model is proposed using an enhancement of a minimal vagueness criterion already discussed in fuzzy regression analysis two different experiments are set up and used for evaluating both models the choice of the fuzzy regression model should be made in the context of a practical application

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

linear fuzzy regression abstract this paper presents an approach which is useful for regression analysis in the case of heterogeneity of a set of observations for which regression is evaluated the proposed procedure consists of two stages first for a set of observations fuzzy classification is determined due to this homogenous classes of observations which are of hyperellipsoidal shape are obtained then for each fuzzy class the so called linear fuzzy regression is evaluated in the paper the method of calculating linear fuzzy regression coefficients is given it is a generalized version of the least squares method the formula for the values of coefficients is given some properties of linear fuzzy regression are analyzed it is proved that in one and two dimensional cases the formulae are analogous to those for usual regression a measure of goodness of fit and the method of determination of the number of fuzzy classes are also given presented examples indicate the superiority of fuzzy regression in comparison to usual regression in the case of heterogenous observations

resolution of fuzzy regression model abstract fuzzy linear regression was originally introduced by tanaka et al to cope with different types of input output information several approaches to fuzzy linear regression have been proposed in this paper a type of problem with crisp input and fuzzy output described by tanaka is considered of which a modified fuzzy least square method was proposed for solution it shows that with such an approach the predictability in the new model is better than tanaka s and its computation efficiency is better than the conventional fuzzy least square method

positive solutions to a type of nonlinear three point boundary value problem with sign changing nonlinearities in this paper by using krasnoselskii s fixed point theorem in a cone we study the existence of positive solutions for the second order three point boundary value problem u t a t u t lf t u t 0 0

simultaneous optimization of multiple responses represented by polynomial regression functions an algorithm is developed for the simultaneous optimization of several response functions that depend on the same set of controllable variables and are adequately represented by polynomial regression models of the same degree the data are first checked for linear dependencies among the responses if such dependencies exist a basic set of responses among which no linear functional relationships exist is chosen and used in developing a function that measures the distance of the vector of estimated responses from the estimated ideal optimum this distance function permits the user to account for the variances and covariances of the estimated responses and for the random error variation associated with the estimated ideal optimum suitable operating conditions for the simultaneous optimization of the responses are specified by minimizing the prescribed distance function over the experimental region an extension of the optimization procedure to mixture experiments is also given and the method is illustrat

existence of positive solutions to second order four point impulsive differential problems with deviating arguments in this paper we discuss four point boundary value problems for impulsive second order differential equations with deviating arguments we investigate separately cases when arguments are of delayed or advanced types we formulate sufficient conditions under which our problems have at least one or two positive solutions to obtain our results we apply the fixed point index

triple solutions for second order three point boundary value problems abstract we establish the existence of at least three positive solutions to the second order three point boundary value problem u f t u 0 u 0 0 u u 1 where 0 lt f 0 1 0 0 is continuous we accomplish this by making growth assumptions on f which can apply to many more cases than the sublinear and superlinear ones discussed in recent works

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

escape dynamics in collinear atomic like three mass point systems abstract the present paper studies the escape mechanism in collinear three point mass systems with small range repulsive large range attractive pairwise interaction specifically we focus on the asymptotic behaviour for systems with non negative total energy on the zero energy level set there are two distinct asymptotic states called 1 1 1 escape configurations where all the three separations infinitely increase as t we show that 1 1 1 escapes are improbable by proving that the set of initial conditions leading to such asymptotic configurations has zero lebesgue measure when the outer mass points are of the same kind we deduce the existence of a heteroclinic orbit connecting the 1 1 1 escape configurations we further prove that this orbit is stable under parameter perturbation in the positive energies case we show that the set of initial conditions leading to 1 1 1 escape configurations has positive lebesgue measure

positive solutions of second order three point boundary value problems with change of sign we study the existence of positive solutions of the second order three point boundary value problems t a t f y t 0 0 t 1 y 0 0 y 1 y n where 0 1 0 1 we show the existence of at least one positive solution by applying the krasnoselskii fixed point theorem in a cone here a t is allowed to changes sign on 0 1 applications of our results are provided to yield positive radial solutions of some elliptic boundary value problems on an annulus

asymptotic solutions for a second order differential equation with three point boundary conditions abstract in this paper we are concerned with the following singularly perturbed second order three point boundary value problem 1 1 y 2 q 1 x q 2 x y 0 1 1 2 y 0 a y 1 y where 0

existence of a non zero fixed point for nondecreasing operators proved via krasnoselskii s fixed point theorem abstract in this paper we use krasnoselskii s fixed point theorem on cone expansions to prove a new fixed point theorem for nondecreasing operators on ordered banach spaces moreover we apply this abstract result to prove the existence of a positive periodic solution for a nonlinear boundary value problem

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

positive solutions of nonlinear third order m point bvp for an increasing homeomorphism and homomorphism with sign changing nonlinearity in this paper several existence theorems of positive solutions are established for a nonlinear m point boundary value problem for the following third order differential equations f u a t f t u t 0 email protected 0 1 f u 0 email protected i 1m 2a email protected u x i u 0 0 u 1 email protected i 1m 2b iu x i where f email protected r is an increasing homeomorphism and homomorphism and f 0 0 the nonlinear term f may change sign as an application an example to demonstrate our results is given

an even order three point boundary value problem on time scales abstract we study the even order dynamic equation 1 nx n t h t f x t t a c satisfying the boundary conditions x i a 0 and x i c x i b for 0 i n 1 the three points a b c are from a time scale t where 0 0 f is a positive function and h is a nonnegative function that is allowed to vanish on some subintervals of a c of the time scale

existence of three positive solutions for boundary value problems with p laplacian abstract by using fixed point theorem we study the following equation g u t a t f u 0 subject to boundary conditions where g v v p 2 v with p 1 the existence of at least three positive solutions is proved

topsis for modm abstract in this study we extend topsis to solve a multiple objective decision making problem the principle of compromise of topsis for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution thus we reduce a k dimensional objective space to a two dimensional objective space by a first order compromise procedure we then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria we obtain a single objective programming problem by using the max min operator for the second order compromise operation to illustrate the procedure the bow river valley water quality management problem is solved by use of topsis