new upper solution bounds of the continuous algebraic riccati matrix equation by utilizing some linear algebraic techniques new upper bounds of the solution of the continuous algebraic riccati equation care are derived according to the present bounds iterative procedures are also developed for obtaining more precise estimations comparing with existing results the obtained bounds are less restrictive

lower summation bounds for the discrete riccati and lyapunov equations lower eigenvalue summation including trace bounds for the solution of the discrete algebraic riccati and lyapunov matrix equations are presented these are tighter than or supplement existing results

existence and uniqueness of positive solutions for singular nonlinear elliptic boundary value problems abstract in this paper we establish the existence and the uniqueness of positive solutions for dirichlet boundary value problems of nonlinear elliptic equations with singularity we obtain the existence and the uniqueness by using the mixed monotone method in the cone theory moreover we give an iterative method of constructing the solution the rate of convergence of the iterative sequence is analyzed

fixed point theorems for weakly c contractive mappings in ordered metric spaces the purpose of this paper is to present some fixed point results for weakly c contractive mappings in a complete metric space endowed with a partial order

matrix bounds of the discrete are solution this paper provides new lower and upper matrix bounds of the solution to the discrete algebraic riccati equation the lower bound always works if the solution exists the upper bounds are presented in terms of the solution of the discrete lyapunov equation and its upper matrix bound the upper bounds are always calculated if the solution of the lyapunov equation exists a numerical example shows that the new bounds are tighter than previous results in many cases

positive solutions of multi point boundary value problems at resonance abstract we establish new results on the existence of positive solutions for some multi point boundary value problems at resonance our results are based on a recent leggett williams norm type theorem due to o regan and zima we also derive a new result for a three point problem previously studied by several authors

on the borda kendall consensus method for priority ranking problems this paper investigates the borda kendall method for the determination of a consensus ranking it is shown that in the case of ties the method does not perform as claimed a minimum variance method for determining the consensus ranking is proposed and its properties examined it is shown to be equivalent to the borda kendall method if ties are not allowed an algorithm to determine the minimum variance consensus ranking in the case of ties is described results obtained from the solution of problems of various sizes are discussed

new lower solution bounds of the continuous algebraic riccati matrix equation in optimal and robust control problems the so called continuous algebraic riccati equation care plays an important part by utilizing some matrix inequalities and linear algebraic techniques new lower matrix bounds for the solution of the care are derived following the derived bounds iterative algorithms are then developed to obtain sharper solution estimates in comparison to existing results the obtained bounds are less restrictive finally we give numerical examples to demonstrate the effectiveness of our results

a note on eigenvalue bounds in algebraic riccati equation in this note an upper bound on the maximum eigenvalue of the solution matrix k of the algebraic riccati equation is established the approach outlined also results in several lower bounds which are more general than those derived in 1 for some of the largest eigenvalues of k

transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations abstract using a new method for dealing with the impulse term of second impulsive differential equations we are concerned with determining values of for which there exist positive solutions of the following boundary value problems in the form of x t f t x t 0 t j t t k x t k x t k c k x t k k 1 2 n a x 0 b x 0 a x 1 b x 1 0 1 h s x t d t where 0 is a positive parameter c k is a real sequence with c k 1 k 1 2 n the dependence of positive solution x t on the parameter is also studied i e lim x or lim x 0 the proof of our main result is based upon transformation techniques and fixed point theories this is probably the first time the existence of positive solutions of second order impulsive differential equations has been studied by applying this technique

iterative matrix bounds and computational solutions to the discrete algebraic riccati equation bilateral matrix bounds for the solution of the discrete algebraic riccati equation dare are presented they are new or tighter than the existing bound computational algorithms to solve the dare follow

a new approach for upper bound estimations of the solution of the continuous riccati equation by utilizing some linear algebraic techniques a new approach for measuring upper bounds of the solution of the continuous algebraic riccati equation care is developed two upper matrix bounds are developed comparing with those appeared in the literature the obtained bounds are less restrictive or more concise therefore they can be applied easily to deal with control problems

new upper solution bounds of the discrete algebraic riccati matrix equation in this note we present upper matrix bounds for the solution of the discrete algebraic riccati equation dare using the matrix bound of theorem 2 2 we then give several eigenvalue upper bounds for the solution of the dare and make comparisons with existing results the advantage of our results over existing upper bounds is that the new upper bounds of theorem 2 2 and corollary 2 1 are always calculated if the stabilizing solution of the dare exists whilst all existing upper matrix bounds might not be calculated because they have been derived under stronger conditions finally we give numerical examples to demonstrate the effectiveness of the derived results

an improved lower matrix bound of the solution of the unified coupled riccati equation a new lower matrix bound of the solution for the unified coupled algebraic riccati equation ucare is proposed this bound improves the drawback of the results presented in a previous paper

a cardinal dissensus measure based on the mahalanobis distance abstract in this paper we address the problem of measuring the degree of consensus dissensus in a context where experts or agents express their opinions on alternatives or issues by means of cardinal evaluations to this end we propose a new class of distance based consensus model the family of the mahalanobis dissensus measures for profiles of cardinal values we set forth some meaningful properties of the mahalanobis dissensus measures finally an application over a real empirical example is presented and discussed

a method for measuring consensus within groups this paper presents a new index of disagreement or measure of consensus for comparison of data collected using likert items this new index which assesses the level of disagreement among group members exploits the conditional distribution of the variance for a given mean the variance is often used as a measure of disagreement with high variance seen as a high disagreement in a group however since the range of the variance is a function of the mean this implies that for a mean close to the end points of the scale the range of the variance is relatively small and for a mean at the center of the scale the range of the variance is larger the index of disagreement introduced in this paper takes into account both the mean and the variance and provides a way to compare two groups that is more meaningful than just considering the variance or other measures of disagreement or consensus that only depend on the variance

distance based and ad hoc consensus models in ordinal preference ranking abstract this paper examines the problem of aggregating ordinal preferences on a set of alternatives into a consensus this problem has been the subject of study for more than two centuries and many procedures have been developed to create a compromise or consensus we examine a variety of structures for preference specification and in each case review the related models for deriving a consensus two classes of consensus models are discussed namely ad hoc methods evolving primarily from parliamentary settings over the past 200 years and distance or axiomatic based methods we demonstrate the levels of complexity of the various distance based models by presenting the related mathematical programming formulations for them we also present conditions for equivalence that is for yielding the same consensus ranking for some of the methods finally we discuss various extensions of the basic ordinal ranking structures paying specific attention to partial ranking voting member weighted consensus ranking with intensity of preference and rank correlation methods as alternative approaches to deriving a consensus suggestions for future research directions are given

second order singular boundary value problems with integral boundary conditions abstract we study the second order singular boundary value problem u f t u 0 t 0 1 u 0 0 1 u s d s u 1 0 1 u s d s sufficient conditions are obtained for the existence and uniqueness of positive solutions the dependence of positive solutions on the parameter is also studied moreover application of our theory to a special problem is discussed to prove our theorem we utilize some results from the mixed monotone operator theory

measuring consensus and dissensus a generalized index of disagreement using conditional probability abstract we generalize an index of disagreement recently proposed by akiyama et al 2016 which can be applied only to surveys that measure opinions expressed using the standard 5 scale likert scale to a general case that uses any scale with more than five response levels as stated in the aforementioned study the variance alone computed from a survey that employs the likert scale is not an adequate indicator for measuring the disagreement within a group because the range of the variance is a function of the mean to overcome this limitation they define the disagreement index using a conditional probability density function which allows us to compare responses to questions having different means or between groups across different time periods however developing a measure that considers likert scales larger than five has not yet been developed and our work addresses this lacuna as an example we illustrate an advantage of our generalized measure by calculating the disagreement within consumers price expectations

existence and uniqueness of solutions for singular fourth order boundary value problems by mixed monotone method the existence and uniqueness are established for singular fourth order boundary value problems the theorems obtained are very general and complement previous known results

a new type of fixed point theorem in metric spaces abstract we prove a generalization of edelstein s fixed point theorem though there are thousands of fixed point theorems in metric spaces our theorem is a new type of theorem

near optimal control for time varying linear discrete systems with additive nonlinearities and random gains in this technical note the near optimal control problem is investigated for a class of time varying linear discrete systems subject to additive nonlinearities and random gains first certain upper bound on the cost function is proposed to quantify the control performance subsequently in virtue of the time varying discrete riccati like recursions drlrs the near optimal control strategy is designed such that this upper bound is minimized over the finite horizon to reflect the steady state behavior of the dynamic system the upper bound of the derived time varying drlrs is also analyzed over the infinite horizon by resorting to the semidefinite programming method finally a numerical example is provided to verify the validity and advantages of the proposed methodology

upper and lower bounds of the solutions of the discrete algebraic riccati and lyapunov matrix equations matrix bounds upper and lower for the solution of the discrete algebraic riccati and lyapunov equations respectively are proposed in this paper they are new or sharper than the majority of existing results by making use of these new matrix bounds the corresponding bounds for each eigenvalue the trace and the determinant of these solution matrices are also presented comparisons are made between these bounds and the majority of those appearing in the literature it is shown that the obtained results are tighter finally we give illustrative examples to show that these estimates appear to be considerably stronger than previously available results in many cases

minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making in some real world decision processes decision makers may prefer to provide their opinions using linguistic expressions instead of a single linguistic term particularly they may hesitate between several linguistic terms in this paper we deal with the consensus issue in the hesitant linguistic group decision making gdm problem firstly a novel distance based consensus measure is proposed then using this consensus measure we develop an optimization based consensus model in the hesitant linguistic gdm which minimizes the number of adjusted simple terms in the consensus building furthermore a two stage model is displayed to further optimize the solutions to the proposed consensus model through which we obtain the unique optimal adjustment suggestion to support the consensus reaching process in the hesitant linguistic gdm finally several desirable properties are proposed to justify the proposal and two examples are used to demonstrate the validity of the models

solution bounds of the continuous riccati matrix equation a new approach is proposed for estimating the solution of the continuous algebraic riccati equation care upper and lower solution bounds of the care are presented comparisons show that the present bounds are more general and or tighter than existing results

genetic algorithms to minimize the weighted number of late jobs on a single machine the general one machine scheduling problem is strongly np hard when the objective is to minimize the weighted number of late jobs few methods exist to solve this problem in an other paper we developed a lagrangean relaxation algorithm which gives good results on many instances however there is still room for improvement and a metaheuristic might lead to better results in this paper we decided to use a genetic algorithm ga although a ga is somewhat easy to implement many variations exist and we tested some of them to design the best ga for our problem three different engines to evaluate the fitness of a chromosome are considered together with four types of crossover operators and three types of mutation operators an improved ga is also proposed by applying local search on solutions determined from the chromosome by the engine numerical experiments on different tests of instances are reported they show that starting from an initial population already containing a good solution is very effective 2003 elsevier b v all rights reserved

subsets of the square with the continuous and order preserving fixed point property abstract this study characterizes the convex sets whose complements in the unit square exhibit the fixed point property for mappings which are jointly continuous and order preserving hence one can readily construct simple sets with this fixed point property but which neither have the fixed point property individually for continuous mappings nor for order preserving mappings this is the first characterization of any non trivial set with this property

bounds in algebraic riccati and lyapunov equations a survey and some new results this paper summarizes and investigates the relations of a number of bounds for the solutions of the algebraic riccati and lyapunov equations that have been reported during the last two decades also presented are bounds for the unified riccati equation using the delta operator and it is shown that some bounds for the continuous and discrete riccati equations can be unified by them

eigenvalue bounds for algebraic riccati and lyapunov equations the majorization result of wimmer 2 relating the eigenvalues of the matrices involved in the lyapunov equation is extended to the algebraic riccati equation this result coupled with certain results on the eigenvalue bounds for sum and product of matrices yields several lower and upper bounds for the eigenvalues of the solution matrix of the algebraic riccati and lyapunov equations

on fixed point theorems of mixed monotone operators and applications abstract in this paper we obtain some new existence and uniqueness theorems of positive fixed point of mixed monotone operators in banach spaces partially ordered by a cone finally we apply the main theorem to a nonlinear parabolic partial differential equation some results are new even for increasing or decreasing operators

an existence and uniqueness result for the singular lane emden fowler equation abstract using a fixed point theorem of general concave operators we present in this paper criteria which guarantee the existence and uniqueness of positive solutions for the singular lane emden fowler equation

a note on the discrete lyapunov and riccati matrix equations abstract inequalities which are satisfied by the determinants of the positive definite solutions of the discrete algebraic riccati and lyapunov matrix equations are presented the results give lower bounds for the product of the eigenvalues of the matrix solutions also for a discrete lyapunov equation an algorithm is presented to determine under what conditions a positive diagonal solution will exist if all the conditions are satisfied the algorithm also provides such a diagonal solution

symmetric positive solutions for p laplacian fourth order differential equations with integral boundary conditions this paper investigates the existence and multiplicity of symmetric positive solutions for a class of p laplacian fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory for cones the nonexistence of a positive solution is also studied

fixed point theorems for weakly contractive mappings in partially ordered sets abstract the purpose of this paper is to present some fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order

lower bounds for the trace of the solution of the discrete algebraic riccati equation two lower bounds for the trace of the solution of the discrete algebraic riccati equation dare are presented it is shown that in many cases these trace bounds are tighter than those in the literature and greater than the trace of the state weighting matrix even when the system matrix is singular the results are illustrated by an example

upper and lower matrix bounds of the solution for the discrete lyapunov equation new matrix bounds of the solution for the discrete algebraic matrix lyapunov equation are established the upper and lower eigenvalue bounds such as each eigenvalue including the extreme ones the trace and the determinant are also determined by these matrix bounds for the same solution the present schemes are tighter as compared with the majority of existing results

on bounds of the riccati and lyapunov matrix equations various bounds for the traces of the solutions of the algebraic riccati and lyapunov matrix equations are established in the continuous and discrete domain respectively the presented results give lower bounds for the sum of the eigenvalue of the matrix solutions

upper bounds for the solution of the discrete riccati equation upper bounds for individual eigenvalues and for summations of eigenvalues including the trace of the solution of the discrete algebraic riccati equation are presented some are new and some supplement bounds in the literature

fixed point theorems of φ concave ψ convex mixed monotone operators and applications abstract in this paper concave convex operators are introduced and some new existence and uniqueness theorems of fixed points of mixed monotone operators with such concavity and convexity are obtained moreover some applications to nonlinear integral equations on bounded or unbounded regions are given

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

a brief summary of the bounds on the solution of the algebraic matrix equations in control theory abstract in recent years several bounds have been reported for different measures of the extent or size of the solution of the algebraic matrix equations arising in control theory such as the riccati equation and the lyapunov equation this paper collects the bounds that have been presented up to now and summarizes them in an unified form this will prove particularly convenient for those wishing to get a ready estimate of the solution while solving the equations numerically or to develop theoretical results that rely on these bounds

on the estimation of solution bounds of the generalized lyapunov equations and the robust root clustering for the linear perturbed systems this paper measures the solution bounds for the generalized lyapunov equations gle by making use of linear algebraic techniques we estimate the upper and lower matrix bounds for the solutions of the above equations all the proposed bounds are new and it is also shown that the majority of existing bounds are the special cases of these results furthermore according to these bounds the problem of robust root clustering in sub regions of the complex plane for linear time invariant systems subjected to parameter perturbations is solved the tolerance perturbation bounds for robust clustering in the given sub regions are estimated compared to previous results the feature of these tolerance bounds is that they are independent of the solution of the gle

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

decay rate estimations for linear quadratic optimal regulators let u t fx t be the optimal control of the open loop system x t ax t bu t in a linear quadratic optimization problem by using different complex variable arguments we give several lower and upper estimates of the exponential decay rate of the closed loop system x t a bf x t main attention is given to the case of a skew hermitian matrix a given an operator a for a class of cases we find a matrix b that provides an almost optimal decay rate we show how our results can be applied to the problem of optimizing the decay rate for a large finite collection of control systems a bj j 1 n and illustrate this on an example of a concrete mechanical system at the end of the article we pose several questions concerning the decay rates in the context of linear quadratic optimization and in a more general context of the pole placement problem

generalized contractions in partially ordered metric spaces and applications to ordinary differential equations the purpose of this paper is to present some fixed point theorems in a complete metric space endowed with a partial order by using altering distance functions we also present some applications to first and second order ordinary differential equations

fixed point theorems for a class of mixed monotone operators with applications abstract in this paper we provide several unique existence theorems for fixed points for mixed monotone operators without continuity and compactness and apply them to study a class of integral equations

bounds for the eigenvalues of the solution of the discrete riccati and lyapunov equations and the continuous lyapunov equation we present some bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the discrete riccati and lyapunov matrix equations and the continuous lyapunov matrix equation nearly all of our bounds for the discrete riccati equation are new the bounds for the discrete and continuous lyapunov equations give a completion of some known bounds for the extremal eigenvalues and the determinant and the trace of the solution of the respective equation

existence and uniqueness of positive solutions for fourth order nonlinear singular continuous and discrete boundary value problems using the mixed monotone method we establish the existence and uniqueness of positive solutions for some fourth order nonlinear singular continuous and discrete boundary value problem the theorems obtained are very general and complement previously known results

random sequencing jobs with deadlines problem growth of the optimal solution values in the paper an asymptotic value of the sequencing jobs with deadlines sjd problem is computed for the case of the random sjd problems it is assumed that problem coefficients are realizations of independent uniformly distributed over 0 1 random variables n with deadlines remaining deterministic

a new consensus ranking approach for correlated ordinal information based on mahalanobis distance the cohesiveness among experts opinions is addressed from a global point of view a new procedure to codify ordinal information is provided and characterized a measurement of the degree of dissensus designed for possibly correlated alternatives is defined a procedure to obtain a social consensus solution based on the mahalanobis distance is investigated we investigate from a global point of view the existence of cohesiveness among experts opinions we address this general issue from three basic essentials the management of experts opinions when they are expressed by ordinal information the measurement of the degree of dissensus among such opinions and the achievement of a group solution that conveys the minimum dissensus to the experts group accordingly we propose and characterize a new procedure to codify ordinal information we also define a new measurement of the degree of dissensus among individual preferences based on the mahalanobis distance it is especially designed for the case of possibly correlated alternatives finally we investigate a procedure to obtain a social consensus solution that also includes the possibility of alternatives that are correlated in addition we examine the main traits of the dissensus measurement as well as the social solution proposed the operational character and intuitive interpretation of our approaches are illustrated by an explanatory example

trace bounds on the covariances of continuous time systems with multiplicative noise matrix equations such as ap pa sup t fpf sup t omega 0 and aq qa sup t qvq fpf sup t omega 0 which arise in the estimation problem of systems with both additive and multiplicative noise are treated trace bounds on the steady state and error covariances p and q are established under complete and incomplete noise information an example illustrates the usefulness of these bounds in determining the size of the estimation error

brief lower matrix bounds for the continuous algebraic riccati and lyapunov matrix equations in this paper we propose lower matrix bounds for the continuous algebraic riccati and lyapunov matrix equations we give comparisons between the parallel estimates finally we give examples showing that our bounds can be better than the previous results for some cases

robust root clustering for linear uncertain systems using generalized lyapunov theory in this paper the problem of matrix root clustering in sub regions of complex plane for linear state space models with real parameter uncertainty is considered the nominal matrix root clustering theory of gutman and jury 1981 ieee trans aut control ac 26 403 using generalized lyapunov equation is extended to the perturbed matrix case and bounds are derived on the perturbation to maintain root clustering inside a given region the theory allows us to get an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space the current literature available on perturbation bounds for robust stability becomes a special case of this unified theory

fixed point results for mappings satisfying ψ φ weakly contractive condition in partially ordered metric spaces abstract we establish coincidence fixed point and common fixed point theorems for mappings satisfying weakly contractive condition in an ordered complete metric space some applications of our obtained results are given

fixed point theorems for mixed monotone operators and applications to integral equations abstract the purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions we also present an application to integral equations

improved integer linear programming formulations for the job sequencing and tool switching problem in this article we investigate the job sequencing and tool switching problem ssp a np hard combinatorial optimization problem arising from computer and manufacturing systems starting from the results described in tang and denardo 1987 crama et al 1994 and laporte et al 2004 we develop new integer linear programming formulations for the problem that are provably better than the alternative ones currently described in the literature computational experiments show that the lower bounds obtained by the linear relaxation of the considered formulations improve on average upon those currently described in the literature and suggest at the same time new directions for the development of future exact solution approaches

positive solutions of nonlinear beam equations with time and space singularities we consider the existence and multiplicity of positive solutions to a nonlinear fourth order two point boundary value problem the nonlinear term may be singular with respect to both the time and space variables in mechanics the problem describes the deformation of an elastic beam fixed at the left and supported at the right by sliding clamps by introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions several local existence theorems are obtained

second order boundary value problems with integral boundary conditions abstract in this paper we investigate the existence of positive solutions of nonlocal second order boundary value problems with integral boundary conditions

a multiple criteria decision model with ordinal preference data abstract this paper develops a model for aggregating ordinal preference ranking across multiple criteria criteria weights are developed as part of the optimization process the model utilizes three levels of ordinal priorities 1 preferences among alternatives on the basis of each criterion 2 preferences among the criteria to reflect the importance of those criteria and 3 preferences among the criteria which express the degree to which the respondent can clearly distinguish among the alternatives the model is based upon a data envelopment analysis structure which permits a flexible weighting mechanism for each alternative being ranked

concordance and consensus this paper deals with the measurement of concordance and the construction of consensus in preference data either in the form of preference rankings or in the form of response distributions with likert items we propose a set of axioms of concordance in preference orderings and a new class of concordance measures the measures outperform classic measures like kendall s t and w and spearman s r in sensitivity and apply to large sets of orderings instead of just to pairs of orderings for sets of n orderings of n items we present very efficient and flexible algorithms that have a time complexity of only o nn 2 remarkably the algorithms also allow for fast calculation of all longest common subsequences of the full set of orderings we experimentally demonstrate the performance of the algorithms a new and simple measure for assessing concordance on likert items is proposed

trace bounds on the solution of the algebraic matrix riccati and lyapunov equation lower and upper bounds on the trace of the positive semidefinite solution of the algebraic matrix riccati and lyapunov equation are derived the upper trace bound obtained in this note in many cases results in a tighter bound as compared to the upper bound for the maximal eigenvalue proposed in 1 and 2

eigenvalue bounds for the discrete lyapunov matrix equation upper and lower bounds for every eigenvalue of the positive definite solution to the discrete lyapunov matrix equation are provided the obtained bounds have an advantage that they can give nontrivial lower bounds even when some existing results yield trivial ones

on the upper and lower bounds of the solution for the continuous riccati matrix equation in this paper concise upper and lower matrix bounds for the solution of the continuous riccati equation are presented these results are new and the lower matrix bound is better than the previously reported one according to these estimates all the bounds for eigenvalues trace determinant etc can then be defined a lower matrix bound and eigenvalue bounds of the solution of the continuous algebraic lyapunov equation are also determined the main feature of this paper is thatallthe presentresults are new and are sharper than the majority ofthose reported in the literature finally we give an illustrative example to make comparisons for the present schemes and existing bounds

impact of deadline intervals on behavior of solutions to the random sequencing jobs with deadlines problem abstract the paper analyzes the influence exerted by the mutual relations of deadline intervals on behavior of the optimal solution values for the random sequencing jobs with deadlines sjd problems an asymptotically sub optimal algorithm is proposed it is assumed that the problem coefficients are realizations of independent uniformly distributed random variables and deadlines are deterministic the results presented in the paper significantly extend knowledge on behavior of the optimal solutions to the sjd problem in the asymptotical case

existence of a positive solution for one dimensional singular p laplacian problems and its parameter dependence article history we consider one dimensional singular p laplacian problems of the form q 1 and may be singular at t 0a nd ort 1 using fixed point techniques combined with the partially ordered structure of banach space we establish some new and more general existence multiplicity and nonexistence results we also study the dependence of the positive solution u t on the parameter t hat is

existence and uniqueness results for the bending of an elastic beam equation at resonance etude d un probleme non lineaire aux valeurs limites pour la flexion d une poutre elastique en appui simple aux deux extremites dans le cas de resonance theoremes d existence et d unicite

a mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints this study investigates scheduling problems that occur when the weighted number of late jobs that are subject to deterministic machine availability constraints have to be minimized these problems can be modeled as a more general job selection problem cases with resumable non resumable and semi resumable jobs as well as cases without availability constraints are investigated the proposed efficient mixed integer linear programming approach includes possible improvements to the model notably specialized lifted knapsack cover cuts the method proves to be competitive compared with existing dedicated methods numerical experiments on randomly generated instances show that all 350 job instances of the test bed are closed for the well known problem 1 r i sum w iu i for all investigated problem types 98 4 of 500 job instances can be solved to optimality within one hour

existence and uniqueness of fixed points for some mixed monotone operators abstract in this paper we introduce the e concave convex operator without any compact or continuous assumptions we prove the existence and uniqueness of fixed points giving monotone iterative sequences for the unique fixed point for the operator finally we apply the results to an integral equation of polynomial type which possesses items of measurable functions

new fixed point theorems and applications of mixed monotone operator in this paper we study the uniqueness and existence of fixed point of mixed monotone operators in the partially ordered banach space the results extend and improve recent related results

improved upper bounds for the solution of the continuous algebraic riccati matrix equation in this paper we present upper bounds for the solution matrix of the continuous algebraic riccati matrix equation care by utilizing some matrix inequalities and linear algebraic techniques also for the derived each bounds iterative algorithms are developed to obtain tighter solution estimates having compared some appearing results in the literature the obtained bounds are less restrictive and more efficient finally numerical examples are given to illustrate the effectiveness of the proposed results

new results for the bounds of the solution for the continuous riccati and lyapunov equations this paper presents upper and lower matrix bounds for the solution of the continuous algebraic matrix riccati equation furthermore a new lower matrix bound for the solution of the continuous algebraic lyapunov equation is also developed these are new results

bounds for the solution of the lyapunov matrix equation a unified approach abstract in recent years several bounds have been reported for the solution of the continuous and the discrete lyapunov equations using the unified lyapunov equation we give in this paper bounds for the solution of this equation in the limiting cases the bounds reduce to existing bounds for both the continuous and discrete lyapunov equations

matrix bounds of the solutions of the continuous and discrete riccati equations a unified approach in this paper a new scheme is introduced to measure the matrix bounds of the continuous and discrete riccati equations by estimating upper and lower matrix bounds of the solution of the unified algebraic riccati equation uare the same measurements for the solutions of the continuous and discrete riccati equations respectively can be obtained in limiting cases according to these obtained matrix bounds several eigenvalue bounds are also defined all the proposed results for the uare are new and more general than previous work some obtained results are compared with those of the literature via numerical examples it is shown that in some cases the presented results are tighter than the existing ones

coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces abstract the purpose of this paper is to establish a coupled coincidence point for a pair of commuting mappings in partially ordered complete metric spaces we also present a result on the existence and uniqueness of coupled common fixed points an example is given to support the usability of our results

improved bounds for the eigenvalues of solutions of lyapunov equations bounds on the solution and on the eigenvalues of the solution of the discrete and of the continuous matrix lyapunov equations are presented these bounds are nontrivial in the case of system matrices having multiple eigenvalues especially in the latter case these bounds are better than bounds found in the literature further these bounds are sharp i e there exist systems such that the lower and upper bounds coincide yielding the solution or its eigenvalues respectively

coupled fixed points of nonlinear operators with applications a partir de quasi solutions couplees des problemes aux valeurs initiales pour des equations differentielles ordinaires on introuit le concept de points fixes couples abstraits pour certains operateurs on donne des theoremes d existence

a statistical comparative study of different similarity measures of consensus in group decision making an essential aim in group decision making gdm problems is to achieve a high level of consensus among experts consensus is defined as general or widespread agreement and it is usually modelled mathematically via a similarity function measuring how close experts opinions or preferences are similarity functions are defined based on the use of a metric describing the distance between experts opinions or preferences in the literature different metrics or distance functions have been proposed to implement in consensus models but no study has been carried out to analyse the influence the use of different distance functions can have in the gdm process this paper presents a comparative study of the effect of the application of some different distance functions for measuring consensus in gdm by using the nonparametric wilcoxon matched pairs signed ranks test it is concluded that different distance functions can produce significantly different results moreover it is also shown that their application also has a significant effect on the speed of achieving consensus finally these results are analysed and used to derive decision support rules based on a convergent criterion that can be used to control the convergence speed of the consensus process using the compared distance functions

on the discrete lyapunov matrix equation some bounds for the arithmetic and the geometric means of the characteristic roots of the positive semidefinite solution to the discrete lyapunov matrix equation are derived

new fixed point theorems of mixed monotone operators and applications in this paper a class of mixed monotone operators with convexity and concavity are investigated and existence and uniqueness theorems of fixed points are obtained moreover some applications to nonlinear integral equations on unbounded regions and differential equations in banach spaces are given

integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations abstract the purpose of this paper is to study a fuzzy multipurpose decision making problem where the information about the alternatives provided by the experts can be of a diverse nature the information can be represented by means of preference orderings utility functions and fuzzy preference relations and our objective is to establish a general model which cover all possible representations firstly we must make the information uniform using fuzzy preference relations as uniform preference context secondly we present some selection processes for multiple preference relations based on the concept of fuzzy majority fuzzy majority is represented by a fuzzy quantifier and applied in the aggregation by means of an owa operator whose weights are calculated by the fuzzy quantifier we use two quantifier guided choice degrees of alternatives a dominance degree used to quantify the dominance that one alternative has over all the others in a fuzzy majority sense and a non dominance degree that generalises orlovski s non dominated alternative concept the application of the two above choice degrees can be carried out according to two different selection processes a sequential selection process and a conjunction selection process