riemann integrability and lebesgue measurability of the composite function abstract if f is continuous on the interval a b g is riemann integrable resp lebesgue measurable on the interval and g a b then f g is riemann integrable resp measurable on a well known fact on the other hand states that f g might not be riemann integrable resp measurable when f is riemann integrable resp measurable and g is continuous if c stands for the continuum in this paper we construct a 2 c dimensional space v and a c dimensional space w of respectively riemann integrable functions and continuous functions such that for every f v 0 and g w 0 f g is not riemann integrable showing that nice properties such as continuity or riemann integrability can be lost in a linear fashion via the composite function similarly we construct a c dimensional space w of continuous functions such that for every g w 0 there exists a c dimensional space v of measurable functions such that f g is not measurable for all f v 0

difference approximations for the second order wave equation difference approximations are derived for the second order wave equation in one and two space dimensions without first writing it as a first order system both the dirichlet and the neumann problems are treated for the one dimensional case relations between the boundary error and the interior phase error are derived for a fully second order accurate discretization as well as a scheme that is fourth order accurate in the interior and second order accurate at the boundary general two dimensional domains are considered for the dirichlet problem where the domain is embedded in a cartesian grid and the boundary conditions are approximated by interpolation a stable conservative scheme is derived where the time step is determined only by the interior discretization formula discretization cells cut by the boundary are treated implicitly but the resulting scheme becomes explicit because the implicit dependence only is pointwise numerical examples are provided to verify the stability and accuracy of the proposed method

nonseparable spaceability and strong algebrability of sets of continuous singular functions abstract let cbv denote the banach algebra of all continuous real valued functions of bounded variation defined in 0 1 we show that the set of strongly singular functions in cbv is nonseparably spaceable we also prove that certain families of singular functions constitute strongly c algebrable sets the argument is based on a criterion of strong c algebrability using compositions with exponential like functions

lineability and integrability in the sense of riemann lebesgue denjoy and khintchine abstract in this paper we continue the ongoing research on lineability related questions on this occasion we shall consider among others the classes of integrable functions in the sense of riemann lebesgue denjoy and khintchine improving some already known results and expanding the study of lineability to other famous integrable classes never considered before

on richardson extrapolation for fitted operator finite difference methods abstract recently there has been a great interest towards the higher order methods for singularly perturbed problems as compared to their lower order counterparts they provide better accuracy with fewer mesh points construction and or implementation of direct higher order methods is usually very complicated thus a natural choice is to use some convergence acceleration techniques e g richardson extrapolation however as we see in this article such techniques do not perform equally well on all type of methods to investigate this we consider two fitted operator finite difference methods fofdms developed by patidar k c patidar high order fitted operator numerical method for self adjoint singular perturbation problems appl math comput 171 1 2005 547 566 and lubuma and patidar j lubuma k c patidar uniformly convergent non standard finite difference methods for self adjoint singular perturbation problems j comput appl math 191 2006 228 238 referred to as fofdm i and fofdm ii respectively the fofdm i is fourth and second order accurate for moderate and smaller values of e respectively unfortunately richardson extrapolation does not improve the order of this method the fofdm ii is second order uniformly convergent and we show that its order can be improved up to four by using richardson extrapolation both the methods are analyzed for convergence and comparative numerical results supporting theoretical estimates are provided

ordinal criteria in stochastic multicriteria acceptability analysis smaa abstract we suggest a method for providing descriptive information about the acceptability of decision alternatives in discrete co operative group decision making problems the new smaa o method is a variant of the stochastic multicriteria acceptability analysis smaa smaa o is designed for problems where criteria information for some or all criteria is ordinal that is experts or decision makers have ranked the alternatives according to each ordinal criterion considerable savings can be obtained if rank information for some or all the criteria is sufficient for making decisions without significant loss of quality the approach is particularly useful for group decision making when the group can agree on the use of an additive decision model but only partial preference information or none at all is available

on algebrability of nonabsolutely convergent series we prove that the set of all complex series which are nonabsolutely convergent is c algebrable we establish a similar result for the set of all divergent complex series with bounded partial sums

correlations and copulas for decision and risk analysis the construction of a probabilistic model is a key step in most decision and risk analyses typically this is done by defining a joint distribution in terms of marginal and conditional distributions for the model s random variables we describe an alternative approach that uses a copula to construct joint distributions and pairwise correlations to incorporate dependence among the variables the approach is designed specifically to permit the use of an expert s subjective judgments of marginal distributions and correlations the copula that underlies the multivariate normal distribution provides the basis for modeling dependence but arbitrary marginals are allowed we discuss how correlations can be assessed using techniques that are familiar to decision analysts and we report the results of an empirical study of the accuracy of the assessment methods the approach is demonstrated in the context of a simple example including a study of the sensitivity of the results to the assessed correlations

multivariate gaussian criteria in smaa abstract we consider stochastic multicriteria decision making problems with multiple decision makers in such problems the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions in many real life problems the uncertainties of criteria measurements may be dependent however it is often difficult to quantify these dependencies also most of the existing methods are unable to handle such dependency information in this paper we develop a method for handling dependent uncertainties in stochastic multicriteria group decision making problems we measure the criteria their uncertainties and dependencies using a stochastic simulation model the model is based on decision variables and stochastic parameters with given distributions based on the simulation results we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies we then use the smaa 2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions we demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated european electricity market

note a preference ranking organisation method the promethee method for multiple criteria decision making principles for a new family of outranking methods are given the main aim of the proposed promethee approach is to be as easily understood as possible by the decision maker it is based on extensions of the notion of criterion six possible extensions are considered these extensions can easily be identified by the decision maker because the parameters to be defined at most 2 have an economic significance a valued outranking graph is constructed by using a preference index two possibilities are considered to solve the ranking problem by using this valued graph promethee i provides a partial preorder and promethee ii a total preorder on the set of the possible actions

large free linear algebras of real and complex functions let x be a set of cardinality such that we prove that the linear algebra rx or cx contains a free linear algebra with 2 generators using this we prove several algebrability results for spaces cc and rr in particular we show that the set of all perfectly everywhere surjective functions f c c is strongly 2c algebrable we also show that the set of all functions f r r whose sets of continuity points equals some fixed g set g is strongly 2c algebrable if and only if r g is c dense in itself

additivity and lineability in vector spaces abstract gamez merino munoz fernandez and seoane sepulveda proved that if additivity a f c then f is a f lineable where f r r they asked if a f c can be weakened we answer this question in negative moreover we introduce and study the notions of homogeneous lineability number and lineability number of subsets of linear spaces

a method for stochastic multiple criteria decision making based on dominance degrees this paper proposes a method for solving the stochastic multiple criteria decision making smcdm problem where consequences of alternatives with respect to criteria are represented by random variables with probability distributions firstly definitions and related analysis of dominance degree of one probability distribution over another are given then by calculating the dominance degrees the dominance degree matrix of alternative pairwise comparisons with respect to each criterion is built further using promethee ii method an overall dominance degree matrix of alternative pairwise comparisons is constructed and a net flow of each alternative is calculated based on the obtained net flows a ranking of alternatives is determined finally numerical examples for the three cases are given to illustrate the use of the proposed method

pseudo criteria versus linear utility function in stochastic multi criteria acceptability analysis abstract stochastic multi criteria acceptability analysis smaa is a multi criteria decision support method for multiple decision makers dms in discrete problems smaa does not require explicit or implicit preference information from the dms instead the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one partial preference information can be represented in the weight space analysis through weight distributions in this paper we compare two variants of the smaa method using randomly generated test problems with 2 12 criteria and 4 12 alternatives in the original smaa a utility or value function models the dms preference structure and the inaccuracy or uncertainty of the criteria is represented by probability distributions in smaa 3 electre iii type pseudo criteria are used instead both methods compute for each alternative an acceptability index measuring the variety of different valuations that supports this alternative and a central weight vector representing the typical valuations resulting in this decision we seek answers to three questions 1 how similar are the results provided by the decision models 2 what kind of systematic differences exists between the models and 3 how could one select indifference and preference thresholds of the pseudo criteria model to match a utility model with given probability distributions

smaa 2 stochastic multicriteria acceptability analysis for group decision making stochastic multicriteria acceptability analysis smaa is a multicriteria decision support method for multiple decision makers in discrete problems in smaa the decision makers need not express their preferences explicitly or implicitly instead the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one inaccurate or uncertain criteria values are represented by probability distributions from which the method computes confidence factors describing the reliability of the analysis in this paper we introduce the smaa 2 method which extends the original smaa by considering all ranks in the analysis in situations where the elitistic smaa may assess large acceptability only for extreme alternatives without sufficient majority support the more holistic smaa 2 analysis can be used to identify good compromise candidates the results are presented graphically we consider also situations where partial preference information is available we demonstrate the new method using a real life decision problem

maximum norm error estimates of efficient difference schemes for second order wave equations the three level explicit scheme is efficient for numerical approximation of the second order wave equations by employing a fourth order accurate scheme to approximate the solution at first time level it is shown that the discrete solution is conditionally convergent in the maximum norm with the convergence order of two since the asymptotic expansion of the difference solution consists of odd powers of the mesh parameters time step and spacings an unusual richardson extrapolation formula is needed in promoting the second order solution to fourth order accuracy extensions of our technique to the classical adi scheme also yield the maximum norm error estimate of the discrete solution and its extrapolation numerical experiments are presented to support our theoretical results

integral analysis method iam this paper presents the theoretical foundations of the new integral analysis method iam and its application to a facility location problem this methodology integrates the cardinal and ordinal criteria of combinatorial stochastic optimization problems in four stages definition of the problem cardinal analysis ordinal analysis and integration analysis the method uses the concepts of stochastic multicriteria acceptability analysis smaa monte carlo simulation optimization techniques and elements of probability the proposed method iam was used to determine optimal locations for the retail stores of a colombian coffee marketing company

smaa stochastic multiobjective acceptability analysis stochastic multiobjective acceptability analysis smaa is a multicriteria decision support technique for multiple decision makers based on exploring the weight space inaccurate or uncertain input data can be represented as probability distributions in smaa the decision makers need not express their preferences explicitly or implicitly instead the technique analyses what kind of valuations would make each alternative the preferred one the method produces for each alternative an acceptability index measuring the variety of different valuations that support that alternative a central weight vector representing the typical valuations resulting in that decision and a confidence factor measuring whether the input data is accurate enough for making an informed decision

an alternating direction implicit method for a second order hyperbolic diffusion equation with convection a numerical method is presented to solve a two dimensional hyperbolic diffusion problem where is assumed that both convection and diffusion are responsible for flow motion since direct solutions based on implicit schemes for multidimensional problems are computationally inefficient we apply an alternating direction method which is second order accurate in time and space the stability of the alternating direction method is analyzed using the energy method numerical results are presented to illustrate the performance in different cases

a numerical algorithm for the solution of telegraph equations abstract in this paper we present a new competitive numerical scheme to solve nonlinear telegraph equations the method is based on rothe s approximation in time discretization and on the wavelet galerkin in the spatial discretization the approximate solutions converge in the space c 0 t l 2 l 2 0 t w 0 1 2 to the variational solution a full error analysis is performed and a numerical experiment is given to illustrate the good convergence behavior of the approximate solution

an alternating direction galerkin method for a class of second order hyperbolic equations in two space variables a new alternating direction implicit adi galerkin method is devised and analyzed for solving a certain class of second order hyperbolic initial boundary value problems in two space variables this class includes the wave equation in cartesian coordinates polar coordinates and cylindrical coordinates with radial symmetry optimal a priori h 0 1 and l 2 error estimates are derived

lineability and algebrability of pathological phenomena in analysis we show that in analysis many pathological phenomena occur more often than one could expect that is in a linear or algebraic way we show this by means of the construction of large algebraic structures infinite dimensional vector spaces or infinitely generated algebras enjoying some special or pathological properties