A bipartite graph with vertex sets X and Y is a triple {X, Y; E), where £ is a subset of X x Y, and a graph with vertex set X is a pair (X; £), where £ is a symmetric subset of X x X minus the diagonal. Nash-Williams [15] proposed the following generalization of these concepts. Let {X,$4,\x) and (Y, 08, v) be measure spaces. A bipartite measure graph with vertex sets X and Y is a triple (X, Y; ...

Here, instead of taking a σ-algebra as given and then defining a measure on this σ-algebra (namely, on the measurable sets), we take an outer measure as given and then define measurable sets using this outer measure. Carathéodory’s theorem states that the collection M of ν-measurable sets is a σ-algebra and that the restriction of ν to M is a complete measure. Suppose that (X, ρ) is a metric sp...

introduction: in this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. epilepsy is considered as a dynamical change in nonlinear and complex brain system. the ability of the proposed measure for characterizing the normal and epileptic eeg signals when the signal is short or is...

the non-differentiability and implicit definition of boundary of production possibility set (pps) in data envelopment analysis (dea) are two important difficulties for obtaining directional characteristics, including different elasticity measures and marginal rates of substitution. also, imposing weight restrictions in dea models have some shortcomings and misunderstandings. in this paper we ut...

data envelopment analysis (dea) is a method for measuring the efficiency of peer decision making units (dmus) with multiple inputs and outputs. the traditional dea treats decision making units under evaluation as black boxes and calculates their efficiencies with first inputs and last outputs. this carries the notion of missing some intermediate measures in the process of changing the inputs to...

simple harmonizable processes (shp) introduced by soltani and parvardeh (2006) are a large class of nonstationary processes which includes stationary and periodically correlated (pc) processes. detection and estimation of shp structure are important problems when dealing with nonstationary data. in this paper, we study the spectral properties of simple processes and propose a method to detect a...

the purpose of this study has been concretized in terms of impact of mobileadvertising on the purchase decision of the consumer and aimed to answer toresearch questions: which is the underlying structure of criteria in mobileadvertising? and which criteria are important for consumers in evaluatingmobile advertising? a sample of consumers in taiwan was surveyed and usingfuzzy judgment to determi...

recommender systems (rs) provide personalized recommendation according to user need by analyzing behavior of users and gathering their information. one of the algorithms used in recommender systems is user-based collaborative filtering (cf) method. the idea is that if users have similar preferences in the past, they will probably have similar preferences in the future. the important part of col...

We study the almost Mathieu operator: 1) + cos(2n +)u(n), on l 2 (Z), and show that for all ; , and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely j4 ? 2jjj. In particular, for jj = 2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and jj = 2) we show that the Hausdorr dimension of the spectrum is smaller than or equal to 1=2.