According to a currently popular principle of classification, mathematics is the study of various "categories. " A category consists of certain "objects" (e.g., groups, topological spaces) and certain "mappings" (e.g., homomorphisms, continuous functions). One possible category has measure spaces for its objects and, correspondingly, measure-preserving transformations for its mappings. The usua...

A simulation study was conducted to address the issue of how purely additive (simple) genetic architecture might impact on the efficacy of parametric and non-parametric genomic prediction methods. For this purpose, we simulated a trait with narrow sense heritability h2= 0.3, with only additive genetic effects for 300 loci in order to compare the predictive ability of 14 more practically used ge...

Necessary and sufficient conditions are given for the existence of a countably additive extension of a given finite measure in the case of any finite or disjoint countable perturbation of its -algebra. It provides a complete description of all countably additive extensions of finite measures in such cases. In particular, simple characterizations are obtained for the existence of some extremal c...

In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...

Interdependency among system parameters may significantly affect the cross-layer design and optimization performance of wireless networks. However, it is very difficult to derive the interdependency among system parameters in a dynamic complex networking system due to the uncertainty of data observation and system modeling. In this research, we propose a new approach for dynamic interdependency...

to estimate combining ability and the model of gene action for some quantitative characters, 5 different rice genotypes were used for producing a half diallel hybrids. to consider 7 quantitative traits, hybrids and their corresponding parents were evaluated based on a randomized complete block design with three replications at the rice research station of amol, iran in 2007. mean squares regard...

On arbitrary topological groups a natural finitely additive measure can be defined via compactifications. It is closely related to Hartman’s concept of uniform distribution on non-compact groups (cf. [Ha]). Applications to several situations are possible. Some results of M. Paštéka and other authors on uniform distribution with respect to translation invariant finitely additive probability meas...