Given two metric spaces S1, S2 and a measurable function f : S1 → S2, sup­ pose S1 is equipped with some probability measure P. This induces a proba­ bility measure on S2 which is denoted by Pf−1 and is defined by Pf−1(A) = P(f−1(A)) for every measurable set A ⊂ S2. Then for any random variable X : S2 → R, its expectation EPf−1 [X] is equal to EP[X(f)]. (Convince your­ self that this is the cas...

Biomedicine requires materials able to respond specific needs without affecting the organism. Organic–inorganic fibrillar polymeric matrices possess unique properties that may fulfill these needs. In present study, different topology-controlled poly(ε-caprolactone)-based containing glycine betaine at varying concentrations (0.5, 1, and 2% w/v) were prepared via electrospinning. The used as subs...

we give the concept of ‘braiding’ for 2-groupoids, and we show that this structure is equivalent tobraided regular, crossed modules.

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In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called affine subgroups., the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_{6}(2...

in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...