We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...

structural and magnetic properties of purine and pyrimidine nucleotides (cmp, ump, dtmp, amp, gmp, imp) were studied at different levels of ab initio molecular orbital theory. these calculations were performed at the hartree-fock level and density functional b3lyp methods. geometries were fully optimized by following cs symmetry restrictions. the standard 6-31g** basis set which includes polari...

introduction: there is many ways to assessing the electrical conductivity anisotropy of a tumor. applying the values of tissue electrical conductivity anisotropy is crucial in numerical modeling of the electric and thermal field distribution in electroporation treatments. this study aims to calculate the tissues electrical conductivity anisotropy in patients with sarcoma tumors using diffusion ...

mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. in theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. the wiener polarity index ...

In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

1 Tensor Categories 4 Extending ̋ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Invertible objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Internal Hom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Rigid tensor categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Tensor functors . . . . ...