Let D be a division ring, T be a variable over D, σ be an endomorphism of D, δ be a σ-derivation on D and R = D[T ;σ, δ] the left skew polynomial ring over D. We show that the set (V alν(R), ) of σ-compatible real valuations which extend to R a fixed proper real valuation ν on D has a natural structure of parameterized complete non-metric tree, where is the partial order given by μ μ̃ if and onl...

We investigate the athermal characteristics of silicon waveguides clad with TiO(2) designed for 1.3 µm wavelength operation. Using CMOS-compatible fabrication processes, we realize and experimentally demonstrate silicon photonic ring resonators with resonant wavelengths that vary by less than 6 pm/°C at 1.3 µm. The measured ring resonance wavelengths across the 20-50°C temperature range show ne...

‎Let $mathcal{A}$ be a unital Banach algebra‎, ‎$mathcal{M}$ be a left $mathcal{A}$-module‎, ‎and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$‎. ‎We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a Jordan left de...

in this work, we investigate the transfer of some homological properties from a ring $r$ to its amalgamated duplication along some ideal $i$ of $r$ $rbowtie i$, and then generate new and original families of rings with these properties.

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...

This paper is concerned with the probability of consensus in a multivariate, spatially explicit version Hegselmann-Krause model for dynamics opinions. Individuals are located on vertices finite connected graph representing social network, and characterized by their opinion, set opinions $\Delta$ being general bounded convex subset dimensional normed vector space. Having confidence threshold $\t...