‎we say that a module $m$ is a emph{cms-module} if‎, ‎for every cofinite submodule $n$ of $m$‎, ‎there exist submodules $k$ and $k^{'}$ of $m$ such that $k$ is a supplement of $n$‎, ‎and $k$‎, ‎$k^{'}$ are mutual supplements in $m$‎. ‎in this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎in particular‎, ‎we prove tha...

We study some of the combinatorial structures related to the signature of G-symmetric products of (open) surfaces SP m G (M) = M /G where G ⊂ Sm. The attention is focused on the question what information about a surface M can be recovered from a symmetric product SP (M). The problem is motivated in part by the study of locally Euclidean topological commutative (m + k, m)-groups, [16]. Emphasizi...

In $26+1$ space-time dimensions, we introduce a gravity theory whose massless spectrum can be acted upon by the Monster group when reduced to $25+1$ dimensions. This generalizes M-theory in many respects and name it Monstrous M-theory, or M$^{2}$-theory. Upon Kaluza-Klein reduction M$^{2}$-theory irreducibly splits as $\mathbf{1}\oplus\mathbf{196,883}$, where $\mathbf{1}$ is identified with dil...

let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...

The main result of the work “The nilpotence conjecture in K-theory of toric varieties” is extended to all coefficient fields of characteristic 0, thus covering the class of genuine toric varieties. 1. The statement Let R be a (commutative) regular ring, M be arbitrary commutative, cancellative, torsion free monoid without nontrivial units, and i be a nonnegative integral number. The nilpotence ...

Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k ≤ n − 3. The smooth Yamabe invariants σ(M) and σ(N) satisfy σ(N) ≥ min(σ(M),Λ) for Λ > 0. We derive explicit lower bounds for Λ in dimensions where previous methods failed, namely for (n, k) ∈ {(4, 1), (5, 1), (5, 2), (9, 1), (10, 1)}. With methods from surgery theory and bordism ...

Kubelka–Munk (K-M) theory is a phenomenological light transport theory that provides analytical expressions for reflectance and transmittance of diffusive substrates such as tissues. Many authors have derived relations between coefficients of K-M theory and that of the more fundamental radiative transfer equations. These relations are valid only in diffusive light transport regime where scatter...