In this paper, we first show that a wavelength division multiplexed (WDM) split crossconnect is strictly, wide-sense, or rearrangeably non-blocking if and only if a corresponding 3-stage Clos network is strictly, wide-sense or rearrangeably non-blocking. This observation implies known results on strictly non-blocking WDM split cross-connects and gives rise to new results on wide-sense and rearr...

The work of Chevalley ([BIBLE], [Chev61]) and Demazure–Grothendieck [SGA3] provides a satisfactory understanding of the reasons for the existence and uniqueness of “Chevalley groups” over Z. These are the reductive group schemes G → Spec(Z) (i.e., smooth affine groups with connected reductive geometric fibers) for which there exists closed subtorus T ⊂ G over Z that is maximal on geometric fibe...

A dominating set D of an IFG G = (V, E) is a non-split dominating set, if the induced intuitionistic fuzzy subgraph 〈ܸ − ‫〉ܦ‬ is connected. The Non-split domination number ߛ ௡௦ ሺ‫ܩ‬ሻ of IFG G is the minimum cardinality of all Non-split dominating set. In this paper we study some theorems in Non-split dominating sets of IFG and some results of ߛ ௡௦ ሺ‫ܩ‬ሻwith other known parameters of IFG G. 1. In...

Here, I study the problem of classification non-split supermanifolds having as retract split supermanifold $(M,\Omega)$, where $\Omega$ is sheaf holomorphic forms on a given complex manifold $M$ dimension $> 1$. propose general construction associating with any $d$-closed $(1,1)$-form $\omega$ $(M,\Omega)$ which whenever Dolbeault class non-zero. In particular, this gives non-empty family for f...

Non-malleable codes are a generalization of classical errorcorrecting codes where the act of “corrupting” a codeword is replaced by a “tampering” adversary. Non-malleable codes guarantee that the message contained in the tampered codeword is either the original messagem, or a completely unrelated one. In the common split-state model, the codeword consists of multiple blocks (or states) and each...

Non-Malleable Codes for the split state model allow to encode a message into two parts such that arbitrary independent tampering on the parts either destroys completely the content or maintains the message untouched. If the code is also leakage resilient it allows limited independent leakage from the two parts. We propose a model where the two parts can be refreshed independently. We give an ab...

The concept of connectedness plays an important role in many networks. Digraphs are considered as an excellent modeling tool and are used to model many types of relations amongst any physical situations. In this paper the concept of strong non-split domination in directed graph D has been introduced by considering the dominating set S is a strong non-split dominating set if the complement of S ...