In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.

Watermarking operation can be defined as a process of embedding special wanted and reversible information in important secure files to protect the ownership or information of the wanted cover file based on the proposed singular value decomposition (SVD) watermark. The proposed method for digital watermark has very huge domain for constructing final number and this mean protecting watermark from conflict. The cover file is the important image need to be protected. A hidden watermark is a unique number extracted from the cover file by performing proposed related and successive operations, starting by dividing the original image into four various parts with unequal size. Each part of these four treated as a separate matrix and applying SVD

We claim that a proper subact Ṅ have been compactly packed (c.P) in generalization idea of c.P modules to S Acts. whether for all family of prime subact {Pα}(α∈λ) for some β∈λ Pβ ⊇ Ṅ when ∪(α∈λ)Pα, ⊇ N. We refer to an S-Act Ṁ as c.P. if every subact is compactly packed. We study various properties of c.P S-Acts.

Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if  for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph K_n, Complete bipartite graph K_m,n and Complete tripartite graph K_l,m,n. It has also been studied how the lucky number changes whi

In the current study, different concentrations of miltefosine drug, which is the first effective and safe oral treatment for visceral leishmaniasis, was evaluated against L. donovani promastigotes in comparison with pentosam drug. Direct counting microscopic assay was used to find 50% inhibitory concentration (IC50) of miltefosine and pentostam against L. donovani promastigotes. The IC50 of miltefosine drug was 45.42μg/ml, 46.76μg/ml and 36.68μg/ml after 24 hr, 48hr and 72hr respectively, In comparison with IC 50 of pentostam drug was 75.39 μg/ml after 72hr. There were significant differences (P˂0.05) between IC50 values of miltefosine and pentostam drugs from first day to third day.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.