In this research investigation, a total of eighteen diverse tetra- and penta-lateral cyclic compounds were synthesized. These included 1,3,4-thiadiazole, thiazolidin-4-one (via an alternative method), 1,2,4-triazole, carbothioamide, thiazole-4-one, azetidin-2-one, and oxazole. The synthesis procedure entailed a sequence of reactions. The thiazolidine-4-one 1 was obtained by reaction p-aminobenzoic acid with thiosemicarbazide, followed by treatment with p-tolualdehyde to produce Schiff base 2. Reaction Schiff base 2 with mercaptoacetic acid in dry benzene was carried out to produce thiazolidine-4-one 3. In another synthesis pathway, the esterification of p-nitro benzoic acid with ethanol in the presence of sulfuric acid was

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

In this paper we define and study new concepts of functions on fibrewise  topological spaces  over  B namely,  fibrewise  weakly  (resp., closure, strongly) continuoac; funttions which are analogous of weakly

(resp., closure,   strongly)   continuous  functions   and  the  main  result is   : Let  <p       : XY  be a fibrewise  closure  (resp.,  weakly,  closure, strongly,  strongly) continuous function,  where  Y  is fibrewise topological  space  over  B and  X  is  a  fibrewise set  which  has  the

in

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.

The family Ormyridae has been very much neglected by workers and only two species has been recorded so far from Iraq. The present study, based mainly on my collection, deals with five species, of which one is new to science. The new species is described together with notes on locality data, host records, distribution and taxonomical remarks for all the species.

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 this paper we give many connections between essentially quasi-Dedekind (quasi-
Dedekind) modules and other modules such that Baer modules, retractable modules,
essentially retractable modules, compressible modules and essentially compressible
modules where an R-module M is called essentially quasi-Dedekind (resp. quasi-
Dedekind) if, Hom(M N ,M )  0 for all N ≤e M (resp. N ≤ M). Equivalently, a
module M is essentially quasi-Dedekind (resp. quasi-Dedekind) if, for each
f End (M) R  , Kerf ≤ e M implies f = 0 (resp. f  0 implies ker f  0 ).

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.