In this work, we introduced and studied  a new kind of soft mapping  on soft topological spaces with an ideal, which we called  soft strongly generalized mapping with respect an ideal I, we studied the concepts like SSIg-continuous, Contra-SSIg-continuous, SSIg-open, SSIg-closed and SSIg-irresolute mapping  and  the relations between these kinds of mappings and the composition of two mappings of the same type of two different types, with proofs or counter examples

      Let S be a commutative ring with identity, and A is an S-module. This paper introduced an important concept, namely strongly maximal submodule. Some properties and many results were proved as well as the behavior of that concept with its localization was studied and shown.

            Density Functional Theory (DFT) method of the type (B3LYP) and a Gaussian basis set (6-311G) were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) at the equilibrium geometry of the Di and Tetra-rings layer (6, 0) zigzag single wall carbon nanotubes (SWCNTs) by using Gaussian-09 program. Both were found to have the same symmetry of D_6d point group with C--C bond alternation in all tube rings (for axial bonds, which are the vertical C--Ca bonds in rings layer and for circumferential bonds C—Cc in the outer and mid rings bonds). Assignments of the modes of vibration IR active and inactive vibration frequ

A variety of liquid crystals comprising heterocyclics 1,3,4-oxadiazol ring [III], aminooxazol [IV]a, and aminothiazol [IV]b were synthesized through a number of steps, beginning of the reaction of 3, 3'- dimethyl - [1, 1'-biphenyl] -4, 4'- diamin, ethyl monochloroacetate and sodium acetate to synthesize diacetate compound[I]. The diester reacted with hydrazine hydrate(N2H4-H2O) to give dihydrazide compound [II], then reacted with Pyruvic acid and phosphorous oxychloride to produce diketone compound [III]. The last compound was reacted with urea and thiourea to give aminooxazol and aminothiazol respectively. The synthesized compounds actually characterized and determined the structures by melting points, FT-IR and 1H-NMR spectroscopies. By u

Some new 2,5-disubsituted-1,3,4-oxadiazole derivatives with azo group were synthesized by known reactions sequence . The structure of the synthesized compounds were confirmed by physical and spectral means .

In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.

We present the concept of maps Γ- periodi2 on Γ -near-ring S. Our main goal is to research and explore the presence and mapping traits such as h Γ –hom anti-Γ –hom, Γ –α-derivations of Γ -periodi2 on Γ- near-rings.

The compound 3-[4Ì„-(4Ë­-methoxy benzoyloxy) benzylideneamino]-2-thioxo-imidazolidine-4-one [III] was prepared from the cyclization of thiosemicarbazone [II] with
ethyl α -chloroacetate in the presence of fused sodium acetate. Treatment the later compound
with acetic anhydride yielded the corresponding 1-Acetyl-3-[ 4Ì„- (4Ë­- methoxy benzoyloxy)
benzylideneamino] – 2 – thioxo -imidazolidine-4-one [IV]. 1,3-Oxazepine derivatives [V]a-d
and [VI]a-d are obtained from the reaction of compounds[III] and [IV] with different acid
anhydrides, in dry benzene. The FTIR and
1
HNMR spectroscopy are indicated a good
evidence for the formation of the synthesized compounds. Some of the synthesized

 The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals of near-rings and some related properties. Interesting results have been reached, the most prominent of which are the following: Let M be a 3-prime left near-ring and A_1,A_2,…,A_n are nonzero semigroup ideals of M, if d is a right n-derivation of M satisfies on of the following conditions,
d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=0 ∀u_1,v_1 〖ϵA〗_1,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u ;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=(u_