For a field F, let R(n,m) be the ring of invariant polynomials for the action of SL(n,F) × SL(n,F) on tuples of matrices – (A,C) ∈ SL(n,F)× SL(n,F) sends (B1, . . . , Bm) ∈ M(n,F) to (AB1C , . . . , ABmC ). In this paper we call R(n,m) the ring of matrix semi-invariants. Let β(R(n,m)) be the smallest D s.t. matrix semi-invariants of degree ≤ D generate R(n,m). Guided by the Procesi-Razmyslov-Fo...

In this study, the reaction of 3-Picrylamino-1, 2, 4-Triazole (PATO) with B12N12 was investigated by density functional theory in the B3LYP/6-31G(d) level of theory. There were two possible isomers for reaction of PATO with B12N12 via carbon and nitrogen atoms of triazole ring to the Born atom of B12N12 (I and II-isomers). Thermo...

In this study, the reaction of 3-Picrylamino-1, 2, 4-Triazole (PATO) with B12N12 was investigated by density functional theory in the B3LYP/6-31G(d) level of theory. There were two possible isomers for reaction of PATO with B12N12 via carbon and nitrogen atoms of triazole ring to the Born atom of B12N12 (I and II-isomers). Thermo...

A group of 1,3-biarylhydrazide derivatives possessing a COX-2 azido pharmacophore at the Para- position of the C-1 phenyl ring in conjunction with a N-3 phenyl or substituted-phenyl ring (4-F,4-Cl,4-OMe) were designed and synthesized based on nucleophilic substitution reaction. A molecular modelling study of these compounds showed that the designed molecules were well bound with the active site...

A ring R is called clean if every element of the sum a unit and an idempotent. Motivated by question proposed Lam on cleanness von Neumann Algebras, Vaš introduced more natural concept for ?-rings, ?-cleanness. More precisely, ?-ring ?- projection (?-invariant idempotent). Let F be finite field G abelian group. In this paper, we introduce two classes involutions group rings form characterize ?-...

We introduce center-like subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a non-identity epimorphism and R a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of R.

The title compound, C(15)H(13)F(3)N(2)O, contains one benzene ring, one cyclo-hexane ring and a pyridazine ring. The dihedral angle formed by the pyridazine ring with the benzene ring is 61.5 (2)°. The crystal structure is stabilized by two inter-molecular hydrogen bonds (N-H⋯O and C-H⋯F). The cyclohexane ring adopts a screw-boat conformation. The CF(3) group is disordered over two positions; t...

‎Let $R$ be a noncommutative prime ring of‎ ‎characteristic different from $2$‎, ‎$U$ the Utumi quotient ring of $R$‎, ‎$C$ $(=Z(U))$ the extended centroid‎ ‎of $R$‎. ‎Let $0neq ain R$ and $f(x_1,ldots,x_n)$ a multilinear‎ ‎polynomial over $C$ which is noncentral valued on $R$‎. ‎Suppose‎ ‎that $G$ and $H$ are two nonzero generalized derivations of $R$‎ ‎such that $a(H(f(x))f(x)-f(x)G(f(x)))in ...

In the title compound, C(17)H(10)F(6)N(4)O(2)S, an intra-molecular N-H⋯N hydrogen bonds forms an S(5) ring whereas N-H⋯O and C-H⋯S inter-actions complete S(6) ring motifs. The dihedral angle between the fused ring system and the phenyl ring is 6.68 (8)°. In the crystal, the mol-ecules are dimerized due to N-H⋯O inter-actions. π-π inter-actions are present between the benzene rings [centroid-cen...