Multiplicities corresponding to irreducible characters are defined for reality-based algebras. These algebras with a distinguished basis include fusion rings, C-algebras, and the adjacency algebras of finite association schemes. The definition of multiplicity generalizes that for schemes. For a broad class of these structures, which includes the adjacency algebras, it is proved that if all the ...

In the title compound, C(11)H(9)F(2)N(5)OS, the pyrazole ring forms a dihedral angle of 16.42 (6)° with the benzene ring. Intra-molecular N-H⋯O hydrogen bonds generate two S(6) ring motifs. In the crystal, an R(2) (2)(8) ring motif is formed by a pair of inter-molecular N-H⋯S hydrogen bonds. Inter-molecular C-H⋯F hydrogen bonds further link the mol-ecules into a three-dimensional network.

Current researches have showed that N3, N5-diaryl-2, 6-dimethyl -1, 4-dihydropyrine-3, 5- dicarboxamide analogues demonstrate notable anti-tubercular activity. In this study, Hantzsch condensation was used to design and synthesize new analogues of dihydropyridine (DHP). Different diary carboxamides were inserted at positions 3 and 5 of the DHP ring. 4(5)-chloro-2-ethyl-5(4)-imidazolyl moiety wa...

A ring R is called a right Ikeda-Nakayama (for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if (I ∩ J) = (I) + (J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f (x) = a0 + a1x + ··· + amx, g(x) = b0 + b1x + ··· + bnx ∈ R[x] satisfy f (x)g(x) = 0, then aibj = 0 for each ...

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...

Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S=$ End$_R(M)$. The module $M$ is called {it Rickart} if for any $fin S$, $r_M(f)=Se$ for some $e^2=ein S$. We prove that some results of principally projective rings and Baer modules can be extended to Rickart modules for this general settings.

The title compound, C(18)H(13)FN(2)OS, is the first structural example of a [6-5] fused ring incorporating the 2,3-dihydro-4H-imidazo[5,1-b][1,3]thiazin-4-one molecular scaffold. The six-membered 2,3-dihydro-1,3-thiazin-4-one ring adopts an envelope conformation, with the S-CH(2) C atom displaced by 0.761 (2) A from the five-atom plane (all within 0.05 A of the mean plane). The imidazole ring i...

Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized telescoping solution, proves algebraic independence of certain types of sums. Combining this fact with summation-theory shows transcendence of whole classes of sums. Parameterized telescoping Given f1(k), ....

Let F be a field of characteristic p > 0. Let Ω(F ) be the F vector space of n-differentials of F over F . Let K = F (g) be the function field of an irreducible polynomial g in m > 1 variables over F . We derive an explicit description of the kernel of the restriction map Ω(F ) → Ω(K). As an application in the case p = 2, we determine the kernel of the restriction map when passing from the Witt...