In order to obtain vitamin D derivatives, which have strong activity for enhancing bone growth, we designed vitamin D derivatives with various substitutions at the C-2 position. Novel 2 α-substituted vitamin D derivatives were synthesized starting from d-glucose as a chiral template of the A-ring with a CD-ring bromoolefin unit using the Trost coupling method. We evaluated these compounds by tw...

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.

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...

let r be a prime ring with extended centroid c, h a generalized derivation of r and n ⩾ 1 a xed integer. in this paper we study the situations: (1) if (h(xy))n = (h(x))n(h(y))n for all x; y 2 r; (2) obtain some related result in case r is a noncommutative banach algebra and h is continuous or spectrally bounded.

In the title compound, C(24)H(21)N(3)OS, the pyrazole ring makes dihedral angles of 5.40 (7) and 6.72 (8)° with the benzo[d]thiazole ring system and the benzene ring, respectively, and a dihedral angle of 85.72 (8)° with the meth-oxy-substituted benzene ring. In the crystal structure, the mol-ecules are linked by C-H⋯π inter-actions.

We present new singular solutions of the biharmonic nonlinear Schrödinger equation (NLS) iψt(t,x)− ψ + |ψ |2σψ = 0, x ∈ R , 4/d σ 4. These solutions collapse with the quasi-self-similar ring profile ψQB , where |ψQB(t, r)| ∼ 1 L2/σ (t) QB ( r − rmax(t) L(t) ) , r = |x|, L(t) is the ring width that vanishes at singularity, rmax(t) ∼ r0L(t) is the ring radius, and α = (4 − σ)/(σ (d − 1)). The blo...

The mol-ecular structure of the title compound, C(28)H(20)N(4)O(6), consists of three fused six-membered rings (A,B,C) and one five-membered ring (D). The latter is linked to an isoxazole ring (E) via a methyl-ene unit. A 4-nitro-phenyl substituent (F) is attached to the isoxazole. The fused five and six-membered rings (C,D) are almost coplanar with an r.m.s. deviation of 0.0345 Å and make a di...

In this paper, the implicitly implemented LES method and fifth order bandwidth-optimized WENO scheme are used to make comprehensive studies on the interaction of vortex rings and shock waves of the MVG controlled flow at M=2.5 and Re θ θ θ θ =5760. The kinetic information of the vortex rings is carefully studied and provided. The interaction of the streamwise vortices and vortex rings are inves...

a ring $r$ is a strongly clean ring if every element in $r$ is the sum of an idempotent and a unit that commutate. we construct some classes of strongly clean rings which have stable range one. it is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

Let D be a division ring with an involution. Assuming that D admits Baer orderings, we can study the Witt group of hermitian froms over D by observing its image in the ring of continuous functions on the space of orderings. We are led to define a new class of rings which, when viewed in an abstract setting, provide a natural generalization of the spaces of orderings and real spectra studied in ...