Let $R$ be a ring and $Z(R)$ the center of $R.$ The aim this paper is to define notions centrally extended Jordan derivations $\ast$-derivations, prove some results involving these mappings. Precisely, we that if $2$-torsion free noncommutative prime admits derivation (resp. $\ast$-derivation) $\delta:R\to R$ such that\[[\delta(x),x]\in Z(R)~~(resp.~~[\delta(x),x^{\ast}]\in Z(R))\text{ for all ...

In the title compound, C(21)H(28)O(4)·H(2)O, the cyclo-hexa-dienone ring is planar (r.m.s. deviation 0.0186 Å), whereas the two cyclo-hexane rings and the cyclo-hexa-none ring adopt chair conformations. The crystal structure is stabilized by O-H⋯O and C-H⋯O hydrogen bonds.

We give a worldsheet proof of the equivalence between the U(N) Chern-Simons gauge theory on S and the topological closed string theory on the resolved conifold geometry. When the ‘t Hooft coupling of the gauge theory is small, the dual closed string worldsheet develops a new branch. We show that the fluctuations of the worldsheet into this branch effectively correspond to “holes” on the worldsh...

In the title mol-ecule, C(30)H(32)N(2)O(2), the two tolyl rings form dihedral angles of 65.8 (1) and 6.6 (1)° with the isoindole-1,3-dione mean plane. The cyclo-hexane ring adopts a chair conformation.

In title compound, C(27)H(36)O, all cyclo-hexane rings within the adamantyl groups adopt chair conformations. There are no obvious inter-molecular hydrogen bonds in the structure, so that van der Waals attractions stabilize the crystal.

Derivations, Jordan derivations, as well as automorphisms and Jordan automorphisms of the algebra of triangular matrices and some class of their subalgebras have been the object of active research for a long time [1, 2, 5, 6, 9, 10]. A well-know result of Herstein [11] states that every Jordan isomorphism on a prime ring of characteristic different from 2 is either an isomorphism or an anti-iso...

In the title compound, C(19)H(33)NO, all three cyclo-hexane rings adopt chair conformations. The crystal packing features weak C-H⋯O inter-actions, forming a supra-molecular chain along the c axis.

Let $A$ be a commutative ring with nonzero identity, and $1leq n

In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

Let $R$ be a commutative ring with identity. A proper submodule $N$ of an $R$-module $M$ is an n-submodule if $rmin N~(rin R, min M)$ with $rnotinsqrt{Ann_R(M)}$, then $min N$. A number of results concerning n-submodules are given. For example, we give other characterizations of n-submodules. Also various properties of n-submodules are considered.