The two oxazolidine rings (A and B) of the title compound, C34H44N2O4, display roughly half-chair conformations, which could be described as twisted on the C-O bond. Together, the fused oxazolidine rings have a butterfly shape, with the H atoms attached to the ring junction C atoms in a cis orientation. The cyclo-hexane rings of both p-menthone fragments display chair conformations. The absolut...

In the title compound, C45H40N4O5, the cyclo-hexane entity on the (3-cyano-2,5-dihydro-furan-2-yl-idene)propane-dinitrile group, which replaces the usual dimethyl substituents, has not perturbed the delocalization geometry significantly. Weak inter-molecular inter-actions, viz. C-H⋯N(cyano), C-H⋯O(ether), C-H⋯π and π-π [between the aromatic rings with the shortest centroid-centroid distance of ...

In the title compound, C19H16BrClO4, both the fused xanthene rings and one of the cyclo-hexane rings adopt envelope conformations, while the other cyclo-hexane ring is in a chair conformation. In the crystal, mol-ecules are linked by C-H⋯O hydrogen bonds, forming infinite chains running along [10-1] incorporating R 2 (2)(16) ring motifs. In addition, C-H⋯π inter-actions and weak π-π stacking in...

In this study, B12N12 Nano ring has been selected because it consist of four 6-side rings and polar bonds B-N which in comparison with non-polar bonds C-C, is more suitable for the study of the absorption of other compounds. So reactivity and stability of Benzene alone and in the presence B12N12 nano ring field checked. To determine the non-bonded interaction energies between Benzene and B12N12...

let $r=k[x_1,x_2,cdots, x_n]$ be a polynomial ring over a field $k$. we prove that for any positive integers $m, n$, $text{reg}(i^mj^nk)leq mtext{reg}(i)+ntext{reg}(j)+text{reg}(k)$ if $i, j, ksubseteq r$ are three monomial complete intersections ($i$, $j$, $k$ are not necessarily proper ideals of the polynomial ring $r$), and $i, j$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...

in this study, b12n12 nano ring has been selected because it consist of four 6-side rings and polar bonds b-n which in comparison with non-polar bonds c-c, is more suitable for the study of the absorption of other compounds. so reactivity and stability of benzene alone and in the presence b12n12 nano ring field checked. to determine the non-bonded interaction energies between benzene and b12n12...

Let $R=k[x_1,x_2,cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $text{reg}(I^mJ^nK)leq mtext{reg}(I)+ntext{reg}(J)+text{reg}(K)$ if $I, J, Ksubseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...

The synthesis of cis-N-[a-carbobenzyloxy-b-(p-hydroxyphenyl)ethyl]-3-phthalimido-4-styryl-2-azetidinone is described. We have found that the electron-rich Schiff bases can afford the cis-b-lactam ring even in the presence of the free hydroxyl functions. The mechanisms of cis and trans-b-lactam ring formation are discuss...

Let $(R,fm)$ be a Gorenstein local ring and$M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are inthe same even liaison class, thenone has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...