let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

the zero-divisor graph of a commutative ring r with respect to nilpotent elements is a simple undirected graph $gamma_n^*(r)$ with vertex set z_n(r)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where z_n(r)={x in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...

there is a paucity of literature regarding iatrogenic aortic valve perforation after cardiac operation is performed in the vicinity of the aortic valve. this report describes the clinical, echocardiographic, and angiocardiographic recognition of iatrogenic aortic valve perforation in a patient who had previously under gone membranous ventricular septal defect and pulmonary stenosis. five days a...

The title compound, C(15)H(18)O(3), was isolated from Lacta-rius piperatus (Fr.) S. F. Gary collected from the Kunming area in Yunnan province, China. The central cyclo-hexyl ring adopts a chair conformation, while the furan-one ring is close to planar (r.m.s. deviation = 0.0174 Å). The remaining methyl-ene cyclo-hexene ring has a flattened chair conformation. In the crystal, mol-ecules are lin...

* [email protected], [email protected] (only before June 3, 1999) Abstract This paper presents DC clearing field to clear ions in vacuum pipe of Hefei ring. It also presents changes of focusing structure parameters caused by the clearing field. It concludes that tune shifts caused by the field are related to real-time close orbit of the beam. The paper points out that the field as...

In the title compound, C(16)H(17)NO(3)S(2), the 2H-chromene ring is close to being planar [maximum deviation = 0.034 (2) Å] and the pyrrolidine ring is twisted about the C-C bond opposite the N atom. The dihedral angle between the ring-system planes is 75.24 (16)° and an intra-molecular C-H⋯S inter-action occurs. In the crystal, mol-ecules are linked by C-H⋯O hydrogen bonds and the packing also...

In the title compound, C(22)H(13)ClN(2), the quinoxaline ring system is close to planar [maximum deviation = 0.061 (2) Å]. The phenyl ring at the 2-position and the phenyl ring of the phenyl-ethynyl substituent make dihedral angles of 49.32 (7) and 11.99 (7) °, respectively, with the quinoxaline mean plane. The two phenyl rings are inclined to one another by 61.27 (9)°. In the crystal, mol-ecul...

The title compound, C(30)H(36)N(2)O(6), was prepared via twofold Suzuki coupling of a diboronic acid with bromo-nitro-benzene. The mol-ecule is located on a crystallographic inversion centre. The lateral benzene ring and the central ring make a dihedral angle of 48.75 (14)° and the nitro group is twisted by 41.47 (13)° out of the plane of the benzene ring. The nitro and hex-yloxy groups are in ...

The title compound, C27H28N2O, is a lophine (2,4,5-triphenyl-1H-imidazole) derivative with an n-pentyl chain on the amine N atom and a 4-meth-oxy substituent on the benzene ring. The two phenyl and meth-oxy-benzene rings are inclined to the imidazole ring at angles of 25.32 (7), 76.79 (5) and 35.42 (7)°, respectively, while the meth-oxy substituent lies close to the plane of its benzene ring, w...

We show that public-key bit encryption schemes which support weak (i.e., compact) homomorphic evaluation of any sufficiently “sensitive” collection of functions cannot be proved message indistinguishable beyond AM ∩ coAM via general (adaptive) reductions, and beyond statistical zero-knowledge via reductions of constant query complexity. Examples of sensitive collections include parities, majori...