N-弱拟Armendariz环

本文研究了N-弱拟Armendariz环的基本性质以及与一些特殊环的关系.利用某些矩阵环的特殊性质,得到了环R是N-弱拟Armendariz环当且仅当环T_n(R)是N-弱拟Armendariz环,推广了弱拟-Armendariz环的相应结果.     

Vinyl Polymerization. CLXXXV. Polymerization of Methyl Methacrylate Initiated with Benzoic Anhydride and Dimethylaniline N-Oxide. Effects of Solvent and the Substituent of the Initiator

Studies on the rate of the reaction of substituted dimethylaniline N-oxide (DMAO) with substituted benzoic anhydride (Bz₂O) and the rate of polymerization of methyl methacrylate (MMA) with their systems were made. The solvent effects on the rate of the reaction of DMAO with Bz₂O and on the polymerization of MMA with the system were also studied.     

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??In this paper, we study a class of stochastic Volterra equations, which include the stochastic differential equation driven by fractional Brownian motion. By using a maximal inequality due to It\^o (1979), we establish the central limit theorem for stochastic Volterra equation on the continuous path space, with respect to the uniform norm.     

Classification of multivariate skew polynomial rings over finite fields via affine transformations of variables

In this work, free multivariate skew polynomial rings are considered, together with their quotients over ideals of skew polynomials that vanish at every point (which includes minimal multivariate skew polynomial rings). We provide a full classification of such multivariate skew polynomial rings (free or not) over finite fields. To that end, we first show that all ring morphisms from the field to the ring of square matrices are diagonalizable, and that the corresponding derivations are all inner derivations. Secondly, we show that all such multivariate skew polynomial rings over finite fields are isomorphic as algebras to a multivariate skew polynomial ring whose ring morphism from the field to the ring of square matrices is diagonal, and whose derivation is the zero derivation. Furthermore, we prove that two such representations only differ in a permutation on the field automorphisms appearing in the corresponding diagonal. The algebra isomorphisms are given by affine transformations of variables and preserve evaluations and degrees. In addition, ours proofs show that the simplified form of multivariate skew polynomial rings can be found computationally and explicitly.     

Determination of the depth of an etch pit through studies of diffraction rings

A Solid State Nuclear Track Detector (SSNTD) can be used to identify an impinging ion as well as to determine the energy of that ion. The track of the ion is made visible by chemically ‘etching’ the detector after exposure. By finding out the ratio of the track-etch rate (V_t) to the bulk-etch rate (V_g), together with the range of the ion in the detector, the identity and the energy of the ion can be ascertained. The required measurements can be conveniently made with the help of a microscope when the angle of incidence of the ion, with respect to the normal direction to the detector surface, is more than 15°. For normal or near normal incidence, uncertainties plague the measurement of the depth of the etch pit and hence the range of the particle. Through this article we wish to suggest an alternative method of assessment, based on the observation of diffraction rings, of the depth of an etch pit.     

Annular Multi‐Shelled Spherulites in Interiors of Bulk‐Form Poly(nonamethylene terephthalate)

Morphology of crystallized spherulites in poly(nonamethylene terephthalate) (PNT) in bulk forms, instead of thin‐film forms, was investigated using scanning electron microscopy (SEM), polarized‐optical microscopy (POM), and transmission electron microscopy (TEM). Ring textures were found to exist on the fractured surfaces or microtomed films from bulk PNT samples. By further SEM and TEM examinations, the fracture surfaces and microtomed films from the interior of the bulk display similar ring‐banded patterns as those in thin films cast on glass slides. Although the cast PNT thin films in two‐dimensional growth are known to display both Type‐1 ring bands as majority and Type‐2 ring bands as minority, this study further shows that the interior of PNT bulk exhibits mainly Type‐1 (single rings with narrower spacing than Type‐2) ring bands, and Type‐2 spherulites exist sporadically in three‐dimensional forms. From these analyses on the ring bands in the interiors of bulk‐form PNT crystallized at several specific temperatures, it can be proposed that the growth of spherulites in three dimensions is layer‐by‐layer, packing into a multi‐shells structure in three‐dimensional ring‐banded spheres.

     

Central region design for a 10 MeV internal ion source cyclotron

Internal ion sources are widely adopted in commercial cyclotrons used for short-life isotopes production. Without beam manipulation provided by the external beam injection line, the central region of this type of cyclotron is more sensitive and should be carefully designed. A design study and beam dynamics simulation for the central region of a 10 MeV compact cyclotron is presented. The OPERA3D/TOSCA code was used to calculate the electric field from a parameterized three dimensional （3D） central region model. With iterative structure optimizations of the central region, the beam centering and vertical focusing is well controlled, and the RF phase acceptance is around 25°. A c＋＋ code for beam simulation in the central region was developed and tested.     

变指标中心BMO空间

本文引进变指标中心有界平均振荡函数空间.作为应用,得到了Hardy算子及其共轭算子的交换子在变指标勒贝格空间上有界性的特征刻画.另外,还考虑了交换子在变指标Herz空间上的向量值不等式.     

On right S-Noetherian rings and S-Noetherian modules

In this paper we study right S-Noetherian rings and modules, extending notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative rings. Two characterizations of right S-Noetherian rings are given in terms of completely prime right ideals and point annihilator sets. We also prove an existence result for completely prime point annihilators of certain S-Noetherian modules with the following consequence in commutative algebra: If a module M over a commutative ring is S-Noetherian with respect to a multiplicative set S that contains no zero-divisors for M, then M has an associated prime.