Some Rings Characterized by Modules

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On the Hilbert function of Artinian local complete intersections of codimension three

In singularity theory or algebraic geometry, it is natural to investigate possible Hilbert functions for special algebras A such as local complete intersections or more generally Gorenstein algebras. The sequences that occur as the Hilbert functions of standard graded complete intersections are well understood classically thanks to Macaulay and Stanley. Very little is known in the local case except in codimension two. In this paper we characterise the Hilbert functions of quadratic Artinian complete intersections of codimension three. Interestingly we prove that a Hilbert function is admissible for such a Gorenstein ring if and only if is admissible for such a complete intersection. We provide an effective construction of a local complete intersection for a given Hilbert function. We prove that the symmetric decomposition of such a complete intersection ideal is determined by its Hilbert function.     

Influence of metal and ligand types on stacking interactions of phenyl rings with square-planar transition metal complexes

In order to find out whether metal type influences the stacking interactions of phenyl rings in square-planar complexes, geometrical parameters for Cu, Ni, Pd and Pt complexes, with and without chelate rings, were analyzed and compared. By searching the Cambridge Structural Database, 220 structures with Cu complexes, 211 with Ni complexes, 285 with Pd complexes, and 220 with Pt complexes were found. The results show that the chelate ring has a tendency to make the stacking interaction with the phenyl ring independent of metal type in the chelate ring. However, there are some differences among metals for complexes without a chelate ring. There are a number of structures containing Pd and Pt complexes, without chelate rings, that have short carbon-metal distances and parallel orientations of the phenyl ring with respect to the coordination plane. It was found that some of these complexes have a common fragment, CN, as a part of the ligands. This indicates that the CN supports stacking interactions of square planar complexes with the phenyl ring.      

Maximally Prüfer Rings

In this paper we consider six Prüfer-like conditions on a commutative ring R, and introduce seventh condition by defining the ring R to be maximally Prüfer if R _M is Prüfer for every maximal ideal M of R, and we show that the class of such rings lie properly between Prüfer rings and locally Prüfer rings. We give a characterization of such rings in terms of the total quotient ring and the core of the regular maximal ideals. We also find a relationship of such rings with strong Prüfer rings.     

变形牛顿环装置干涉结果的仿真模拟

在分析各种变形牛顿环干涉装置的基础上,阐述了它们在测量、检测、表面科学等方面的应用,并借助MATLAB程序语言对各种变形装置的干涉结果进行仿真模拟,有助于物理教学的直观化以及推动牛顿环干涉技术在光学技术方面的广泛应用。     

Rhodium‐Catalyzed Intramolecular [5+2] Cycloaddition of Inverted 3‐Acyloxy‐1,4‐enyne and Alkyne: Experimental and Theoretical Studies

By switching the position of the alkene and alkyne, a new type of 3‐acyloxy‐1,4‐enyne (ACE) five‐carbon building block was developed for Rh‐catalyzed intramolecular [5+2] cycloaddition. An electron‐withdrawing acyl group on the alkyne termini of the ACE was essential for a regioselective 1,2‐acyloxy migration. This new method provided bicyclic [5.3.0]decatrienes that are different from previous methods because of the positions of the alkenes and the acyloxy group. Multiple mechanistic pathways become possible for this new [5+2] cycloaddition and they are investigated by computational studies.     

交换环上辛代数的导子代数(英文)

对含幺交换环上辛代数的导子代数做了详细的描述.     

Quantum rings in tilted magnetic fields

The electronic states of semiconductor quantum rings (QRs) under tilted magnetic fields are studied in the framework of the effective mass and envelope function approximations. For an axial field, the orbital Zeeman contribution prevails leading to the well-known Aharanov–Bohm spectrum, but it slowly decreases as the magnetic field direction declines. For an in-plane field, only the diamagnetic shift survives and it leads to the formation of double quantum well solutions, this result being relevant for experimental techniques which use in-plane magnetic fields to determine the spin of QR ground states. We also investigate the magnetic response of partially overlapped QRs, which are characteristic of high-density samples of self-assembled rings, and find that the spectrum is quite sensitive to ring coupling.     

Inductive Rings and Systems of Diophantine Equations

In this paper, by using model-theoretic methods, it is shown that some systems of unsolved cubic diophantine equations in number theory can have solutions in certain inductive extension rings of the ring I of rational integers. These inductive rings are not fields, and every element of them is a sum of 4 cubes and a sum of 3 squares. Also some of them satisfy the Goldbach conjecture and some others don＇t.