Comparison of graphs associated to a commutative Artinian ring

Let R be a commutative ring with \(1\ne 0\) and the additive group \(R^+\). Several graphs on R have been introduced by many authors, among zero-divisor graph \(\Gamma _1(R)\), co-maximal graph \(\Gamma _2(R)\), annihilator graph AG(R), total graph \( T(\Gamma (R))\), cozero-divisors graph \(\Gamma _\mathrm{c}(R)\), equivalence classes graph \(\Gamma _\mathrm{E}(R)\) and the Cayley graph \(\mathrm{Cay}(R^+ ,Z^*(R))\). Shekarriz et al. (J. Commun. Algebra, 40 (2012) 2798–2807) gave some conditions under which total graph is isomorphic to \(\mathrm{Cay}(R^+ ,Z^*(R))\). Badawi (J. Commun. Algebra, 42 (2014) 108–121) showed that when R is a reduced ring, the annihilator graph is identical to the zero-divisor graph if and only if R has exactly two minimal prime ideals. The purpose of this paper is comparison of graphs associated to a commutative Artinian ring. Among the results, we prove that for a commutative finite ring R with \(|\mathrm{Max}(R)|=n \ge 3\), \( \Gamma _1(R) \simeq \Gamma _2(R)\) if and only if \(R\simeq \mathbb {Z}^n_2\); if and only if \(\Gamma _1(R) \simeq \Gamma _\mathrm{E}(R)\). Also the annihilator graph is identical to the cozero-divisor graph if and only if R is a Frobenius ring.     

Small generators of the ideal class group

Assuming the Generalized Riemann Hypothesis, Bach has shown that the ideal class group of a number field can be generated by the prime ideals of having norm smaller than . This result is essential for the computation of the class group and units of by Buchmann's algorithm, currently the fastest known. However, once has been computed, one notices that this bound could have been replaced by a much smaller value, and so much work could have been saved. We introduce here a short algorithm which allows us to reduce Bach's bound substantially, usually by a factor 20 or so. The bound produced by the algorithm is asymptotically worse than Bach's, but favorable constants make it useful in practice.

     

Cyclicity of the adjoint of weighted composition operators on the hilbert space of analytic functions

In this paper, we discuss the hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic functions.     

LocalSolver 1.x: a black-box local-search solver for 0-1 programming

This paper introduces LocalSolver 1.x, a black-box local-search solver for general 0-1 programming. This software allows OR practitioners to focus on the modeling of the problem using a simple formalism, and then to defer its actual resolution to a solver based on efficient and reliable local-search techniques. Started in 2007, the goal of the LocalSolver project is to offer a model-and-run approach to combinatorial optimization problems which are out of reach of existing black-box tree-search solvers (integer or constraint programming). Having outlined the modeling formalism and the main technical features behind LocalSolver, its effectiveness is demonstrated through an extensive computational study. The version 1.1 of LocalSolver can be freely downloaded at and used for educational, research, or commercial purposes.     

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

Acta Mathematica Sinica, English Series - In this research article, we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators...     

Performance evaluation of praseodymium doped fiber amplifiers

Optical Review - In this paper, we report the performance evaluation of praseodymium doped fiber amplifier (PDFA) operating in 1.25–1.35 μm band of wavelengths based on...     

Parallel optical fuzzy logic inference using a SLM-based architecture

A new optoelectronic fuzzy inference system is proposed for processing a large number of fuzzy rules in parallel. The proposed system using spatial light modulator implements various membership functions as well as max–min inference. It has the features of easy implementation and large data processing capability. The membership function decomposition method is used to save space bandwidth and accommodate multiple-input fuzzy inference.     

Practical aspects of shimming a high resolution magic angle spinning probe

High resolution magic angle spinning (HRMAS) has become an extremely versatile tool to study heterogeneous systems. HRMAS relies on magic angle spinning of the sample to average out to zero magnetic susceptibility differences in the sample and to obtain resonance linewidths approaching those of liquid state NMR. Shimming such samples therefore becomes an important issue. By analyzing the different sources of magnetic field perturbations present in a sample under MAS conditions, we propose a simple protocol to obtain optimum shim settings in HRMAS. In the case of aqueous samples, we show that the lock level cannot be used as a reliable indicator of the quality of the shims at high spinning speeds. This effect is explained by the presence of temperature gradients imparted by the sample rotation.     

Rapidity density distributions in antiproton-proton collisions

Data on the density of charged particles in rapidity space for annihilation and non-annihilation p?p interactions at 7.3 and 12 GeV/c are reported. It is shown that the central rapidity density for non-annihilation processes is a simple linear function of $\text{ln}\text{(}\text{s}\text{)}$ from these low energies up to p?p collider energies ($\text{s}\text{=540}\text{GeV}$). Significant differences in density distributions for p?p and e^?e⁺ annihilations at comparable energies are found.