Annihilator Properties of Skew Monoid Rings

Let R be a ring with an endomorphism σ and F ∪ {0} the free monoid generated by U = {u ₁,…, u _t } with 0 added, and M a factor of F setting certain monomial in U to 0, enough so that, for some n, M ⁿ  = 0. In this article, we study various annihilator properties and a variety of conditions and related properties that the skew monoid ring R[M; σ] is inherited from R.     

Weak Module Amenability for Semigroup Algebras

We study the weak module amenability of Banach algebras which are Banach module over another Banach algebra with compatible actions. As an example we show that the semigroup algebra of a commutative inverse semigroup is always weakly amenable as a module over the semigroup algebra of its subsemigroup of idempotents.     

Resource allocation with stochastic optimal control approach

A control-theoretic decision making system is proposed for an agent (decision maker) to “optimally” allocate and deploy his/her resources over time among a dynamically changing list of opportunities (e.g., financial assets), in an uncertain market environment. The solution is a sequence of actions with the objective of optimizing total reward function. This control-theoretic approach is unique in a sense that it solves the problem at distinct time epochs over a finite time horizon and strategies are discovered directly. Rather than basing a decision making system on forecasts or training via a reinforcement learning algorithm using current state data, we train our system via a Q-learning algorithm using Geometric Brownian Motion as an asset price function. While the above problem is quite general, we focus solely on the problem of dynamic financial portfolio management with the objective of maximizing the expected utility for a given risk level. The performance functions that we consider for our system are realized mean return, drawdown and standard deviation. We find that our model achieves a better return and drawdown compared to a known market index as a benchmark.     

Module derivations on semigroup algebras

We show that for an inverse semigroup S with the set idempotents E acting on S trivially from left and by multiplication from right, any bounded module derivation from \(\ell ^1(S)\) to \(({\ell ^1(S)}/{J})^*=J^{\perp }\) is inner, where J is the closed ideal generated by elements of the form \(\delta _{set}-\delta _{st}\) with \(s,t\in S\) and \(e\in E\).     

Approximate solution of non-Newtonian viscoelastic fluid flow on a turbine disc for cooling purposes by using Adomian decomposition method

In this work, a powerful semi-analytical method, called Adomian decomposition method (ADM) is introduced to obtain the exact solution of heat transfer equation of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall which is useful for turbine cooling applications. This method is employed to obtain the expressions for velocity and temperature fields. Then, the influence of the two dimensionless numbers: the Prandtl number (Pr) and the Reynolds number (Re) for the dynamic forces have been considered. Comparisons are made between the numerical method (NM) solution, Homotopy perturbation method (HPM), Variation iteration method (VIM) and the results of Adomian decomposition method (ADM). The results reveal that this method is very effective and simple and can be applied for other nonlinear problems.     

2-Domination number of generalized Petersen graphs

Let \(G=(V,E)\) be a graph. A subset \(S\subseteq V\) is a k-dominating set of G if each vertex in \(V-S\) is adjacent to at least k vertices in S. The k-domination number of G is the cardinality of the smallest k-dominating set of G. In this paper, we shall prove that the 2-domination number of generalized Petersen graphs \(P(5k+1, 2)\) and \(P(5k+2, 2)\), for \(k>0\), is \(4k+2\) and \(4k+3\), respectively. This proves two conjectures due to Cheng (Ph.D. thesis, National Chiao Tung University, 2013). Moreover, we determine the exact 2-domination number of generalized Petersen graphs P(2k, k) and \(P(5k+4,3)\). Furthermore, we give a good lower and upper bounds on the 2-domination number of generalized Petersen graphs \(P(5k+1, 3), P(5k+2,3)\) and \(P(5k+3, 3).\)     

Wavelet–fractal approach to surface characterization of nanocrystalline ITO thin films

In this study, indium tin oxide (ITO) thin films were prepared by electron beam deposition method on glass substrates at room temperature (RT). Surface morphology characterization of ITO thin films, before and after annealing at 500 °C, were investigated by analyzing the surface profile of atomic force microscopy (AFM) images using wavelet transform formalism. The wavelet coefficients related to the thin film surface profiles have been calculated, and then roughness exponent (α) of the films has been estimated using the scalegram method. The results reveal that the surface profiles of the films before and after annealing process have self-affine nature.     

One-pot electrochemical synthesis of highly symmetric and conjugated coumarin derivative

A facile and one pot electrochemical synthesis of disubstituted hydroquinone generated from the electrochemical oxidation of 4-1-(4-(4-hydroxyphenyl)piperazin-1-yl)ethanone (1) in the presence of 4-hydroxy-6,7-dimethylcoumarin (3) has been reported. The results revealed that p-quinone imine derived from oxidation of (1) participate in Michael addition reactions with 3 and followed by a hydrolysis reaction attain to the highly symmetric and conjugated coumarin derivative. We derived a new product in good yield based on controlled potential electrochemical oxidation at carbon electrode in a divided cell.     

A facile and one-pot electrochemical method for the synthesis of a new anthraquinonethioether

The reaction of electrochemically generated anthradiquinone as a Michael acceptor with 2-mercaptobenzothiazole and 2- mercaptobenzoxazole,as nucleophiles in ethanol/water mixtures has been studied by means of cyclic voltammetry.Our voltammetric data indicate that produced anthradiquinone participates in Michael addition reaction with nucleophiles and via an ECEC mechanism converts to the new anthraquinonethioether derivatives.Based on an EC mechanism,the observed homogeneous rate constant of the Michael reaction of anthradiquinone with nucleophiles were estimated by comparing the experimental cyclic voltammograms with the digital simulated results.