Direct limits of Cohen–Macaulay rings

Let A be a direct limit of a direct system of Cohen–Macaulay rings. In this paper, we describe the Cohen–Macaulay property of A. Our results indicate that A is not necessarily Cohen–Macaulay. We show A is Cohen–Macaulay under various assumptions. As an application, we study Cohen–Macaulayness of non-affine normal semigroup rings.     

Design,synthesis, and biological activities of novel azole-bonded \upbeta -hydroxypropyl oxime O-ethers

The synthesis and biological effects of 15 novel azole-bonded \(\upbeta \) -hydroxypropyl oxime \(O\) -ethers have been described. In this synthesis, the oximation of aromatic ketones followed by an \(O\) -alkylation reaction with epichlorohydrin and/or epibromohydrin led to the corresponding \(O\) -oxime ether adducts. Subsequently, the attained \(O\) -oxime ether adducts were used to synthesize the target molecules after treating them with the appropriate azole derivatives. The in vitro antifungal and antibacterial activities of title compounds were obtained against several pathogenic fungi, Gram-positive and/or Gram-negative bacteria. Benzophenone \(O\) -2-hydroxy-3-(2-phenyl-1 \(H\) -imidazol-1-yl) propyl oxime and 9 \(H\) -fluoren-9-one \(O\) -2-hydroxy-3-(2-phenyl-1 \(H\) -imidazol-1-yl)propyl oxime proved to have considerable antifungal activity against Candida albicans, Candida krusei, Aspergillus niger, and Trichophyton rubrum. These two compounds demonstrated comparable antifungal activity to clotrimazole and fluconazole (standard drugs). All compounds were also tested against Escherichia coli and Staphylococcus aureus as Gram-negative and Gram-positive bacteria, respectively, and their activities were compared to gentamycin and ampicillin (reference drugs). In general, marginal antibacterial activity against tested bacteria was observed for the title compounds. A molecular docking study is also discussed for the two most potent compounds against fungi. The docking study reveals a considerable interaction between the two most potent compounds and the active site of Mycobacterium P450DM. Moreover, these two compounds are much strongly bound to the active site of Mycobacterium P450DM compared to fluconazole.     

Modeling investigation of membrane biofouling phenomena by considering the adsorption of protein, polysaccharide and humic acid

The importance of solute adsorption in the biofouling membrane has been clearly verified for the performance of membrane bioreactor (MBR). In order to quantify the mechanism of static adsorption in biofouling during of MBR process, we characterize membrane biofouling caused by model solutions containing a protein (bovine serum albumin, BSA), a humic substance (humic acid, HA) and a polysaccharide (alginic acid, Alg) on commercial hydrophilic polyethersulfone (PES) membrane. For static adsorption experiments, membranes were immersed in well-defined model solutions in three temperatures (298, 308 and 318 K) to obtain equilibrium data. To determine the characteristic parameters for this process, 7 isotherm models were applied to the experimental data. Three error analysis methods; the coefficient of nonlinear regression (R(2)), the sum of the squared errors (SSE) and standard deviation of residuals (S(yx)), were used to evaluate the data and determine the best fit isotherm for each model solutions. The error values demonstrated that the Sips isotherm model provided the best fit to the experimental data. AFM images were used for determination of changes in membrane surface after adsorption. These images confirmed the results obtained from adsorption isotherm study. Thermodynamic parameters such as standard free energy (Δ(r)G(θ)), enthalpy (Δ(r)H(θ)) and entropy (Δ(r)S(θ)) changes were determined; these adsorption processes were found to be feasible and endothermic but not spontaneous. The distribution of the substances adsorbed on PES surface were more chaotic than that in the aqueous solutions. Parameters obtained in this study can be used to determine the "fouling potential" of a given feed stream and a membrane.     

An overview of some classical models and discussion of the signature-based models of preventive maintenance

In reliability engineering literature, a large number of research papers on optimal preventive maintenance (PM) of technical systems (networks) have appeared based on preliminary many different approaches. According to the existing literature on PM strategies, the authors have considered two scenarios for the component failures of the system. The first scenario assumes that the components of the system fail due to aging, while the second scenario assumes the system fails according to the fatal shocks arriving at the system from external or internal sources. This article reviews different approaches on the optimal strategies proposed in the literature on the optimal maintenance of multi-component coherent systems. The emphasis of the article is on PM models given in the literature whose optimization criteria (cost function and stationary availability) are developed by using the signature-based (survival signature-based) reliability of the system lifetime. The notions of signature and survival signature, defined for systems consisting of one type or multiple types of components, respectively, are powerful tools assessing the reliability and stochastic properties of coherent systems. After giving an overview of the research works on age-based PM models of one-unit systems and $k$-out-of-$n$ systems, we provide a more detailed review of recent results on the signature-based and survival signature-based PM models of complex systems. In order to illustrate the theoretical results on different proposed PM models, we examine two real examples of coherent systems both numerically and graphically.     

A characterization of well-posedness for the second order abstract Cauchy problems with finite delay

In this work, we introduce a strongly continuous one-parameter family of bounded linear operators that completely describes the well-posedness of a second order abstract differential delay equation in the initial history space $L^p([-r,0];X)$, $r>0$. This family, which satisfies a specific functional equation is applied to characterize the mild solution of the considered second order delay equation.