Fitting ideals and the Gorenstein property

Let p be a prime number and G be a finite commutative group such that p ² does not divide the order of G. In this note we prove that for every finite module M over the group ring Z _p [G], the inequality #M  ￡  #Z_p[G]/Fit_Zp[G](M){\#M\,\leq\,\#{\bf Z}_{p}[G]/{{\rm Fit}}_{{\bf Z}_{p}[G]}(M)} holds. Here, Fit_Zp[G](M){\rm Fit}_{{\bf Z}_{p}[G]}(M) is the Z _p [G]-Fitting ideal of M.     

Optimization of Microwave-Assisted Extraction (MAE) for the Isolation of Antioxidants from Basil (Ocimum basilicum L.) by Response Surface Methodology (RSM)

Abstract

The recovery of antioxidants from basil (Ocimum basilicum L.) was modeled with the aid of response surface methodology (RSM) using microwave-assisted extraction (MAE). Face-centered central design (FCCD) was employed to optimize the MAE operational parameters including the extraction time (1 to 7?min), extraction temperature (30 to 120?°C), solid-to-solvent ratio (0.1 to 0.4), and solvent concentration (20 to 80% ethanol, v/v), and to obtain the best possible combinations of these parameters for a high antioxidant yield from basil. The total antioxidant capacity (TAC) was expressed in trolox (TR) equivalents per gram of dried sample (DS). Three of the operational parameters (temperature, extraction time and solvent concentration) were shown to have significant effect on the extraction efficiency of antioxidants in basil extracts (p?<?0.05). The solvent concentration was shown to be the most significant factor on antioxidant yield obtained by MAE. There was a close relationship between experimental and predicted values using the proposed method. This optimized MAE method shows an application potential for the efficient extraction of antioxidants from basil in the food and pharmaceutical industries.     

Thermal and gas (CH4 and C2H4) adsorption characteristics of nitric acid-treated clinoptilolite

In this study, in order to consider the effect of the time of the nitric acid treatment on thermal, structural and gas adsorption properties, clinoptilolite was modified with 1.0 M acid solutions at 80 °C for 2, 4, 6, 12 and 24 h. Structural and thermal properties of natural and acid-treated clinoptilolites were investigated by powder X-ray diffraction, X-ray fluorescence, thermogravimetric analysis, differential thermal analysis and nitrogen adsorption methods. Methane (CH₄) and ethylene (C₂H₄) are hazardous gases for human and plant health, respectively. Therefore, some measures should be taken to reduce emissions of methane and ethylene. CH₄ and C₂H₄ adsorption capacities of clinoptilolite (CLN) from Turkey and that of acid-treated forms at 273 K up to 100 kPa were found between 0.556–0.683 and 0.470–1.295 mmol g^?1, respectively.

     

Electroanalytical investigation and determination of pefloxacin in pharmaceuticals and serum at boron-doped diamond and glassy carbon electrodes

The anodic behavior and determination of pefloxacin on boron-doped diamond and glassy carbon electrodes were investigated using cyclic, linear sweep, differential pulse and square wave voltammetric techniques. In cyclic voltammetry, pefloxacin shows one main irreversible oxidation peak and additional one irreversible ill-defined wave depending on pH values for both electrodes. The results indicate that the process of pefloxacin is irreversible and diffusion controlled on boron-doped diamond electrode and irreversible but adsorption controlled on glassy carbon electrode. The peak current is found to be linear over the range of concentration 2 × 10⁻⁶ to 2 × 10⁻⁴ M in 0.5 M H₂SO₄ at about +1.20 V (versus Ag/AgCl) for differential pulse and square wave voltammetric technique using boron-doped diamond electrode. The repeatability, reproducibility, precision and accuracy of the methods in all media were investigated. Selectivity, precision and accuracy of the developed methods were also checked by recovery studies. The procedures were successfully applied to the determination of the drug in pharmaceutical dosage forms and humans serum samples with good recovery results. No electroactive interferences from the excipients and endogenous substances were found in the pharmaceutical dosage forms and biological samples, respectively.     

Singular approximation in polydiscs by summability process

In this paper, we approximate a continuous function in a polydisc by means of multivariate complex singular operators which preserve the analytic functions. In this singular approximation, we mainly use a regular summability method (process) from the summability theory. We show that our results are non-trivial generalizations of the classical approximations. At the end, we display an application verifying the singular approximation via summation process, but not the usual sense.     

Partial Geometric Difference Families

We introduce the notion of a partial geometric difference family as a variation on the classical difference family and a generalization of partial geometric difference sets. We study the relationship between partial geometric difference families and both partial geometric designs and difference families, and show that partial geometric difference families give rise to partial geometric designs. We construct several infinite families of partial geometric difference families using Galois rings and the cyclotomy of Galois fields. From these partial geometric difference families, we generate a list of infinite families of partial geometric designs and directed strongly regular graphs.     

Comparative evaluation of various total antioxidant capacity assays applied to phenolic compounds with the CUPRAC assay

It would be desirable to establish and standardize methods that can measure the total antioxidant capacity level directly from vegetable extracts containing phenolics. Antioxidant capacity assays may be broadly classified as electron transfer (ET)- and hydrogen atom transfer (HAT)-based assays. The majority of HAT assays are kinetics-based, and involve a competitive reaction scheme in which antioxidant and substrate compete for peroxyl radicals thermally generated through the decomposition of azo compounds. ET-based assays measure the capacity of an antioxidant in the reduction of an oxidant, which changes colour when reduced. ET assays include the ABTS/TEAC, CUPRAC, DPPH, Folin-Ciocalteu and FRAP methods, each using different chromogenic redox reagents with different standard potentials. This review intends to offer a critical evaluation of existing antioxidant assays applied to phenolics, and reports the development by our research group of a simple and low-cost antioxidant capacity assay for dietary polyphenols, vitamins C and E, and human serum antioxidants, utilizing the copper(II)-neocuproine reagent as the chromogenic oxidizing agent, which we haved named the CUPRAC (cupric ion reducing antioxidant capacity) method. This method offers distinct advantages over other ET-based assays, namely the selection of working pH at physiological pH (as opposed to the Folin and FRAP methods, which work at alkaline and acidic pHs, respectively), applicability to both hydrophilic and lipophilic antioxidants (unlike Folin and DPPH), completion of the redox reactions for most common flavonoids (unlike FRAP), selective oxidation of antioxidant compounds without affecting sugars and citric acid commonly contained in foodstuffs and the capability to assay -SH bearing antioxidants (unlike FRAP). Other similar ET-based antioxidant assays that we have developed or modified for phenolics are the Fe(III)- and Ce(IV)-reducing capacity methods.     

A modular curve of level 9 and the class number one problem

In this note we give an explicit parametrization of the modular curve associated to the normalizer of a non-split Cartan subgroup of level 9. We determine all integral points of this modular curve. As an application, we give an alternative solution to the class number one problem.