On the number of eigenvalues for parameter‐dependent diffusion problem on time scales

In this study, we consider parameter‐dependent diffusion eigenvalue problem on time scales. An upper bound on the number of eigenvalues for this problem on a finite time scale is given.     

On The Spaces of Linear Operators Acting Between Asymmetric Cone Normed Spaces

An asymmetric norm is a positive sublinear functional p on a real vector space X satisfying \(x=\theta _X\) whenever \(p(x)=p(-x)=0\). Since the space of all lower semi-continuous linear functionals of an asymmetric normed space is not a linear space, the theory is different in the asymmetric case. The main purpose of this study is to define bounded and continuous linear operators acting between asymmetric cone normed spaces. After examining the differences with symmetric case, we give some results related to Baire’s characterization of completeness in asymmetric cone normed spaces.     

Evaluation of quercetin as a potential β-lactamase CTX-M-15 inhibitor via the molecular docking,dynamics simulations,and MMGBSA

Antimicrobial resistance (AMR) threatens millions of people around the world and has been declared a global risk by the World Economic Forum. One of the important AMR mechanisms in Enterobacteriaceae is the production of extended-spectrum β-lactamases. The most common ESBL, CTX-M β-lactamases, is spread to the world by CTX-M-15 and CTX-M-14. Sulbactam, clavulanic acid, and tazobactam are first-generation β-lactamase inhibitors and avibactam is a new non-β-lactam β-lactamase inhibitor. We studied that avibactam, sulbactam, clavulanic acid, tazobactam, and quercetin natural flavonoids were docked to target protein CTXM-15. Subsequently, the complexes were simulated using the molecular dynamics simulations method during 100 ns for determining the final binding positions of ligands. Clavulanic acid left CTX-M-15 and other ligands remained in the binding site after the simulation. The estimated binding energies were calculated during 100 ns simulation by the MMGBSA-MMPBSA method. The estimated free binding energies of avibactam, sulbactam, quercetin, tazobactam, and clavulanic acid were sorted as –33.61 kcal/mol, –16.04 kcal/mol, –14 kcal/mol, –12.68 kcal/mol, and –2.95 kcal/mol. As a result of both final binding positions and free binding energy calculations, Quercetin may be evaluated an alternative candidate and a more potent β-lactamases inhibitor for new antimicrobial combinations to CTX-M-15. The results obtained in silico studies are predicted to be a preliminary study for in vitro studies for quercetin and similar bioactive natural compounds. These studies are notable for the discovery of natural compounds that can be used in the treatment of infections caused by β-lactamase-producing pathogens.     

An adaptive large neighborhood search heuristic for the Pollution-Routing Problem

The Pollution-Routing Problem (PRP) is a recently introduced extension of the classical Vehicle Routing Problem with Time Windows which consists of routing a number of vehicles to serve a set of customers, and determining their speed on each route segment so as to minimize a function comprising fuel, emission and driver costs. This paper presents an adaptive large neighborhood search for the PRP. Results of extensive computational experimentation confirm the efficiency of the algorithm.     

The bi-objective Pollution-Routing Problem

The bi-objective Pollution-Routing Problem is an extension of the Pollution-Routing Problem (PRP) which consists of routing a number of vehicles to serve a set of customers, and determining their speed on each route segment. The two objective functions pertaining to minimization of fuel consumption and driving time are conflicting and are thus considered separately. This paper presents an adaptive large neighborhood search algorithm (ALNS), combined with a speed optimization procedure, to solve the bi-objective PRP. Using the ALNS as the search engine, four a posteriori methods, namely the weighting method, the weighting method with normalization, the epsilon-constraint method and a new hybrid method (HM), are tested using a scalarization of the two objective functions. The HM combines adaptive weighting with the epsilon-constraint method. To evaluate the effectiveness of the algorithm, new sets of instances based on real geographic data are generated, and a library of bi-criteria PRP instances is compiled. Results of extensive computational experiments with the four methods are presented and compared with one another by means of the hypervolume and epsilon indicators. The results show that HM is highly effective in finding good-quality non-dominated solutions on PRP instances with 100 nodes.     

Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

The Ramanujan Journal - In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of...     

Determination of the hydroxyl radical by its adduct formation with phenol and liquid chromatography/electrochemical detection

An HPLC-ECD method is described for the indirect determination of the hydroxyl (OH) radical. Fenton's reaction is used to produce OH, which simultaneously attacks phenols (phenol or pyrocatechol) to form the adducts, pyrocatechol or pyrogallic acid. Thus, [OH] quantification is based on the separation and detection of pyrogallic acid and/or pyrocatechol by an isocratic HPLC-ECD method. The quantification of OH is also performed alternatively by a chronoamperometric detection in an electrochemical cell, where simultaneously formed Fe^III (Fenton's reaction) combines [Fe^II(CN)₆]⁴⁻ to produce the Prussian blue (PB) molecules (Fe₄^III[Fe^II(CN)₆]₃). Newly formed PB molecules are then immediately converted to colorless Everitts salt (K₄Fe₄^II[Fe^II(CN)₆]₃) with the reduction of the high-spin Fe^III to Fe^II at the surface of a glassy carbon electrode at +0.150 V (versus Ag/AgCl). The calculated concentration of OH during incubation (0.626 ppm) can be detected with negative errors by the HPLC-ECD (0.595 and 0.615 ppm with the errors −5.2 and −1.8%, respectively) and by the chronoamperometric method (0.552 and 0.607 ppm with the errors −11.8 and −3.0%, respectively). For the comparison of the two sets of data, HPLC-ECD method is much more promising.     

Isocyanate formation in the catalytic reaction of CO + NO on Pd(111): an in situ infrared spectroscopic study at elevated pressures

The catalytic CO + NO reaction to form CO2, N2, and N2O has been studied on a Pd(111) surface at pressures up to 240 mbar using in situ polarization modulation infrared reflection absorption spectroscopy (PM-IRAS). At 240 mbar, for a pressure ratio of PCO:PNO = 3:2 and under reaction conditions, besides adsorbed CO, the formation of isocyanate (-NCO) was observed. Once produced at 500-625 K, the isocyanate species was stable within the entire temperature range studied (300-625 K). On the other hand, its formation required a total CO + NO pressure of at least 0.6 mbar, illustrating the importance of in situ infrared experiments under high-pressure conditions. The significance of the isocyanate formation for the CO + NO reaction on Pd(111) is discussed.