Knapsack problem with probability constraints

This paper is dedicated to a study of different extensions of the classical knapsack problem to the case when different elements of the problem formulation are subject to a degree of uncertainty described by random variables. This brings the knapsack problem into the realm of stochastic programming. Two different model formulations are proposed, based on the introduction of probability constraints. The first one is a static quadratic knapsack with a probability constraint on the capacity of the knapsack. The second one is a two-stage quadratic knapsack model, with recourse, where we introduce a probability constraint on the capacity of the knapsack in the second stage. As far as we know, this is the first time such a constraint has been used in a two-stage model. The solution techniques are based on the semidefinite relaxations. This allows for solving large instances, for which exact methods cannot be used. Numerical experiments on a set of randomly generated instances are discussed below.     

On using the modified variational iteration method for solving the nonlinear coupled equations in the mathematical physics

This paper applied the modified variational iteration method to the nonlinear coupled partial differential equations via the generalized nonlinear Hirota Satsuma coupled KdV equations, the nonlinear coupled Kortewge–de Vries KdV equations and the nonlinear shallow water equations together with the initial conditions. The proposed modification is made by introducing Adomian’s polynomials in the correct functional. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the solution without any discritization, liberalization, perturbation, or restrictive assumptions.     

Nonlinear electrohydrodynamic instability of a finitely conducting cylinder: Effect of interfacial surface charges

The nonlinear electrohydrodynamic stability of cylindrical interface, supporting surface charge, among two conducting fluids is investigated. The two fluids are subjected to a radial electric field. The analysis based on the multiple scale technique. It is shown that the evolution of the amplitude is governed by two partial differential equations. These equations are combined to yield two alternate Schrödinger equations with cubic nonlinearity. One of which calculates the nonlinear cutoff electric field, separating stable and unstable disturbances, while the other is used to analyze the stability of the system. The stability criteria are analytically discussed and numerically confirmed. Numerical calculations resulted in set of graphs to indicate the stability picture of the considered system.     

Nonlinear electrohydrodynamic Kelvin-Helmholtz and Marangoni instabilities near the marginal state

The effects of surface tension and adsorption on the electrohydrodynamic Kelvin-Helmholtz instability are studied. The system is stressed by a normal electric field such that it allows for the presence of surface charges at the interface. The method used is that of multiple scales. The nonlinear Schrödinger equation describing the behavior of the disturbed system is derived. The stability of the perturbed system is discussed both analytically and numerically and the stability diagrams are obtained. At the critical point, a generalized formulation of the evolution equation is developed, which leads to the nonlinear Klein-Gordon equation. The various stability criteria are derived from this equation.     

Nonlinear instability of superposed magnetic fluids in the presence of an oblique magnetic field

The nonlinear evolution of interfacial waves separating two magnetic fluids subjected to an oblique magnetic field is studied in two dimensions, with the use of the method of multiple scales. It is shown that the evolution of the envelope is governed by two partial differential equations. These equations can be combined to yield two alternate Schrödinger equations with cubic nonlinearity; one of them leads to the determination of the cutoff wave number separating stable from unstable deformations while the other Schrödinger equation is used to analyze the stability of the system. The stability of the system is discussed both theoretically and computationally, and the stability diagrams are obtained. It is found in the linear theory that the oblique magnetic field has a stabilizing influence if 0 ₁ + ₂ < /2, or 3/2 < ₁ + ₂ 2 and a destabilizing influence if /2 < ₁ + ₂ < 3/2, where 0 _j , (j=1, 2) and , is the angle between the field and the horizontal axis.In the nonlinear theory, the stability analysis reveals that there exist different regions of stability and instability. It is reported that the oblique magnetic field plays a dual role in the stability criterion and the angles ₁ and ₂ play a distinctive role in this analysis besides the effect of the variation of the magnetic permeabilities.     

CO adsorption on MgO, CaO and SrO crystals periodic Hartree-Fock calculations

The adsorption of carbon monoxide at the defect-free (1 0 0), (1 1 0) and (2 1 0) five-atomic layer slab of the three oxides: MgO, CaO, and SrO has been investigated using the periodic Hartree-Fock level of ab initio theory, together with the 1 × 1 supercell model. All the calculated CO/oxide interaction energies exhibit exothermic character. The HF interaction energies increase monotonically in the order MgO < CaO < SrO. The surface morphology of adsorbate/substrate interaction is confirmed by considering relaxation energies, Mulliken population analysis, charge density contours, and electrostatic potential maps.     

Exploiting the 1,2,3‐Triazole Moiety to Generate Carbazole Molecular Architectures through Click Approach

Reaction of 3,6‐dichlorocarbazole with propargyl bromide in the presence of a basic medium gave an N‐propargylated carbazole. The latter compound was converted into molecular architectures containing 1,2,3‐triazole moiety through Cu(I)‐catalyzed 1,3‐cycloaddition reaction with different azides. Similarly, 2‐azidomethyl benzothiazole was cliched with N‐Boc‐protected N´‐propargyl glutamate to give the biomolecule 2‐triazolylmethyl product.     

A new method for the isolation and estimation of Furan-2,5-dicarboxylic acid in human urine

Summary A new, concise and efficient method of isolation and estimation of F. D. A. avoiding heating with acids, has been devised.Inositol and calcium gluconate when added to urine and subjected to the old method of isolation of F. D. A. result in no increase in the amount of F. D. A. This indicates that the increase in the output of this acid obtained before⁴ was a process within the body itself.Metabolic experiments with inositol and calcium gluconate adopting the new method gave a 3–4 fold increase in the F. D. A. output confirming that this increase is anin vivo process.

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Zusammenfassung Eine neue, genaue Methode zur Isolierung und Bestimmung von Furandicarbonsäure (F. D. C.) ohne Erhitzen des angesäuerten Untersuchungs-materials wurde ausgearbeitet. Werden Inosit und Calciumgluconat dem Harn vor Aufarbeitung nach der alten Methode zugesetzt, so führt dies zu keiner Erhöhung der F. D. C.-Menge. Die früher beobachtete Vermehrung der F. D. C.-Menge ist also die Folge von Vorgängen innerhalb des Organismus. Stoffwechselexperimente mit Inosit und Calciumgluconat mit der neuen Methode zeigen eine drei bis vierfach gesteigerte F. D. C.-Ausscheidung und bestätigen damit deren vermehrte Bildung in vivo.

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Résumé On a imaginé une nouvelle méthode rapide et efficace pour isoler et doser le F. D. A. en évitant le chauffage avec les acides. L'inositol et le gluconate de calcium, ajoutés à l'urine et soumis à la vieille méthode d'isolement du F. D. A. ne produisent pas de surcharge sur la quantité de F. D. A. Ce fait indique que l'augmentation du rendement de cet acide, obtenue auparavant, était un processus dans le corps humain lui-même.Des expériences sur le métabolisme avec l'inositol et le gluconate de calcium, en adoptant la nouvelle méthode, ont donné une augmentation de trois à quatre fois le rendement en F. D. A., ce qui confirme que cette augmentation se produitin vivo.

     

Anti-Quorum Sensing and Anti-Biofilm Activity of Pelargonium × hortorum Root Extract against Pseudomonas aeruginosa: Combinatorial Effect of Catechin and Gallic Acid

HPLC-UV was used to compare the major constituents of two Pelargonium × hortorum cultivars and Pelargonium sidoides root extract. It revealed the presence of catechin and gallic acid in high concentrations and the absence of umckalin in P. × hortorum root extracts. The antibacterial activity of these extracts was screened against 19 Pseudomonas aeruginosa clinical isolates. P. × hortorum root extracts showed the lowest MIC values (512–1024 µg/mL). This activity was concluded to be attributable to the high concentrations of catechin and gallic acid. The anti-biofilm activity of catechin, gallic acid, and their combination was examined by a crystal violet assay. The combination reduced the percentage of strong and moderate biofilm-forming isolates from 52.63% to 5.26%. The impact on lasI and lasR genes expression using qRT-PCR and simultaneous docking against LasR protein was explored. The combination downregulated lasI and lasR gene expression in eight and six P. aeruginosa isolates, respectively, and showed the greatest docking score. Additionally, the in vivo protection capability of this combination in infected mice showed enhancement in the survival rate. Our study revealed the potential biofilm and quorum-sensing-inhibitory activity of the catechin and gallic acid combination as a novel alternative to inhibit bacterial pathogenicity.