Regularization and Fourier Series for Fredholm Integral Equations of the Second Kind with a Weakly Singular Kernel

To compute an approximate solution, of a weakly singular integral equation, we first regularize the kernel, and then truncate the associated Fourier series. An application to an astrophysical transfer equation is presented.     

Synthesis and X-ray crystal structure of pyrrolo[1,2-a]benzimidazoles

Reaction of nitrilimines 1 with 2-cyanomethylbenzimidazole 2 gave the 3-arylazo-2-methylpyrrolo[1,2-a]benzimidazole 4a rather than the reported 2-arylazo-3-methylpyrrolo[1,2-a]benzimidazole 3a. The correct structure of the product was determined using X-ray crystal structure analysis. The similar reaction of nitrilimines with 2-aminobenzimidazole 5 gave the acyclic nucleophilic addition product 6.     

Existence of positive homoclinic solutions for damped differential equations

This paper is concerned with the existence of positive homoclinic solutions for the second-order differential equation

$$\begin{aligned} u^{\prime \prime }+cu^{\prime }-a(t)u+f(t,u)=0, \end{aligned}$$

where \(c\ge 0\) is a constant and the functions a and f are continuous and not necessarily periodic in t. Under other suitable assumptions on a and f, we obtain the existence of positive homoclinic solutions in both cases sub-quadratic and super-quadratic by using critical point theorems.

     

Reaction of nitrilimines with 2-substituted aza-heterocycles. Synthesis of pyrrolo[1,2-a]pyridine and pyrimido[2,1-d]1,2,3,5- tetrazine

The reaction of nitrilimine 6a with ethyl pyridine-2-acetate (7) gave the corresponding pyrrolo[1,2-a]pyridine 8, while the reaction of 6b containing an ester moiety afforded the acyclic adduct 9. The reaction of 6a with 2-aminopyrimidine (10) gave the novel unexpected pyrimido[2,1-d]1,2,3,5-tetrazine 11. Acyclic adducts 16 and 17 were obtained from the reaction of 6b with 2-cyanomethylbenzimidazole (14) and 2-aminobenzimidazole (15), respectively.     

Computational method for solving space fractional Fisher's nonlinear equation

This paper aims to present a general framework of the quadratic spline functions to develop a numerical method for solving the nonlinear space fractional Fisher's equation. Using Von Neumann method, the proposed method is shown to be conditionally stable. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm. The results reveal that the proposed approach is very effective, convenient, and quite accurate to such considered problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthesis of 1,2,4-Triazol-3-ylmethyl-, 1,3,4-Oxa-, and -Thiadiazol-2-ylmethyl-1H-[1,2,3]-triazolo[4,5-d]pyrimidinediones

1-Carbethoxymethyl-4,6-dimethyl-1H-[1,2,3]triazolo[4,5-d]pyrimidine-5,7(4H,6H)-dione was synthesized and treated with hydrazine hydrate to give the corresponding hydrazide. The latter hydrazide was treated either with phenylisothiocyanate or with carbon disulfide/alc. KOH to afford the corresponding thiosemicarbazide and oxadiazole derivatives. Alkylation of 2-mercapto-1,3,4-oxadiazole with dimethyl sulfate or ethyl chloroacetate gave the corresponding 2-methylthio-, and 2-ethylthioglycolate derivatives. Formation of 1,3,4-thiadiazole, 5-mercapto-1,2,4-triazole, and 1,3,4-oxadiazole were carried out by treating of the latter thiosemicarbazide with conc. H₂SO₄, NaOH/HCl, and HgO. Treating of 5-mercapto-1,2,4-triazole with ethyl chloroacetate afforded the thioglycolate ester. Hydrolysis of the latter with hydrazine hydrate afforded the hydrazide derivatives. Condensation of these hydrazides with monosaccharide aldoses gave the corresponding sugar hydrazones. The novel compounds were tested for antiviral activity against hepatitis B virus and showed moderate activities.     

Effects of the bond dilution on the phase diagrams of a spin-1 transverse Ising model with crystal field interaction on a honeycomb lattice

A bond diluted spin-1 Ising model with crystal and transverse field interactions is examined for honeycomb lattice by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse field and dilution on the phase diagrams and order parameter m_z are discussed in detail. A number of interesting and unusual phenomena such as reentrant phenomena and three successive phase transitions originating from the crystal field as well as the transverse field and bond dilution have been found.     

Synthesis,structural characterizations,spectroscopic and magnetic properties of MnII and MnIII complexes with an unprecedented bridging coordination mode of 2-salicylichydrazono-1,3-dithiolane ligand

Two new complexes [Mn^III(HL)₂(acac)] and [Mn^II(HL)₂]_n have been obtained by reacting manganese(III) acetylacetonate monohydrate or manganese(II) chloride monohydrate with 2-salicylichydrazono-1,3-dithiolane ligand (H₂L). Both compounds have been fully characterized by spectroscopic methods and single crystal X-ray diffraction. In the solid state, the molecular packing are described and discussed in term of weak H-bonds and short contacts. The unprecedented bridging coordination mode of this ligand lead to the first 2-salicylichydrazono-1,3-dithiolane-bridged coordination polymer [Mn^II(HL)₂]_n. The EPR spectrum of this compound was obtained with g ≈ 2.07, corresponding to a manganese ion (+II) in octahedral high-spin coordination sphere. The Mn^II complex exhibit paramagnetic behavior corresponding to quasi-isolated metal centers.     

Effects of anionic additives on the rheological behavior of aqueous calcium montmorillonite suspensions

Three different experimental measurements, namely, rheology, particle sizing, and x-ray diffraction (XRD), were used to study the effect of anionic additives on the properties of bentonite suspensions. The three additives were sodium carboxymethylcellulose, xanthan gum, and sodium dodecyl sulfate. Flow curves were obtained from shear stress–shear rate measurements, and the viscoelastic properties were determined from oscillatory and transient measurements. Mineralogical data were evaluated by XRD and the particle size analysis performed by light scattering technique. The presence of the surfactant modifies the face-to-face interactions and yields changes of the mixtures rheological behavior at low deformation rates. Polymers act by coating each clay particle and prevent their agglomeration. Therefore, the additives are responsible for the mechanisms of destructuration and structure reorganization as well as the mixtures viscous and viscoelastic behavior.     

Multi-objectives Tabu Search based algorithm for progressive resource allocation

Military course of action planning involves time and space synchronization as well as resource and asset allocation. A mission could be seen as a defined set of logical ordered tasks with time and space constraints. The resources to task rules require that available assets should be allocated to each task. A combination of assets might be required to execute a given task. The couple (task, resources) constitutes an action. This problem is formulated as a multi-objectives scheduling and resource allocation problem. Any solution is assessed based on a number of conflicting and heterogeneous objectives. In fact, military planning officers should keep perfecting the plan based on the Commander’s criteria for success. The scheduling problem and resource allocation problem are considered as NP-Hard Problems [A. Guitouni, B. Urli, J.-M. Martel, Course of action planning: A project based modelling, Working Paper, Faculté des sciences de l’ administration, Université Laval, Québec, 2005]. This paper is concerned with the multi-objectives resource allocation problem. Our objective is to find adequate resource allocation for given courses of action schedule. To optimize this problem, this paper investigates non-exact solution methods, like meta-heuristic methods for finding potential efficient solutions. A progressive resource allocation methodology is proposed based on Tabu Search and multi-objectives concepts. This technique explores the search space so as to find a set of potential efficient solutions without aggregating the objectives into a single objective function. It is guided by the principle of maximizing the usage of any resource before considering a replacement resource. Thus, a given resource is allocated to the maximum number of tasks for a given courses of action schedule. A good allocation is a potential efficient solution. These solutions are retained by applying a combination of a dominance rule and a multi-criteria filtering method. The performance of the proposed Pareto-based approach is compared to two aggregation approaches: weighted-sum and the lexicographic techniques. The result shows that a Pareto-based approach is providing better solutions and allowing more flexibility to the decision-maker.