Legendre polynomial solutions of high-order linear Fredholm integro-differential equations

In this study, a Legendre collocation matrix method is presented to solve high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the interval [−1, 1], which corresponding to systems of linear algebraic equations with Legendre coefficients. Thus, by solving the matrix equation, Legendre coefficients and polynomial approach are obtained. Also examples that illustrate the pertinent features of the method are presented and by using the error analysis, the results are discussed.     

Selectively increasing of polyunsaturated (18:2) and monounsaturated (18:1) fatty acids in Jatropha curcas seed oil by crystallization using D-optimal design

ABSTRACT: BACKGROUND: This study was done to obtain concentrated polyunsaturated fatty acid (PUFA) linoleic acid (LA; 18:2) and monounsaturated fatty acid (MUFA) oleic acid (OA; 18:1) from Jatropha curcas seed oil by urea complexation. Urea complexation is a method used by researchers to separate fatty acids (FAs) based on their molecular structure. Effects the ratio of urea-to-FAs, crystallization temperature and crystallization time on the final products of urea complexation were examined. D-optimal Design was employed to study the significance of these factors and the optimum conditions for the technique were predicted and verified. RESULTS: Optimum conditions of the experiment to obtain maximum concentration of LA were predicted at urea-to-FAs ratio (w/w) of 5:1, crystallization temperature of 10 C and 24 h of crystallization time. Under these conditions, the final non-urea complex fraction (NUCF) was predicted to contain 92.81% of LA with the NUCF yield of 7.8%. The highest percentage of OA (56.14%) was observed for samples treated with 3:1 urea-to-FAs ratio (w/w) at 10 C for 16 h. The lowest percentage of LA (8.84%) was incorporated into urea complex fraction (UCF) with 1:1 urea-to-FAs ratio (w/w) at 10 C for 8 h. CONCLUSIONS: The separation of PUFA (LA) and MUFA (OA) described here. Experimental variables should be carefully controlled in order to recover a maximum content of PUFA and MUFA of interest with reasonable yield% with a desirable purity of fatty acid of interest.     

Phthalocyanine with a giant dielectric constant

Compound 1 has been prepared by the reaction of 4-nitrophthalonitrile and trans-2-methoxy-4-(2-nitrovinil)phenol by the common method of nucleophilic substitution of an activated nitro group in an aromatic ring. The metallophthalocyanines 2, 3 were prepared by the reaction of a dinitrile derivative with Co(OAc)(2) or Zn(OAc)(2) in DMSO. The lutetium bis-(phthalocyaninato) complex 4 was obtained by treating the dinitrile derivative with lutetium acetate and DBU in 1-hexanol. The new compounds were characterized by elemental analyses, FT-IR, (1)H-NMR, MALDI-TOF MS and UV/Vis spectral data. The spectroscopic data of the new compounds were in accordance with the structures. The temperature and frequency dependence of dielectric and conduction properties of the spin coated film of compounds (2-4) have been studied by fabricating metal-Pc-metal structures. The results show that compound 2 has giant dielectric constant. At a low range of frequency and room temperature, ε' is found to be equal to 2.33 × 10(6), 1.53 × 10(4) and 1.03 × 10(4) for 2, 3 and 4, respectively. The giant dielectric behavior of 2 is mainly attributed to Maxwell-Wagner polarization. The obtained results also indicated that the frequency dependence of the dielectric permittivity, ε'(ω), exhibits non-Debye type relaxation for all temperatures investigated. The ac conductivity results gave a temperature dependent frequency exponent s. The results were compared with the prediction of the Quantum Mechanical Tunneling and Correlated Barrier Hopping models.     

Evaluation of Schiff bases of 2,5-dimercapto-1,3,4-thiadiazole as photostabilizer for poly(methyl methacrylate)

The photostabilization of poly(methyl methacrylate) (PMMA) films by Schiff bases of 2,5-dimercapto-1,3,4-thiadiazole compounds was investigated. The PMMA films containing concentration of complexes 0.5% by weight were produced by the casting method from chloroform solvent. The photostabilization activities of these compounds were determined by monitoring the hydroxyl index with irradiation time. The changes in viscosity average molecular weight of PMMA with irradiation time were also tracked (using benzene as a solvent). The quantum yield of the chain scission (Φ_cs) of these complexes in PMMA films was evaluated and found to range between 4.19 × 10^?5 and 8.75 × 10^?5. Results obtained showed that the rate of photostabilization of PMMA in the presence of the additive followed the trend:[1] > [2] > [3] > [4] > [5].According to the experimental results obtained, several mechanisms were suggested depending on the structure of the additive. Among them, UV absorption, peroxide decomposer, and radical scavenger for photostabilizer mechanisms were suggested.     

Theory of sheath in a collisional multi-component plasma

The aim of this brief report is to study the behaviour of sheath structure in a multi-component plasma with dust-neutral collisions. The plasma consists of electrons, ions, micron size negatively charged dust particles and neutrals. The sheath-edge potential and sheath width are calculated for collisionally dominated sheath. Comparison of collisionless and collisionally dominated sheath are made.     

Effects on measurement of photon-atom scattering of applied pressures on sample at different thickness

N_coh/N_Comp and NK_β/NK_α intensity ratios of scattered photons by Zn in the linear region and the infinite mass thickness region are measured as functions of the pressure used for compressing the pellets with a Si(Li) detector using Am-241 and Fe-55 annular source. Besides, the effect on the experimental intensity ratio of relation between two different thicknesses of sample with applied different pressures on the sample is investigated in this study. Harmony between the linear and infinitive (critical) thickness region and the applied pressure on the sample has directly affected the experimental intensity ratios. Experimental results were not compared with various theoretical values in the literature, for present results constitute the first experimental measurements.     

Two-Parametric Extension of h-Deformation of GL(1|1)

The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL(1|1) via a contraction of GL_p,q(1|1) is presented. Related differential calculus on the quantum superplane is introduced.     

A study on 3-D stress distributions in the bi-adhesively bonded T-joints

In this study, the normal (σ_x, σ_y, σ_z) and shear stress (τ_xy, τ_yz, τ_zx) distributions occurring in a bi-adhesively bonded T-joint with was investigated via a non-linear three dimensional finite element analysis. For this purpose, first of all, using 2024-T3 aluminum alloy as the adherend and the support, a two-part paste (DP 460) and a film type (SBT 9244) as adhesive, two different types of T-joint samples (single-adhesively bonded T-joint and bi-adhesively bonded T-joint) were produced for experimental studies. After experimental studies on the three different T-joint types were conducted, stress analyses in the T-joints were performed with a three-dimensional finite element analysis by considering the geometrical non-linearity and the material non-linearities of the adhesive (DP460 and SBT9244) and adherend (AA2024-T3). Finally, for a given adherend, the lower the stiffness of the adhesive used in the overlap, the lower the stress concentration, leading to potentially higher joint strength. The use of relatively low stiffness adhesives at the ends of the overlap in a bi-adhesive can decrease the stress concentration and, therefore, potentially lead to higher joint strength.     

Synthesis,Spectroscopic and Electrochemical Studies of Novel Transition Metal Complexes with Quadridentate Schiff Base

A novel quadridentate, N₂O₂ type Schiff base, synthesized from 1,4‐bis‐(o‐aminophenoxy)butane and 2‐hydroxynaphthalin‐1‐carbaldehyde, forms stable complexes with transition metal ions such as Co(II), Cu(II) and Ni(II) in DMF. Microanalytical data, elemental analysis, magnetic measurements, UV‐visible and IR‐spectra as well as conductance measurements were used to confirm the structures. Electrochemical measurements show that metal complexes undergo quasi‐reversible one‐electron redox processes. The voltammetric results also revealed that the CuL complex has the highest electron transfer rate indicating that both the Cu(II) and Cu(I) forms appear in a similar planar configuration, so the electron transfer does not require larger reorganization of the complex.