Application of generalized differential transform method to multi-order fractional differential equations

In a recent paper [Odibat Z, Momani S, Erturk VS. Generalized differential transform method: application to differential equations of fractional order, Appl Math Comput. submitted for publication] the authors presented a new generalization of the differential transform method that would extended the application of the method to differential equations of fractional order. In this paper, an application of the new technique is applied to solve fractional differential equations of the form y^(μ)(t)=f(t,y(t),y^(β₁)(t),y^(β₂)(t),…,y^(β_n)(t)) with μ>β_n>β_n-1>…>β₁>0, combined with suitable initial conditions. The fractional derivatives are understood in the Caputo sense. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the new generalization.     

On the perturbation determinants of a singular dissipative boundary value problem with finite transmission conditions

In this paper a singular dissipative boundary value problem with finite transmission conditions is investigated. Using Livšic’s theorem, it is proved that the system of all eigen and associated functions of this problem is complete in the Hilbert space.     

Formation constants of chromium(III), scandium(III) and yttrium(III) complexes of some hydroxy naphthoic acids

The complexes of chromium(III), scandium(III) and yttrium(III) formed by 1-hydroxy-2-naphthoic acid (1,2-HNA: H2L) and 3-hydroxy-2-naphthoic acid (3,2-HNA: H2L) were investigated by potentiometry and spectroscopy at 25+/-0.1 degrees C and at an ionic strength of 0.1 M KNO3 in 50% ethanol-water (v/v) medium. The stoichiometries of these three M(III) complexes formed with these hydroxy-naphthoic acids and with hydroxo ion were defined and their formation constants were determined and compared. Thus, the removing capacities of these ligands could be examined by calculating the equilibrium concentration of Cr(III) that exists in the discharge water of various industries since Cr(III) ions are the main pollutants present during waste water treatment in our city, Bursa.     

Effect of electron donor-acceptor interaction on the thermal stability of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane)

Supramolecular side chain liquid crystalline polymers were prepared from poly(3-carboxypropylmethylsiloxane) (PSI100) and azobenzene-based derivatives through intermolecular hydrogen bonding between the carboxylic acid groups of PSI100 and the imidazole rings in the azobenzene-based derivatives. The presence of H-bonding was confirmed using FTIR spectroscopy. The polymeric complexes behave as liquid crystalline polymers and exhibit nematic mesophases identified on the basis of the observation of Schlieren textures. The mesogenic behaviour of these complexes was studied by polarizing optical microscopy and X-ray diffraction. The thermal behaviour of the complexes was investigated by differential scanning calorimetry. On increasing the spacer length, the transition temperatures initially increase. A further increase in spacer length, however, leads to a decrease in the transition temperatures. The electron donor-acceptor interaction between unlike mesogenic units in supramolecular copolymeric complexes helps to stabilize the mesophase.     

Compositional and electrical properties of line and planar defects in Cu(In,Ga)Se2 thin films for solar cells – a review

The present review gives an overview of the various reports on properties of line and planar defects in Cu(In,Ga)(S,Se)₂ thin films for high‐efficiency solar cells. We report results from various analysis techniques applied to characterize these defects at different length scales, which allow for drawing a consistent picture on structural and electronic defect properties. A key finding is atomic reconstruction detected at line and planar defects, which may be one mechanism to reduce excess charge densities and to relax deep‐defect states from midgap to shallow energy levels. On the other hand, nonradiative Shockley–Read–Hall recombination is still enhanced with respect to defect‐free grain interiors, which is correlated with substantial reduction of luminescence intensities. Comparison of the microscopic electrical properties of planar defects in Cu(In,Ga)(S,Se)₂ thin films with two‐dimensional device simulations suggest that these defects are one origin of the reduced open‐circuit voltage of the photovoltaic devices. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Similar biological activities of two isostructural ruthenium and osmium complexes

In this study, we probe and verify the concept of designing unreactive bioactive metal complexes, in which the metal possesses a purely structural function, by investigating the consequences of replacing ruthenium in a bioactive half-sandwich kinase inhibitor scaffold by its heavier congener osmium. The two isostructural complexes are compared with respect to their anticancer properties in 1205 Lu melanoma cells, activation of the Wnt signaling pathway, IC(50) values against the protein kinases GSK-3beta and Pim-1, and binding modes to the protein kinase Pim-1 by protein crystallography. It was found that the two congeners display almost indistinguishable biological activities, which can be explained by their nearly identical three-dimensional structures and their identical mode of action as protein kinase inhibitors. This is a unique example in which the replacement of a metal in an anticancer scaffold by its heavier homologue does not alter its biological activity.     

The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators

In this paper, a reliable algorithm based on an adaptation of the standard differential transform method is presented, which is the multi-step differential transform method (MSDTM). The solutions of non-linear oscillators were obtained by MSDTM. Figurative comparisons between the MSDTM and the classical fourth-order Runge-Kutta method (RK4) reveal that the proposed technique is a promising tool to solve non-linear oscillators.