Some congruences for modulus 13 related to partition generating function

In this study, we obtain some congruences modulo 13 related to the partition generating function with the help of a congruence between q-series. We use an elementary method which appears in the work of Kolberg.     

Some singular third-order boundary value problems

In this paper, we consider some singular formally symmetric (self-adjoint) boundary value problems generated by a singular third-order differential expression and separated and coupled boundary conditions. In particular, we consider that the minimal symmetric operator generated by the third-order differential expression has the deficiency indices (3,3). We investigate same spectral properties related with these problems, and we introduce a method to find the resolvent operator.     

Synthesis,characterization, antioxidant properties and DFT calculation of some new pyrimidine derivatives

Abstract

In this study, 5-benzoyl-4-(4-(methylthio)phenyl)-6-phenyl-1,2,3,4-tetrahydro-2-thioxo (1), oxo (2) and imino (3) pyrimidine derivatives were prepared via Multicomponent Cyclocondensation Reactions (MCRs). The compounds thiazolo[3,2-a]pyrimidin-3(5H)-one (4) and thiazin-4(6H)-one (5) were obtained via the reaction of compound 1 with bromoacetic acid and 3-bromopropionic acid, respectively. Structures were determined by using FT-IR, ¹H/¹³C NMR and elemental analyses. Also the compounds 4 and 5 were analyzed by X-ray single crystal analysis. All compounds were investigated as corrosion inhibitors using density functional theory (DFT) at the level of B3LYP/6-31G (d, p). According to the calculations, the compound 3 appears to be a good inhibitor for corrosion. On the other hand, total antioxidant properties were measured in vitro by DPPH^?, ABTS^?+ test, hemolysis of phenylhydrazine erythrocytes and metal chelating effect. The results were compared with standard antioxidants such as trolox and α-tocopherol. These data revealed that compounds 1, 2 and 5 are more active with respect to 3 and 4 in scavenging the radicals.     

A novel metaheuristics approach for continuous global optimization

This paper proposes a novel metaheuristics approach to find the global optimum of continuous global optimization problems with box constraints. This approach combines the characteristics of modern metaheuristics such as scatter search (SS), genetic algorithms (GAs), and tabu search (TS) and named as hybrid scatter genetic tabu (HSGT) search. The development of the HSGT search, parameter settings, experimentation, and efficiency of the HSGT search are discussed. The HSGT has been tested against a simulated annealing algorithm, a GA under the name GENOCOP, and a modified version of a hybrid scatter genetic (HSG) search by using 19 well known test functions. Applications to Neural Network training are also examined. From the computational results, the HSGT search proved to be quite effective in identifying the global optimum solution which makes the HSGT search a promising approach to solve the general nonlinear optimization problem.     

Spectral analysis of the Direct Sum Hamiltonian Operators

In this paper we investigate the deficiency indices theory and the selfad-joint and nonselfadjoint (dissipative, accumulative) extensions of the minimal symmetric direct sum Hamiltonian operators. In particular using the equivalence of the Lax-Phillips scattering matrix and the Sz.-Nagy-Foia¸s characteristic function, we prove that all root (eigen and associated) vectors of the maximal dissipative extensions of the minimal symmetric direct sum Hamiltonian operators are complete in the Hilbert spaces.     

Miscellaneous PEDOT:PTS (polythiophenesulfonyl chloride) based conductive binder for silicon anodes in lithium ion batteries

Lithium ion batteries which are an energy storage system have increasing attention owing to suitability and advantages for many applications. Although it has ideal specifications, the capacity properties still have to be developed. In this study, the electrical conductivity of the anode was increased by using a conductive polymer binder and the active material content of the anode was also enhanced without adding carbon additives. Silicon based anodes were manufactured by using poly(3,4-ethylenedioxythiophene)/polystyrene sulfonate (PEDOT:PSS) and poly(3,4-ethylenedioxythiophene)/polythiophenesulfonyl chloride (PEDOT:PTS) conductive polymer binders. Si/PEDOT:PTS anode showed about 2000 mAh/g specific capacities after 60 cycles with decreasing impedance.     

Complexes of chromium(III) with 2,3-dihydroxynaphthalene-6-sulfonic acid and 4,5-dihydroxynaphthalene-2,7-disulfonic acid in aqueous solution

The chromium(III) complex species formed, in acidic and basic solutions at 25.0+/-0.1 degrees C, between Cr(III) and 2,3-dihydroxynaphthalene-6-sulfonic acid (2,3-DHN-6-SA, H(2)L(2-)) and 4,5-dihydroxynaphthalene-2,7-disulfonic acid (4,5-DHN-2,7-DSA, H(2)L(-)) were determined. Over the acidic pH range, the coordination of 2,3-DHN-6-SA and 4,5-DHN-2,7-DSA to Cr(III) in 1 : 1 mole ratio occurs, and CrL and CrL(-) type complexes are formed. At near neutral pH, CrL(OH)(-) and CrL(OH)(2-) type hydroxo complexes are formed. The acid-dissociation constants of ligands and the formation constants of chromium(III) complexes were determined in 0.1 m KNO(3) ionic medium by potentiometric titration using the BEST computer program. 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.