Identities for the Widder transform and transforms with Bessel function kernels

In the present paper, we consider the classical Widder transform, the H_ν-transform, the K_ν-transform, and the Y_ν-transform. Some identities involving these transforms and many others are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and other well-known integral transforms.     

A rational approximation based on Bernstein polynomials for high order initial and boundary values problems

We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann [1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution f ∈ C^d+2[a, b].     

Speciation studies on the complex formation reactions of [Pd(N,N-diethyl-ethylendiamine)(H2O)2]2+ with some bio-relevant ligands and displacement reaction by mercaptoethylamine

Pd(deen)Cl2 and Pd(deen)(CBDCA) complexes, where deen=N,N-diethylethylenediamine and CBDCA=1,1-cyclobutanedicarboxylate, were synthesized and characterized by elemental analysis and spectroscopic techniques. The stoichiometry and stability of the complexes formed between various biologically relevant ligands (amino acids, peptides, DNA constituents and dicarboxylic acids) and [Pd(deen)(H2O)2]2+ were investigated at 25 °C and 0.1 M ionic strength. The speciation diagrams of the complexes formed in solutions are evaluated. The mode of coordination of glycylglycine is investigated by spectrophotometric measurements. The equilibrium constants for the displacement of coordinated ligands as inosine, glycine or methionine by mercaptoethylamine are calculated. The results are expected to contribute to the chemistry of antitumour agents.     

Routing problems: A bibliography

This bibliography contains 500 references on four classical routing problems: the Traveling Salesman Problem, the Vehicle Routing Problem, the Chinese Postman Problem, and the Rural Postman Problem. References are presented alphabetically under a number of subheadings.     

Gas-phase thermolysis of benzotriazole derivatives. Part 3: Kinetic and mechanistic evidence for biradical intermediates in pyrolysis of aroylbenzotriazoles and related compounds

Gas-phase pyrolysis (static and FVP) of 1-aroylbenzotriazoles gave the corresponding substituted benzoxazole, benzimidazole, benzamide, N-phenylbenzamide, phenanthridin-6(5H)-one derivatives and 1-cyanocyclopentadiene. The present kinetic and mechanistic findings also provide further evidence of the involvement of biradical or carbene reactive intermediates in the reaction pathway of gas-phase pyrolysis of benzotriazoles.     

Simultaneous square-wave voltammetric determination of riboflavin and folic acid in pharmaceutical preparations

The square-wave voltammetric (SWV) behaviour of riboflavin and folic acid was studied at a static mercury drop electrode by square wave voltammetry. In 0.05M KCl (pH 5.89) a cathodic scan gave peaks at — 0.56 and — 0.87 V vs. Ag/AgCl for riboflavin and folic acid, respectively. The reduction peak currents are linearly dependent on the concentration of vitamins. Both vitamins can be simultaneously determined from the same voltammogram. The method proposed for the determination of riboflavin and folic acid in multivitamin tablets is very simple, rapid and does not involve time-consuming separation steps. The average contents of riboflavin and folic acid were found to be 14.8 ± 1.26% and 1.46 ± 2.66%, for tablet A and 9.86 ±1.40% and 1.47 ± 2.0% for tablet B, respectively.     

Kinetics and mechanism of gas‐phase pyrolysis of N‐aryl‐3‐oxobutanamide ketoanilides,their 2‐arylhydrazono derivatives,and related compounds

Rates and products of reaction and Arrhenius activation parameters were determined for the gas‐phase thermolysis of 14 substrates of the title compounds using sealed pyrex reactor tubes and HPLC/UV‐VIS to monitor substrate pyrolysis. The 14 compounds under study are N‐phenyl‐3‐oxo‐ ( 1 ), N‐(p‐chlorophenyl)‐3‐oxo‐ ( 2 ), N‐(p‐methylphenyl)‐3‐oxo‐ ( 3 ), and N‐(p‐methoxyphenyl)‐3‐oxobutanamide ( 4 ), in addition to (i) four substrates ( 5–8 ) obtained by the replacement of the pairs of methylene hydrogens at the 2‐position of compounds ( 1–4 ), each pair by a phenylhydrazono group; (ii) three arylhydrazono derivatives ( 9–11 ) in which Cl, CH₃, or OCH₃ groups are substituted at the para position of the phenylhydrazono moiety of compound 5 ; (iii) 3‐oxobutanamide (acetoacetamide, 12 ), N‐phenyl‐3‐oxo‐3‐phenylpropanamide ( 13 ), and N,N′‐diphenylpropanediamide ( 14 ). The reactions were conducted over 374–546 K temperature range, and the values of the Arrhenius log A(s^?1) and E_a(kJ mol^?1) of these reactions were, respectively, 12.0 ± 2.0 and 119.2 ± 17.0 for the ketoanilides ( 1–4, 12–14 ), and 13.0 ± 0.7 and 157.5 ± 8.6 for the arylhyrazono compounds ( 5–11 ). Kinetically, the arylhydrazono derivatives were found to be ca. 1.4 × 10³ to 5.7 × 10³ times less reactive than the parent ketoanilides. A mechanism is proposed to account for reaction products and to rationalize molecular reactivities. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 39: 82–91, 2007     

Characterization of a 2‐Benzo[c]cinnoline Modified Glassy Carbon Electrode by Raman Spectroscopy,Electrochemical Impedance Spectroscopy,and Ellipsometry

This work describes the characterization of the grafted 2‐benzo[c]cinnoline (2BCC) molecules at a glassy carbon (GC) electrode surface by voltammetry and spectroscopy. Attachment of the molecule to the carbon substrate was achieved by the electrochemical reduction of 2‐benzo[c]cinnoline diazonium salt (2BCC‐DAS). GC electrode modification was carried out in aprotic solution with 2BCC diazonium salt. Dopamine (DA) and ascorbic acid (AA) were used to prove the surface modification to see the blockage of the electron transfer. The presence of 2BCC at the GC electrode surface was characterized by cyclic voltammetry and Raman spectroscopy. Raman spectroscopy was used to monitor molecular bound properties of the adsorbates at the 2BCC‐GC surface and confirm the attachment of 2BCC molecules onto the GC surface. The thickness of the 2BCC film on GC was also investigated by ellipsometric measurement.     

An integral transformation for integer programming problems

It is shown that every integer programming problem can be transformed into an equivalent integer program with free variables in polynomial time. The transformation is advantageous because the equivalent problem it generates can be solved very easily in some restricted cases.