On co-ordinated quasi-convex functions

A function f: I → ?, where I ? ? is an interval, is said to be a convex function on I if $$f(tx + (1 - t)y) \le tf(x) + (1 - t)f(y)$$ holds for all x, y ∈ I and t ∈ [0, 1]. There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensenconvex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex functions on the coordinates. We also prove some inequalities of Hadamard-type as Dragomir’s results in Theorem 5, but now for Jensen-quasi-convex and Wright-quasi-convex functions. Finally, we give some inclusions which clarify the relationship between these new classes of functions.     

The synthesis,characterization and antibacterial activities of dinuclear Ni(II), Cu(II) and Fe(III) Schiff base complexes

Schiff base; N,N′-bis-(2-hydroxy-1-naphthaldimine)-1,3-diaminopropanol (napdapOH) reacts with metal chlorides to form dinuclear complexes of the type [M₂L₂] · nCl₂ where M = Ni, Cu, Fe and n = 0, 1. Schiff base complexes were characterized by using FT-IR, LC-MS, magnetic moments and conductance measurements. Coordination was found to be through the phenolic oxygen atoms and azomethine nitrogen atoms. The electronic properties of the compounds were investigated theoretically by performing semiempirical molecular orbital theory PM3 method in Hyperchem 7 (Release). The antibacterial activities of the compounds were investigated against Escherichia coli ATCC 11230, Bacillus subtilis RSKK 244, Bacillus megaterium RSKK 5117, Salmonella enteritidis ATCC 13076, Staphylococcus aureus ATCC 25923 by using microdilution method.     

Fractional optimal control of a 2-dimensional distributed system using eigenfunctions

This paper presents an eigenfunctions expansion based scheme for Fractional Optimal Control (FOC) of a 2-dimensional distributed system. The fractional derivative is defined in the Riemann–Liouville sense. The performance index of a FOC problem is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE) containing two space parameters and one time parameter. Eigenfunctions are used to eliminate the terms containing space parameters and to define the problem in terms of a set of generalized state and control variables. For numerical computation Grünwald–Letnikov approximation is used. A direct numerical technique is proposed to obtain the state and the control variables. For a linear case, the numerical technique results into a set of algebraic equations which can be solved using a direct or an iterative scheme. The problem is solved for different number of eigenfunctions and time discretization. Numerical results show that only a few eigenfunctions are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced.     

Reactions of 1‐amino‐5‐benzoyl‐4‐phenyl‐1H‐pyrimidine‐2‐one with carboxylic anhydrides: Experimental data and AM1 calculations

1‐Amino‐5‐benzoyl‐4‐phenyl‐1H‐pyrimidine‐2‐one 1 reacts with several carboxylic anhydrides 2a‐d under different conditions and gives new amide and imide derivatives. The structure of these compounds, 3a‐d , are determined by spectroscopic methods. Electronic and geometric structures of reactants, transition states, intermediates and final products of the reaction are calculated by the AM1 method. Transition states are further confirmed by vibrational analysis (computation of force constants analytically) and characterized by the corresponding imaginary vibration modes and frequencies.     

Conjugate heat transfer in thermally developing laminar flow with viscous dissipation effects

In this study, thermally developing laminar forced convection in a pipe including viscous dissipation and wall conductance is investigated numerically. The constant heat flux is assumed to be imposed at the outer surface of the pipe wall. The finite volume method is used. The distributions for the developing temperature and local Nusselt number in the entrance region are obtained. The dependence of the results on the Brinkman number and the dimensionless thermal conductivity are shown. The viscous heating effect on the wall is shown. Significant viscous dissipation effects have been observed for large Br.     

Energy elastic effects and the concept of temperature in flowing polymeric liquids

The incorporation of energy elastic effects in the modeling of flowing polymeric liquids is discussed. Since conformational energetic effects are determined by structural features much smaller than the end-to-end vector of the polymer chains, commonly employed single conformation tensor models are insufficient to describe energy elastic effects. The need for a local structural variable is substantiated by studying a microscopic toy model with energetic effects in the setting of a generalized canonical ensemble. In order to examine the dynamics of flowing polymeric liquids with energy elastic effects, a thermodynamically admissible set of evolution equations is presented that accounts for the evolution of the microstructure in terms of a slow tensor, as well as a fast, local scalar variable. It is demonstrated that the temperature used in the definition of the heat flux is directly related to the Lagrange multiplier of the microscopic energy in the generalized canonical partition function. The temperature equation is discussed with respect to, first, the dependence of the heat capacity on the polymer conformation and, second, the possibility to measure experimentally the effects of the conformational energy.

On the flow in a uniformly porous pipe

This article considers fully laminar flow of an incompressible viscous fluid in a uniformly porous pipe with suction and injection. An exact solution of the Navier–Stokes equations is given. The velocity filed can be expressed in a series form in terms of the modified Bessel function of the first kind of order n. The volume flux across a plane normal to the flow, the vorticity and the stress on the boundary are presented. The flow properties depend on the cross-Reynolds number, Ua/ν, where U is the suction velocity, a is the radius of the pipe and ν is the kinematic viscosity of the fluid. It is found that for large values of the cross-Reynolds number, the flow near the region of the suction shows a boundary layer character. In this region the velocity and the vorticity vary sharply. Outside the boundary layer, the velocity and the vorticity do not show an appreciable change.     

Formulas and numerical table for the radial part of overlap integrals with the same screening parameters of Slater-type orbitals

 The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = ξR over Slater-type orbitals have been studied and obtained by using three different methods. For that purpose, the characteristics of auxiliary functions were used first, then Fourier transform convolution theorem, and recurrence relations for the basic coefficients of A ^s _{n l λ, n ′ l ′λ} were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 ≤ n ≤ 75, 1 ≤ n′ ≤ 75, and 10⁻⁶ ≤ p. Received: 18 January 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

A novel bidentate ligand containing oxime,hydrazone and indole moieties and its BF2+ bridged transition metal complexes and their efficiency against prostate and breast cancer cells

In this study, a novel bidentate ligand containing oxime, hydrazone, and indole moieties and its BF₂⁺-bridged transition metal complexes [Ni(II), Cu(II), and Co(II)] were synthesized and their cytotoxic activities against prostate and breast cancer cells were investigated. The vic-dioxime ligand bearing indole–hydrazone side groups was synthesized by reacting antiglyoximehydrazine (GH₂) with 3-methoxy indole. The ligand forms mononuclear complexes with a metal-to-ligand ratio of 1:2 with M = Co(II)(H₂O)₂, Ni(II), and Cu(II). These metal complexes were then reacted with BF₃(C₂H₅)₂O to obtain BF₂⁺-bridged transition metal complexes. The Co(II) complex of the ligand is proposed to be octahedral with water molecules as axial ligands, whereas the Ni(II) and Cu(II) complexes are proposed to be square planar. Spectral studies showed that the ligand bonded to the metal ion in a neutral bidentate fashion through the azomethine nitrogen atom and the imine oxime group. Structural assignments are supported by a combination of ¹H nuclear magnetic resonance (NMR), ¹³C NMR, Fourier-transform infrared, LC/MS, elemental analyses, and magnetic susceptibility testing. For determining the cytotoxic effects of the novel anticancer products, cancer cells were cultured. The antiproliferative effects were determined using the MCF-7 breast cancer and PC-3 prostate cancer cell lines. The antiproliferative effects of the products were analyzed and their apoptotic or necrotic effects were determined with the Hoechst/propidium iodide double staining method in both cancer cell lines. Paclitaxel was used as the positive control (1 μm ). The results indicated that the newly synthesized compounds are effective on both cell lines between concentrations of 5 and 40 μm and show their effects by apoptotic mechanisms. Besides, these products were found to be more effective on the MCF-7 cell line. The cytotoxic efficiency of the newly synthesized products was more than that of paclitaxel (depending on concentration), which is a chemotherapeutic agent used in cancer therapy.