On shortest cocycle covers of graphs

A cocycle (resp. cycle) cover of a graph G is a family C of cocycles (resp. cycles) of G such that each edge of G belongs to at least one member of C. The length of C is the sum of the cardinalities of its members. While it is known (see [5, 6]) that every bridgeless graph G = (V, E) has a cycle cover of length not greater than $\text{5}\text{3}\text{|E|}$, it is shown that there exists no α < 2 such that every loopless graph G = (V, E) has a cocycle cover with length not greater than α |E|. To do this, cocycle covers of minimal length are determined for the complete graphs, thus solving a problem stated at the end of [6].     

A damped simple pendulum of constant amplitude

A simple pendulum acted on by gravity and subjected to a resistance proportional to the velocity of the bob is considered. If the length of the string and the mass of the bob are held constant, the amplitude of the bob decreases gradually because of the damping. We want to keep the maximum swing of the bob constant for all time; this we achieve by varying the length of the string, the mass of the bob or both. The key to the solution of our problem is a second-order nonlinear differential equation having arbitrary nonlinearity and an arbitrary coefficient function, for which we give the exact integral. We also give an application of this differential equation to a boundary-value problem for a nonlinear generalization of a hypergeometric equation.     

Approximation of the semigroup generated by the Hamiltonian of Reggeon field theory in Bargmann space

The Reggeon field theory is governed by a non-self adjoint operator constructed as a polynomial in A, A^*, the standard Bose annihilation and creation operators. In zero transverse dimension, this Hamiltonian acting in Bargmann space is defined by

Hλ^′,μ=λ^′A*2A²+μA^*A+iλA^*(A^*+A)A,     

Circuits with totally-fluctuating reactive elements

Summary Considered here first is a circuit consisting of resistanceR, inductanceL, capacitanceK, in series with a periodically variable capacitanceC(1 + cos t), with maximum value 2C and minimum value zero (i.e. open circuit). The exact solution of the Hill-type differential equation for the charge on the condensers is shown to be expressible in terms of associated Legendre functions of general degree and order. However, considerable analytical simplification is effected by appropriate choice of the value of capacitanceK, for then the solution (likewise exact) is in terms of more elementary functions. It is found that the value of the angular frequency , in relation to the circuit parameters, influences the character of the solution, which varies considerably with . Secondly, a lossless circuit consisting of a variable inductanceM(1+cos t), shunted by a fixed inductanceL and a capacitanceC, is considered. As before, appropriate choice ofL simplifies the solution functions. Actually, the circulating charge in the variable-inductance case has the same mathematical expression as that for the current in the variable-capacitance case.     

Determination of the Heat of Adsorption and Desorption of a Volatile Organic Compound Under Dynamic Conditions Using Fourier‐Transform Infrared Spectroscopy

Quantitative Fourier‐transform infrared spectroscopic analysis was used for the determination of adsorption capacity of a model volatile organic compound (VOC) under dynamic conditions. The analytical method used also offers the possibility of distinguishing between reversible and irreversible adsorption as well as further detection of adsorbed VOC transformation. The obtained adsorbed amounts have been used for the determination of the heat of adsorption and the activation energy of desorption using, respectively, isosteric and temperature programmed desorption methods. The approach has been applied to explore the potential use of local clay as an adsorbent material for VOC pollutants.     

Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type. An explicit L² norm estimate for the gradient of the solution of this problem is established. This leads to an explicit bound of the H¹ norm of this solution. Note that the obtained upper-bound is not optimal.     

Effect of VGs on a turbulent hydrogen jet

The aim of this study is to investigate numerically the effects of four vortices on the dynamic, scalar, and turbulent fields of the hydrogen jet. These vortices, which appear in the vicinities of the nozzle, are created by the vortex generators (VGs), and they are assembled with periodicity or symmetry in order, respectively, to give four vortices of the same or opposite direction. A second-order Reynolds stress model is used to investigate asymmetric turbulent jet. The results indicate that the presence of the vortex near the emission jet section noticeably enhances mixing to ensure a good combustion.     

Distances entre exponentielles et puissances d’éléments de certaines algèbres de Banach

Let A be a Banach algebra which does not contain any nonzero idempotent element, let γ > 0, and let . We show that if then . We also show, assuming a suitable spectral condition on x, that if , then Received: 12 July 2006 Revised: 31 January 2007     

Synthesis and Molecular Structure Investigation by DFT and X-Ray Diffraction of ARNO

Abstract  

We report here the synthesis of (Z)-5-(4-nitrobenzyliden)-3-N(2-ethoxyphenyl)-2-thioxo-thiazolidin-4-one (ARNO) compound. The crystal structure has been determined by X-ray diffraction. The compound crystallizes in the triclinic system with space group P[`1] P\bar{1} and cell parameters: a = 9.1289(19), b = 9.3717(7), c = 12.136(3) ?, α = 102.133(11)°, β = 90.99(2)°, γ = 117.165(9)°, V = 895.4(3) ?³ and Z = 2. The structure has been refined to a final R = 0.05 for 2591 observed reflections. The refined structure was found to be significantly non planar. The molecule exhibits intermolecular hydrogen bond of type C–H⋯O and C–H⋯S. ab initio calculations were also were performed at Hartree–Fock and density functional theory levels. The full HF and DFT geometry optimization was carried out using LANL2DZ, 6-31G* and B3LYP/6-31+G** basis sets. The optimized geometry of the title compound was found to be consistent structure determined by X-ray diffraction. The minimum energy of geometrical structure is obtained by using level HF/LANL2DZ basis sets.     

First-principles calculations of adhesion,bonding and magnetism of the Fe/HfC interface

First-principles plane-wave pseudopotential calculations of the adhesion, bonding and magnetism of the interface between the ferromagnetic bcc Fe and non-magnetic HfC are performed. The work of adhesion for C- and Hf-site Fe/HfC interfaces is calculated. High adhesion at C-site interface is found and Fe–C polar covalent bonds are formed across the interface. The magnetic moments of Fe atoms at interface are increased in both interfaces. The effect of the magnetism on the electronic structure of Fe/HfC interface is also investigated. It is shown that the change in band of majority-spin leads to enhance the magnetic moment of Fe.