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.     

Sorption/desorption study of strontium on Ain Oussera soils around the Es-Salam reactor facility

Four types of undisturbed soils around the Es-Salam reactor (Algeria) were used to evaluate the sorption behavior of strontium. The batch study was carried out under different experimental conditions. The kinetics were well fited by pseudosecond order model. Soils’s activation energies were 12.37, 14.76, 15.5 and 16.17 kJ mol⁻¹, corresponding to ion-exchange-type sorption. Sorption was exothermic (ΔH° < 0), spontaneous (ΔG° < 0) and favorable at low temperature. Competing cations, particularly Ca²⁺ reduce the Sr adsorption. Desorption reaction showed a higher value of Sr in the easily extractible phase indicating a relative availability of the element.

     

Band gap and band offsets of GaNAsBi lattice matched to GaAs substrate

In this paper, we calculate the band gap and the band discontinuities of a GaN _y AsBi _x structure lattice matched to GaAs substrate using the conduction and the valence band anticrossing models at the same time. The results obtained show a good agreement with experiment. The nitrogen and the bismuth concentrations leading to a wavelength emission of 1.55 μm have been determined (x = 3.5%, y = 2%). This structure shows a good electron confinement resulting in a high characteristic temperature.     

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.     

Novel palladium nanoparticles supported on mesoporous natural phosphate: Catalytic ability for the preparation of aromatic hydrocarbons from natural terpenes

Various ratios of palladium nanoparticles supported on mesoporous natural phosphate (Pd@NP) were prepared using the wetness impregnation method. The prepared catalysts were characterized by IR, XRD, CV, SEM, EDX, XRF, TEM and BET analysis. The reduction and preparation of the palladium nanoparticles afford a crystallite size of 10.88 nm. The performance of the synthesized catalyst was investigated in the solvent-free dehydroaromatization of α-, β- and γ-himachalene mixture from Cedrus atlantica oil as a model substrate. In order to achieve an efficient and selective catalysis, the catalytic dehydroaromatization of various terpenes such as limonene, limonaketone, carvone, carveol and perillyl alcohol was studied. The Pd@NP catalyst performed a high catalytic activity, selectivity and recyclability in the terpenes dehydroaromatization reaction.     

Analytical solution of optimal Meixner-like pole

In this paper, we prove the possibility of optimization of some free parameters of Meixner-like discrete-time linear filters using orthonormal basis functions (OBF) in an analytical way. Since the z-transform of the Meixner filters is impossible and it is possible for Meixner-like filters, we are motivated to study closely the optimization of the Meixner-like's pole. As a result, the differential equation associated with Meixner-like filters has been developed. On the other hand, the effective width of the energy distribution in the transformation domain is a function of the free parameter (Meixner-like pole) and simple signal measurements and can be calculated by the second-order moment. Analytic minimization of the second-order moment gives an optimal value of the free parameter. To validate the effectiveness of the proposed approach, numerical results are used to determine the free parameters.