Information theories for time-dependent harmonic oscillator

Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville–von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.     

The Real Powers of the Convolution of a Gamma Distribution and a Bernoulli Distribution

In this paper, we essentially compute the set of x,y>0 such that the mapping \(z\longmapsto(1-r+re^{z})^{x}(\frac{\lambda}{\lambda-z})^{y}\) is a Laplace transform. If X and Y are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by μ the distribution of X+Y. The above problem is equivalent to finding the set of x>0 such that μ ^*x exists.     

Self assembled tetranuclear Cu4(II), Ni4(II) [2 × 2] square grids and a dicopper(II) complex of heterocycle based polytopic ligands - Magnetic studies

The ditopic ligand PyPzOAP (N-[(Z)-amino(pyridin-2-yl)methylidene]-5-methyl-1-(pyridin-2-yl)-1H-pyrazole-3-carbohydrazonic acid) and the polytopic ligand 2-PzCAP (N'(3),N'(5)-bis[(1E)-1-(pyridin-2-yl)ethylidene]-1H-pyrazole-3,5-dicarbohydrazide) were synthesized in situ by condensation of methyl imino picolinate with 5-methyl-1-(2-pyridyl) pyrazole-3-carbohydrazide and 2-acetyl pyridine with pyrazole-3,5-dicarbohydrazide respectively. The ligands PyPzOAP and PzOAP (reported earlier, Dalton Trans., 2007, 1229) self-assemble to form homoleptic [2 × 2] tetranuclear M(4) (M = Cu(II) and Ni(II)) square grids structures [Cu(4)(PyPzOAP)(4)](NO(3))(4) (1), [Cu(4)(PzOAP)(4)](ClO(4))(4) (2) and [Ni(4)(PyPzOAP)(4)](NO(3))(4)·8H(2)O·2CH(3)CN (3). While the ligand 2-PzCAP forms a dicopper(II) complex [Cu(2)(2-PzCAP)(OH)(NO(3))(H(2)O)](NO(3))·2H(2)O (4). The complex 1 is a perfect square grid (a = 4.201 ?), whereas, 2 and 3 are almost square grids. All these compounds have been characterized by X-ray structural analyses and variable temperature magnetic susceptibility measurements. EPR studies have also been carried out for complexes 1, 2 and 4. In the Cu(4) grid (1), all the Cu(II) centers are in a distorted octahedral environment with N(4)O(2) chromophore, while, in complex 2, all four Cu(II) centers have a square pyramidal environment with N(3)O(2) chromophore. In complex 3, all four Ni(II) centers have distorted octahedral geometry with N(4)O(2) chromophore. In compound 4, the Cu(II) centers are in square pyramidal environment with N(3)O(2) chromophore. The magnetic properties of compounds 1 and 2 show the presence of intramolecular ferromagnetic exchange interaction (J = 5.88 cm(-1) for 1 and 4.78 cm(-1) for 2). The complex 3 shows weak intramolecular antiferromagnetic interaction (J = -4.02 cm(-1)). While, complex 4, shows strong antiferromagnetic behavior (J = -443 cm(-1)).     

General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity

This work deals with the study of a new class of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity. A decay result of the energy of solutions for the problem without imposing the usual relation between a certain relaxation function and its derivative is established. This result generalizes earlier ones to an arbitrary rate of decay, which is not necessarily of exponential or polynomial decay.     

Biosorption of strontium from aqueous solutions onto spent coffee grounds

A set of experiments was carried out to evaluate the strontium uptake potential of spent coffee grounds (SCG) by batch tests in aqueous medium. Adsorption of Sr²⁺ as a function of contact time and adsorbent dose, pH, particles size, agitation speed, temperature and co-ions presence was investigated. Obtained results revealed that the maximum adsorption took place at pH range of 5–8 and temperature values between 283 and 333 K. Particles size effect was not very significant and agitation speed influenced on the equilibrium time. Competitive adsorption experiments allowed us to classify the negative effect on the Sr²⁺ uptake according to this order Al³⁺ ? Co²⁺ > Mg²⁺ > Ca²⁺ ? Na⁺ > K⁺ > Cs⁺. Kinetic study indicated that the Sr²⁺ uptake was fast and it was well fitted by the pseudo second order reaction model. Adsorption isotherm was well interpreted by Langmuir model. The maximum adsorption capacity was found to be 69.01 mg g^?1 at pH 7, 293 K, particles sizes = 200–400 μm and agitation speed 250 rpm. The thermodynamic study revealed that the process was spontaneous (ΔG ⁰ < 0), exothermic (ΔH ⁰ < 0) with a raised affinity for Sr²⁺ (ΔG ⁰ < 0, ΔS ⁰ > 0) and occurred by physical adsorption (E _a = 8.37 kJ mol^?1). FTIR analysis showed carboxylic acid and amino group presence on SCG surface playing a vital role in Sr²⁺ biosorption.     

Synthesis of New Benzylic Di-, Tri-, and Tetraphosphonic Acids as Potential Chelating Agents

Abstract

New di-, tri-, and tetraphosphonic acids were synthesized starting from four o-hydroxymethyl phenol derivatives and obtained in three steps in good overall yield. The phosphonic acids were isolated and purified using semi-preparative C₁₈ HPLC column. The new compounds were characterized using different spectroscopic methods (¹H, ¹³C, and ³¹P NMR; ESI MS; and MSⁿ, IR).

GRAPHICAL ABSTRACT     

Utilization of electric arc furnace dust as an admixture to Portland cement pastes

Electric arc furnace dust (EAFD) is termed as a hazardous waste due to its contamination with heavy metals. Inertization of such very fine dust can be occurred via stabilization and solidification process within the hydrated Portland cement matrix. In this paper, the effect of the addition of various ratios of EAFD on the properties of the hardened Portland cement paste was investigated. Compressive strength, chemically combine water and free lime contents were determined. In addition, phase composition using XRD; DTA analysis; as well as microstructure of the formed hydrates for some selected samples were investigated using SEM. The obtained results showed that the paste containing 1/mass% EAFD give the highest compressive strength values at most hydration ages, specially the later ages, compared to the neat Portland cement blank paste. Whileas, the pastes containing 3 and 5/mass% EAFD showed lower values of compressive strength compared to those of the blank paste.     

Three new dinuclear manganese(II) complexes with bis(μ-phosphinato)-bridges

A new series of dinuclear phosphinato-bridged manganese(II) complexes [Mn(μ-bmp)(bpy)(NO₃)]₂ (1), [Mn(μ-bmp)(phen)(NO₃)]₂·4CH₂Cl₂ (2) and [Mn₂(μ-bmp)₂(5-dmbpy)₂(NO₃)]₂ (3) where Hbmp is bis(4-methoxyphenyl)phosphinic acid, bpy = 2,2′-bipyridyl, phen = 1,10-phenanthroline and 5-dmbpy = 5,5′-dimethyl-2,2′-dipyridyl, have been synthesized and structurally characterized by X-ray crystallography. In this series, the structures consist in bis(4-methoxyphenyl)phosphinato anions (bmp) bridging the two Mn(II) centers in a syn-syn coordination mode. The coordination geometry around the Mn(II) ions in 1-3 is six-coordinate with distorted octahedral environment. The magnetic behavior of these complexes is reported. The complexes show weak antiferromagnetic coupling with |J| in the range 0.1-0.6 cm⁻¹. The magnetic properties are discussed in relation to the structural data.