On the difference equation y_{n + 1} = \frac{{\alpha + y_n^p }} {{\beta y_{n - 1}^p }} - \frac{{\gamma + y_{n - 1}^p }} {{\beta y_n^p }}

In this paper, we investigate the global stability and the periodic nature of solutions of the difference equation $y_{n + 1} = \frac{{\alpha + y_n^p }} {{\beta y_{n - 1}^p }} - \frac{{\gamma + y_{n - 1}^p }} {{\beta y_n^p }},n = 0,1,2,... $ where α, β, γ ∈ (0,∞), α(1 ? p) ? γ > 0, 0 < p < 1, every y _n ≠ 0 for n = ?1, 0, 1, 2, … and the initial conditions y?1, y0 are arbitrary positive real numbers. We show that the equilibrium point of the difference equation is a global attractor with a basin that depends on the conditions of the coefficients.     

trans-2,4,4,6,8,8-Hexamorpholino-2,6-bis­(n-propyl­amino)cyclo-2λ5,4λ5,6λ5,8λ5-tetraphosph­aza­tetraene

The title compound, C₃₀H₆₄N₁₂O₆P₄, consists of a centrosymmetric chair-shaped cyclic tetrameric phosphazene ring with six bulky morpholino and two n-propyl­amino side groups. The two n-propyl­amino side groups are in trans positions. The bulky substituents mainly determine the eight-membered-ring conformation. The endocyclic N—P—N angles around the P atoms having different substituents are not the same as the P—N—P angles of the macrocyclic ring.     

Fine and hyperfine structure in the atomic spectrum of niobium

A parametric analysis of the fine and the magnetic dipole hyperfine structure for the three configurations of odd parity 4d³5s5p, 4d⁴5p and 4d²5s²5p was performed. Effective one-electron parameters were determined and theoretical predictions are given for the magnetic dipole hyperfine structure constants A for the levels of these three configurations. Additionally, 12 new energy levels could be found, four of odd and eight of even parity, by re-analysing data for experimental wavelengths of Nb.     

Utilizing true periodic orbits in chaos-based cryptography

Nonlinear Dynamics - Digital realizations of chaos-based cryptosystems suffer from lack of a reliable method for implementation. The common choice for implementation is to use fixed or...     

Encapsulation of N-heterocyclic carbene–gold (I) catalysts within magnetic core/shell silica gels: A reusable alkyne hydration catalyst

In this study, N-heterocyclic carbene–Au(I) complex, chloro[1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene]gold (I), was successfully encapsulated within mesopores of a magnetic core/shell (γ-Fe₂O₃@SiO₂) silica gel through post-pore-size reduction by silylation reactions The post-reduction of the pore size not only minimizes the catalyst leaching during the alkyne hydration reactions but also eliminates any need for covalent modification of the catalyst or support surface. The resulting catalyst exhibits high activity in hydration reactions of various alkynes even under low catalytic loadings. The catalyst can be easily recycled from the reaction mixture using a magnet and can be reused in alkyne hydration reactions up to six times with only 52. wt% Au leaching.     

Contamination by butyltin compounds in harbour porpoise (Phocoena phocoena) from the Black Sea

Concentrations of butyltin compounds (BTs) were determined in harbour porpoise (Phocoena phocoena) collected from the Turkish coastal waters of the Black Sea. Total butyltin compounds (∑ BTs) in the liver were in the range of 89–219 ng/g on a wet weight basis. The dibutyltin (DBT) residues were higher than those of tributyltin (TBT), suggesting the degradation of TBT to DBT in the liver and the metabolic capacity comparable to other marine mammals. Any sex difference and age-dependent accumulation of BTs residues were not found in harbour porpoises, but residue levels increased until maturity and then remained constant. When compared with other marine mammals, the present results indicate that the Black Sea is also contaminated with butyltin compounds, but to a lesser degree than coastal waters of developed nations. The biomagnification factor in harbour porpoises was 0.8, which was comparable with pinnipeds and lower than cetaceans. Received: 23 December 1996 / Revised: 15 April 1997 / Accepted: 16 April 1997     

Electrochemical Analysis of Antipsychotic Drug Quetiapine Fumarate Using Multi-walled Carbon Nanotube Modified Glassy Carbon Electrode

Electrochemical properties of quetiapine fumarate were examined on the anodic direction with multi-walled carbon nanotube modified glassy carbon electrode using voltammetric methods. The ratio of multi-walled carbon nanotube has been optimized using its various concentrations. The oxidation process was found to be irreversible, and adsorption controlled. The linear ranges were determined as 4×10⁻⁹–2×10⁻⁶ M for differential pulse stripping voltammetry and 2×10⁻⁹–2×10⁻⁶ M for square-wave stripping voltammetry with detection limits of 8.07×10⁻¹⁰ and 2.71×10⁻¹⁰ M, respectively. The methods were validated and successfully applied for the analysis of quetiapine fumarate tablets. The groups responsible for the oxidation reaction of quetiapine fumarate were investigated with model substances.     

The solutions of the<Emphasis Type="Italic">n</Emphasis>-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution

In this article, the operator is introduced and named as the Bessel diamond operator iteratedk times and is defined by

Excited state aromatization assisted push-pull abilities of two unsaturated oxazolone derivatives

Molecular structures of two unsaturated oxazolone derivatives involving furan rings, which are decorated with p-tolyl (FurM) and 4-nitro phenyl (FurN), were investigated by X-ray crystallography and quantum chemical calculations. Their ground and excited states were examined by DFT and TD-DFT computations with the aid of topological electron density studies, NBO and Charge Decomposition Analysis. Both compounds have push-pull (D–π–A) framework using oxazolone ring as π-linker. Depending on the transitions from the ground to excited states, intramolecular charge transfer (ICT) in both compounds results in aromatization of oxazolones. Push-pull ability of FurN has more pronounced than that of FurM. The use of furan instead of almost fully aromatic benzenoid ring reduces HOMO?LUMO band gap due to relatively low aromaticity level of furan. Introduction of nitro substituent leads to a further reduction in HOMO?LUMO gap. In addition, electronic redistribution in the excited state results in aromatization of oxazolone moieties without elongation of carbonyl bonds.     

Can an observable with discrete eigenvalues be conjugate to a continuum observable?

We point out that, in combination with the normalization and completeness relations for the eigenkets of the operators, the commutation relation [O, O]=±ih places severe restrictions on the eigenvalues of the two operators O and O. These restrictions can be used both to determine the character of the pairs of conjugate observables that can be involved in uncertainty relations and to predict thequantized form of the eigenvalues of a discrete observable which is conjugate to a continuum observable with a finite spectrum.