Exponential-like responses analysis method

An exponential-like responses analysis method is presented. The method enables one: 1) to evaluate the similarity of a curve to the ideal exponential characteristic; 2) to find the most appropriate final value of a curve; and 3) to find the value of Τ giving the best approximation between the analyzed curve and the ideal exponential one.     

The cyanide-catalyzed conversion of β-formylmuconates into triglochinates: A useful biomimetic synthesis

Upon treatment with cyanide under slightly basic conditions, β-formyl-cis,cis-muconic acid and esters, prepared from vanillin, undergo a sequence of prototropic shifts equivalent to an internal redox process in which 1,4-reduction of the diene system is blanaced by oxidation of the formyl group.     

The kinetics of tritium-hydrogen exchange between xanthine,theophylline,caffeine and water

Isotopic hydrogen exchange at C-8 of xanthine, theophylline and caffeine in water has been studied at several temperatures and constant pH. The rates of detritiation of these compounds have been determined over a pH range at constant temperature. The rate-pH profiles for theophylline and caffeine are interpreted in terms of rate determining attack by hydroxide ion on protonated substrate. For caffeine and xanthine at high pH an additional mechanism involving hydroxide catalysed exchange of the neutral compound is suggested.     

A tetranuclear 3d-4f single molecule magnet: [CuIILTbIII(hfac)2]2

We report now the first single molecule magnet (SMM) consisting of d-f elements. The present study demonstrates that the synthesis of the d-f polynuclear molecule is a very promising approach to SMMs. (1) The d-f polynuclear molecule can be easily synthesized by the assembly reaction of the d-component and the f-component, (2) the high-spin ground state can be generated by a smaller number of metal ions than the d complex, and (3) the molecular magnetic anisotropy is easily derived from the f-component.     

Computing the tame kernel of quadratic imaginary fields

J. Tate has determined the group (called the tame kernel) for six quadratic imaginary number fields where Modifying the method of Tate, H. Qin has done the same for and and M. Skaba for and

In the present paper we discuss the methods of Qin and Skaba, and we apply our results to the field

In the Appendix at the end of the paper K. Belabas and H. Gangl present the results of their computation of for some other values of The results agree with the conjectural structure of given in the paper by Browkin and Gangl.

     

The construction of the Gilmore–Perelomov coherent states for the Kratzer–Fues anharmonic oscillator with the use of the algebraic approach

By applying the algebraic approach and the displacement operator to the ground state, the unknown Gilmore–Perelomov coherent states for the rotating anharmonic Kratzer–Fues oscillator are constructed. In order to obtain the displacement operator the ladder operators have been applied. The deduced SU(1, 1) dynamical symmetry group associated with these operators enables us to construct this important class of the coherent states. Several important properties of these states are discussed. It is shown that the coherent states introduced are not orthogonal and form complete basis set in the Hilbert space. We have found that any vector of Hilbert space of the oscillator studied can be expressed in the coherent states basis set. It has been established that the coherent states satisfy the completeness relation. Also, we have proved that these coherent states do not possess temporal stability. The approach presented can be used to construct the coherent states for other anharmonic oscillators. The coherent states proposed can find applications in laser-matter interactions, in particular with regards to laser chemical processing, laser techniques, in micro-machinning and the patterning, coating and modification of chemical material surfaces.     

Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method

The study involves finding exact eigenvalues of the radial Schrödinger equation for new expansion of the anharmonic potential energy function. All analytical calculations employ the mathematical formalism of the supersymmetric quantum mechanics. The novelty of this study is underlined by the fact that for the first time the recurrence formulas for rovibrational bound energy levels have been derived employing factorization method and algebraic approach. The ground state and the excited states have been determined by means of the hierarchy of the isospectral Hamiltonians. The Riccati nonlinear differential equation with superpotentials has been solved analytically. It has been shown that exact solutions exist when the potential and superpotential parameters satisfy certain supersymmetric constraints. The results obtained can be utilized both in computations of quantum chemistry and theoretical spectroscopy of diatomic molecules.     

Low-birefringence liquid crystal mixtures for photonic liquid crystal fibres application

ABSTRACT

Series of low-birefringence liquid crystal mixtures composed of alkyl alkylbicyclohexyl carbonates and modified mixtures with other compounds have been formulated, their refractive indices and electric permittivity measured upon temperature. They exhibit the ordinary refraction index n_o lower than the refractive index of silica glass in a different range of temperature. This enables to observe in photonic liquid crystal fibres (PLCFs) a change in the light propagation mechanism from photonic band gap guiding to modified total internal reflection at different temperatures. Selected applications of PLCFs are also discussed.     

In silico modeling of functionalized graphene oxide-metal cluster conjugates as Raman probe: Raman activity of pyridine

Functionalized graphene – metal nano-conjugates are used as Raman probes, in recent years, for trace level identification of materials having specific Raman active modes. In the present paper, model Raman probes were modeled through conjugation of Au₄ and Ag₄ clusters with functionalized graphene systems. In silico models of functionalized (5,5)-graphene sheets were designed at the density functional theory (DFT) level through attachments of epoxy, -OH and –NH(CH₃)₂SH/-CONH(CH₃)₂SH groups. Model Raman probes were designed through attachment of Au₄ and Ag₄ clusters to the functional sites. Full geometry optimizations followed by vibrational analysis were carried out to ensure that the designed Raman probes have acceptable geometric characteristics to attach Raman-active molecules to the metal site. Pyridine was used as a test system to investigate the functionality of such model Raman probes through attachment with the metal clusters. It was observed that the chemical effects due to such attachments increase the Raman intensities (RI) of specific Raman modes of pyridine (in-plane symmetric bending (1040 cm^-1) and asymmetric stretch-bend (1634 cm^-1)), which are too weak in the isolated molecule. Furthermore, the suggested in silico system could provide an important model for basic understanding of RI-enhancements of molecules through increase of the size of the metal clusters, as the observed enhancement was found to be dependent on the polarizability of the metal clusters attached to the molecule of interest.     

Copper Crystallization from Aqueous Solution: Initiation and Evolution of the Polynuclear Clusters

The initial steps of copper electrocrystallization process from aqueous solutions have been studied at DFT level of theory. It has been shown that Cu(H₂O) unit is the final product of Cu²⁺-ions electroreduction. From this particle clusters Cu_n·aq are formed and grow. Aggregation of copper atoms to the Cu_n·aq clusters consists of two steps. The first step includes condensation of Cu(H₂O) units to hydrated clusters Cu_n(H₂O)_n (n = 2–6). At the second step bonding of Cu(H₂O) particles is accompanied by dehydration of clusters yielding Cu_n(H₂O)_m structures (n > m). Cluster Cu₇·aq has been singled out as key structure based on calculated values of energies and Cu–Cu bond distances of Cu_n·aq clusters. This cluster is of D_5h symmetry which is typical for copper microcrystals formed from aqueous solutions in electrocrystallization processes on foreign surface. This key particle could be considered as a critical nucleus. Number of copper atoms therein matches average dimension of critical nucleus.