Homonuclear long-range correlation spectra from HMBC experiments by covariance processing

We present a new application of covariance nuclear magnetic resonance processing based on 1H--13C-HMBC experiments which provides an effective way for establishing indirect 1H--1H and 13C--13C nuclear spin connectivity at natural isotope abundance. The method, which identifies correlated spin networks in terms of covariance between one-dimensional traces from a single decoupled HMBC experiment, derives 13C--13C as well as 1H--1H spin connectivity maps from the two-dimensional frequency domain heteronuclear long-range correlation data matrix. The potential and limitations of this novel covariance NMR application are demonstrated on two compounds: eugenyl-beta-D-glucopyranoside and an emodin-derivative.     

On Weakly Formulated Sylvester Equations and Applications

We use a “weakly formulated” Sylvester equation

A quadratic programming approach to the Randić index

Let G(k, n) be the set of connected graphs without multiple edges or loops which have n vertices and the minimum degree of vertices is k. The Randi? index χ = χ(G) of a graph G   is defined by χ(G)=_∑(uv)(_δuδv)^-1/2$\chi (G)={\sum }_{(\mathit{uv})}({\delta }_u{\delta }_v{)}^{-1/2}$, where δ_u is the degree of vertex u and the summation extends over all edges (uv) of G. Caporossi et al. [G. Caporossi, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs IV: Chemical trees with extremal connectivity index, Computers and Chemistry 23 (1999) 469–477] proposed the use of linear programming as one of the tools for finding the extremal graphs. In this paper we introduce a new approach based on quadratic programming for finding the extremal graphs in G(k, n) for this index. We found the extremal graphs or gave good bounds for this index when the number n_k of vertices of degree k is between n − k and n. We also tried to find the graphs for which the Randi? index attained its minimum value with given k (k ? n/2) and n. We have solved this problem partially, that is, we have showed that the extremal graphs must have the number n_k of vertices of degree k less or equal n − k and the number of vertices of degree n − 1 less or equal k.     

On the difference equationx_{n + 1} = \frac{{a + bx_{n - k} - cx_{n - m} }}{{1 + g(x_{n - 1} )}}

In this paper we consider the difference equation $$x_{n + 1} = \frac{{a + bx_{n - k} - cx_{n - m} }}{{1 + g(x_{n - 1} )}},$$ wherea, b, c are nonegative real numbers,k, l, m are nonnegative integers andg(x) is a nonegative real function. The oscillatory and periodic character, the boundedness and the stability of positive solutions of the equation is investigated. The existence and nonexistence of two-period positive solutions are investigated in details. In the last section of the paper we consider a generalization of the equation.     

Lie Superalgebras and Irreducibility of $$A_1^{(1)}$$ –Modules at the Critical Level

We introduce the infinite-dimensional Lie superalgebra and construct a family of mappings from a certain category of –modules to the category of –modules at the critical level. Using this approach, we prove the irreducibility of a large family of –modules at the critical level parameterized by . As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations. Partially supported by the MZOS grant 0037125 of the Republic of Croatia     

Preparation of an ion-selective electrode by chemical treatment of copper wire for the measurement of copper(II) and iodide by batch and flow-injection potentiometry

The preparation of an ion-selective electrode by chemical treatment of copper wire and its application for the measurements of copper (II) and iodide ions is described. The proposed reaction mechanism at the sensing surface, which explains the response of the electrode to Cu²⁺ and iodide ions, is discussed. The prepared electrode was suitable for direct potentiometric measurements of iodide and copper (II) in batch experiments down to concentrations of 1 × 10^–5 mol L^–1. A tubular electrode, prepared in the same way, may be used as a potentiometric sensor in a flow-injection analysis for Cu (II) and/or iodide determinations.     

Interaction of two-dimensional spatial incoherent solitons in photorefractive medium

We present a review of our recent theoretical and experimental results on the interaction of incoherent two-dimensional solitary beams in PR SBN crystals. We show that the inherent anisotropy of PR nonlinearity strongly affects the interaction between solitons. Theoretical and experimental results reveal that solitons interacting in a plane perpendicular to the direction of external biasing field always attract, whereas those colliding in a plane of the field exhibit anomalous behaviour. They may experience both attractive and repulsive forces, depending on their mutual separation. We also show that this anisotropy results in the complicated topology of soliton trajectories, featuring periodic collisions, prolonged mutual spiraling and collapse, depending on the initial conditions. Received: 16 November 1998 / Revised version: 12 February 1999 / Published online: 12 April 1999     

A simple,convenient and expeditious approach to cineol

A convenient two‐step protocol preparation of cineol (1‐isopropyl‐4‐methyl‐7‐oxabicyclo[2,2,1]heptane) from α‐terpineol (p‐menth‐1‐en‐8‐ol) is reported. The phenylselenoetherification of α‐terpineol with PhSeX (X = Cl, Br, I) as a key step is described. α‐Terpineol reacts with PhSeX to form the corresponding phenylselenoether in short reaction time and in quantitative yield. A subsequent reduction with Bu₃SnH to cineol proceeds in high yield (98%) © 2004 Wiley Periodicals, Inc. Heteroatom Chem 15:468–470, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20044