Axiplyns A-E, new sesquiterpene isothiocyanates from the marine sponge Axinyssa aplysinoides

Five new isothiocyanate sesquiterpenes, designated axiplyns A-E (1-5) have been isolated, together with two known isothiocyanate sesquiterpenes (6, 7), from the sponge Axinyssa aplysinoides collected at Misali Island, Tanzania. Axiplyns 4 and 5 embody a new indane sesquiterpene skeleton, and compounds 1, 2, and 5 contain unprecedented ring systems, namely a 6,8-dioxabicyclo[3.2.1]octane and a 2-oxabicyclo[2.2.1]heptane. Axiplyns A, B, and C are potent brine shrimp toxins with LD₅₀ values between 1.5 and 1.8 μg/mL.     

Photophysics of (1-butyl-4-(1H-inden-1-ylidene)-1,4-dihydropyridine (BIDP): an experimental test for conical intersections

Fluorescence experiments on (1-butyl-4-(1H-inden-1-ylidene)-1,4-dihydropyridine (BIDP) are reported in liquid and glassy solutions. The data indicate a fast decay in the fluid nonpolar, nonprotic solutions (decay times approximately 10(-12) s) and rapid but considerably slower decay in polar ones. In frozen solutions (polar and nonpolar), the fluorescence quantum yield is much higher (near 0.5 and around 0.1 in polar and nonpolar glasses, respectively). The rapid nonradiative transitions in fluid solutions are assigned to internal conversion in both solvent classes, as intersystem crossing is much slower and no net reaction is observed. These results are in agreement with predictions made for the closely related (in terms of electronic structure) but simpler molecule cyclopentadienyl-1,4-dihydropyridine (CPDHP) for which an S1/S0 conical intersection was recently proposed [Int. J. Quant. Chem. 2005, 102, 961]. The crossing of the two lowest singlet states is calculated to vanish in polar solvents such as methyl cyanide, leading to longer lifetime of S1 of CPDHP. As BIDP has a very similar electronic structure, the model predicts a corresponding change in this larger molecule. The strong fluorescence observed in the glassy environments is rationalized by the hindering of the internal torsion required to reach the geometry of the conical intersection.     

Anti-Ramsey Numbers of Graphs with Small Connected Components

The anti-Ramsey number, AR(n, G), for a graph G and an integer \(n\ge |V(G)|\), is defined to be the minimal integer r such that in any edge-colouring of \(K_n\) by at least r colours there is a multicoloured copy of G, namely, a copy of G that each of its edges has a distinct colour. In this paper we determine, for large enough \(n,\, AR(n,L\cup tP_2)\) and \(AR(n,L\cup kP_3)\) for any large enough t and k, and a graph L satisfying some conditions. Consequently, we determine AR(n, G), for large enough n, where G is \(P_3\cup tP_2\) for any \(t\ge 3,\, P_4\cup tP_2\) and \(C_3\cup tP_2\) for any \(t\ge 2,\, kP_3\) for any \(k\ge 3,\, tP_2\cup kP_3\) for any \(t\ge 1,\, k\ge 2\), and \(P_{t+1}\cup kP_3\) for any \(t\ge 3,\, k\ge 1\). Furthermore, we obtain upper and lower bounds for AR(n, G), for large enough n, where G is \(P_{k+1}\cup tP_2\) and \(C_k\cup tP_2\) for any \(k\ge 4,\, t\ge 1\).     

The Twin-Excited State as a Probe for the Transition State in Concerted Unimolecular Reactions: The Semibullvalene Rearrangement

A twin of the transition state , which can be investigated spectroscopically and can thus supply information about the structure of the transition state, has now been characterized for the Cope rearrangement of semibullvalene (shown below). It involves an excited state with B₂ symmetry and results from a linear combination of the ground-state wave functions of (mirror-image) reactant and product.     

A scale-dependent equation for solute transport in porous media

The governing equation describing solute transport in porous media is reformulated using standard volume averaging techniques. The alternative formulation is based on a modified definition of the deviation, which allows for variation of macroscopic velocity across the REV. The new equation contains additional scale-dependent terms which are functions of the size of the averaging volume (REV). This result indicates that the scale-dependent nature of the dispersion phenomenon is inherent even at the scale of the REV.     

Automated antenna positioning algorithms for wireless fixed-access networks

This article addresses a real-life problem - obtaining communication links between multiple base station sites, by positioning a minimal set of fixed-access relay antenna sites on a given terrain. Reducing the number of relay antenna sites is considered critical due to substantial installation and maintenance costs. Despite the significant cost saved by eliminating even a single antenna site, an inefficient manual approach is employed due to the computational complexity of the problem. From the theoretical point of view we show that this problem is not only NP hard, but also does not have a constant approximation. In this paper we suggest several alternative automated heuristics, relying on terrain preprocessing to find educated potential points for positioning relay stations. A large-scale computer-based experiment consisting of approximately 7,000 different scenarios was conducted. The quality of alternative solutions was compared by isolating and displaying factors that were found to affect the standard deviation of the solutions supplied by the tested heuristics. The results of the simulation based experiments show that the saving potential increases when more base stations are needed to be interconnected. The designs of a human expert were compared to the automatically generated solutions for a small subset of the experiment scenarios. Our studies indicate that for small networks (e.g., connecting up to ten base stations), the results obtained by human experts are adequate although they rarely exceed the quality of automated alternatives. However, the process of obtaining these results in comparison to automated heuristics is longer. In addition, when more base station sites need to be interconnected, the human approach is easily outperformed by our heuristics, both in terms of better results (fewer antennas) and in significant shorter calculation times.     

Subdirect decomposition of rings and the axiom of choice

The second author is supported in part by a research grant of the Council of Scientific and Industrial Research of South Africa.     

Charge separation in ground-state 1,2,4,5-tetra-substituted benzene derivatives

The conditions required for a formal biradical to exist in a zwitterionic form in the ground state are discussed following the recent experimental observation of zwitterionic structure in the ground state of a quinoid molecule (di-tert-butyl derivative of 2,5-diamino-1,4-benzoquinonediimine, I). A unique characteristic of molecules of this class is the fact that they may be considered as being formed by the union of two radicals, each having an odd number of pi electrons. In the case of I, one fragment carries the two amino group having 7 pi electrons; it acts as the electron donor. The other fragment carries the two oxygen atoms (carrying 5 pi electrons) and acts as an electron acceptor. A model that predicts the properties of these systems is presented, based on previous work on non-Kekule hydrocarbons(2,3) and on the electron donating and attracting properties of the donor and acceptor groups, respectively. The zwitterion is formed by an electron transfer leading to two subunits carrying 6 pi electrons each and may become more stable than the triplet biradical even in the gas phase (i.e., in the absence of an external field) if the ionization potential of the donor is small (of the order of 3-4 eV). In some cases solvation in a polar solvent is required to make the zwitterionic form the lowest energy species on the ground-state surface. The 'spacer' between the donor and acceptor groups (which need not be necessarily derived from an aromatic structure) can be varied and influences the overall dipole moment that is calculated in some cases to be quite large (over 20 D in the gas phase).