Preparation of ethyl 2-aryl 2,3-alkadienoates via palladium-catalyzed selective cross-coupling reactions

Pd-catalyzed cross-coupling reactions of aryl iodides containing not only an electron-donating group but also an electron-withdrawing group on the aryl ring with organoindium reagents generated in situ from indium and ethyl 4-bromo-2-alkynoates produced selectively ethyl 2-aryl-2,3-alkadienoates in good yield.     

Quasi-Stationarity of Discrete-Time Markov Chains with Drift to Infinity

We consider a discrete-time Markov chain on the non-negative integers with drift to infinity and study the limiting behavior of the state probabilities conditioned on not having left state 0 for the last time. Using a transformation, we obtain a dual Markov chain with an absorbing state such that absorption occurs with probability 1. We prove that the state probabilities of the original chain conditioned on not having left state 0 for the last time are equal to the state probabilities of its dual conditioned on non-absorption. This allows us to establish the simultaneous existence, and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasi-stationary distribution in the usual sense, a similar statement is not possible for the original chain.     

A Hodge decomposition interpretation for the coefficients of the chromatic polynomial

Let be a simple graph with nodes. The coloring complex of , as defined by Steingrimsson, has -faces consisting of all ordered set partitions, in which at least one contains an edge of . Jonsson proved that the homology of the coloring complex is concentrated in the top degree. In addition, Jonsson showed that the dimension of the top homology is one less than the number of acyclic orientations of .

In this paper, we show that the Eulerian idempotents give a decomposition of the top homology of into components . We go on to prove that the dimensions of the Hodge pieces of the homology are equal to the absolute values of the coefficients of the chromatic polynomial of . Specifically, if we write , then .

     

Boundedness and Dissipativity of Truncated Rotations on Uniform Planar Lattices

The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated.     

Uniqueness,Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction

We examine basic properties regarding uniqueness, extinction, and explosivity for the generalised Markov branching processes with pairwise interaction. First we establish uniqueness criteria, proving that in the essentially-explosive case the process is honest if and only if the mean death rate is greater than or equal to the mean birth rate, while in the sub-explosive case the process is dishonest only in exceptional circumstances. Explicit expressions are then obtained for the extinction probabilities, the mean extinction times and the conditional mean extinction times. Explosivity is also investigated and an explicit expression for mean explosion time is established.     

Tractable Partially Ordered Sets Derived from Root Systems and Biased Graphs

We study new posets Q obtained by removing from a geometric lattice L ofa biased graph certain flats indexed by a simplicial complex . (One example of L is the lattice of flats of thevector matroid of a root system B _n .) We study the structureand compute the characteristic polynomial of Q. With certainchoices of L and , including ones for which Q is alattice interpolating between those of B _n and D _n , we observe curious relationships among the roots of thecharacteristic polynomials of Q, L, and .     

Optical behavior of antibiofouling additives in environment‐friendly coverglass materials for bio‐sensors and solar panels

Solar panels and bio‐optical sensors play a significant and growing role in a number of applications that are of importance to many organizations. Many of these instruments require a high transmission of radiation into the device for it to work properly. A major issue faced is that harsh marine environments often aid in the growth or development of fouling on the coverglass used to protect the instruments. Over a period of time in an ocean environment, some plant or animal may attach itself to the coverglass, ultimately obscuring the glass and rendering the instrument useless. As such, an antifouling mechanism is needed for these instruments that is inexpensive, long‐lasting, and environment friendly. The approach discussed herein involves the use of known antifouling chemicals which have been incorporated into the polymer matrix. Polymethylmethacrylate (PMMA), bisphenol A polycarbonate (Bis A PC), and a co‐polyterephthalate (CPTE) were examined. The plaques are optically transparent and previous work has shown that, for most samples, the materials display a minimal decrease in mechanical behavior upon the addition of the algaecides. This paper will discuss the effects on the materials' optical properties when exposed to both harsh marine conditions as well as high intensity UV light. Specifically, the decrease in transmission of visible light was examined over a 6 month period of time. Copyright © 2008 John Wiley & Sons, Ltd.     

A -deformation of a trivial symmetric group action

Let be the arrangement of hyperplanes consisting of the reflecting hyperplanes for the root system . Let be the Varchenko matrix for this arrangement with all hyperplane parameters equal to . We show that is the matrix with rows and columns indexed by permutations with entry equal to where is the number of inversions of . Equivalently is the matrix for left multiplication on by

Clearly commutes with the right-regular action of on . A general theorem of Varchenko applied in this special case shows that is singular exactly when is a root of for some between and . In this paper we prove two results which partially solve the problem (originally posed by Varchenko) of describing the -module structure of the nullspace of in the case that is singular. Our first result is that

in the case that where Lie denotes the multilinear part of the free Lie algebra with generators. Our second result gives an elegant formula for the determinant of restricted to the virtual -module with characteristic the power sum symmetric function .

     

GENETIC AND MOLECULAR ANALYSES OF UV RADIATION-INDUCED MUTATIONS IN THE FEM-3 GENE OF CAENORHABDITIS ELEGANS

The utility of a new target gene (fem-3) is described for investigating the molecular nature of mutagenesis in the nematode Caenorhabditis elegans. As a principal attribute, this system allows for the selection, maintenance and molecular analysis of any type of mutation that disrupts the gene, including deletions. In this study, 86 mutant strains were isolated, of which 79 proved to have mutations in fem-3. Twenty of these originally tested as homozygous inviable. Homozygous inviability was expected, as Stewart and coworkers had previously observed that, unlike in other organisms, most UV radiation-induced mutations in C. elegans are chromosomal rearrangements of deficiencies (Mutat. Res. 249 , 37–54, 1991). However, additional data, including Southern blot analyses on 48 of the strains, indicated that most of the UV radiation-induced fem-3 mutations were not deficiencies, as originally inferred from their homozygous inviability. Instead, the lethals were most likely “coincident mutations” in linked, essential genes that were concomitantly induced. As such, they were lost owing to genetic recombination during stock maintenance. As in mammalian cells, yeast and bacteria, the frequency of coincident mutations was much higher than would be predicted by chance.