Porphyrin system containing [2.2]paracyclophane units

Meso-tetrakis([2.2]paracyclophanyl)porphyrin was obtained from [2.2]paracyclophanecarbaldehyde and pyrrole. Replacement of phenyl groups in meso-tetraphenylporphyrin by paracyclophanyl substituents remarkably influences the electronic structure of the molecule, causing bathochromic shifts of all uv-vis absorption bands, and changing the ring current of the porphyrin core. The shifts in the electron spectrum are substantially greater than those observed for other porphyrin derivatives characterized by their extended π-electron systems, such as meso-tetrakis(2-phenylethenyl)porphyrin and meso-tetrakisbiphenylporphyrin.     

Genome-wide single-nucleotide polymorphism arrays demonstrate high fidelity of multiple displacement-based whole-genome amplification

Whole-genome DNA amplification by multiple displacement (MD-WGA) is a promising tool to obtain sufficient DNA amounts from samples of limited quantity. Using Affymetrix' GeneChip Human Mapping 10K Arrays, we investigated the accuracy and allele amplification bias in DNA samples subjected to MD-WGA. We observed an excellent concordance (99.95%) between single-nucleotide polymorphisms (SNPs) called both in the nonamplified and the corresponding amplified DNA. This concordance was only 0.01% lower than the intra-assay reproducibility of the genotyping technique used. However, MD-WGA failed to amplify an estimated 7% of polymorphic loci. Due to the algorithm used to call genotypes, this was detected only for heterozygous loci. We achieved a 4.3-fold reduction of noncalled SNPs by combining the results from two independent MD-WGA reactions. This indicated that inter-reaction variations rather than specific chromosomal loci reduced the efficiency of MD-WGA. Consistently, we detected no regions of reduced amplification, with the exception of several SNPs located near chromosomal ends. Altogether, despite a substantial loss of polymorphic sites, MD-WGA appears to be the current method of choice to amplify genomic DNA for array-based SNP analyses. The number of nonamplified loci can be substantially reduced by amplifying each DNA sample in duplicate.     

Understanding relativistic effects of chemical bonding

To elucidate the physical origin of relativistic changes of molecular properties, exact theorems, perturbation theory, and Hartree-Fock-Slater-Pauli calculations are exploited. The relativistic molecular virial theorem offers insight into the relativistic and nonrelativistic, kinetic, and potential energy contributions to the bond energy. In general, there exist two contributions to the relativistic correction of a molecular property: the relativistic change at the nonrelativistic equilibrium geometry and the change of the nonrelativistic property due to the relativistic change of the equilibrium geometry. Sometimes the first and sometimes the second contribution is the dominant one. Accurate numerical results for H⁺₂-like systems are obtained using direct relativistic double perturbation theory. In some cases, near-degenerate perturbation theory is mandatory. Relativistic changes of chemical bond energies are often proportional to the density change in the K-shell when the bond is formed. Relativistic corrections to many properties (and also to the 1s²-correlation energy) are often proportional to Z²α². © 1996 John Wiley & Sons, Inc.     

Effective cross-sections for molecular aggregation in external orienting fields

Effects of an external orienting field and orientational cross-section for molecular association on the kinetics of crystal nucleation and critical temperature of crystallization is discussed. Dipole and quadrupole effects of an electric (magnetic) field and quadrupole effects of hydrodynamic potential of uniaxial flow are considered. Critical temperature of crystallization, free energy barrier of nucleation and nucleation rates are orientation-dependent. Smaller orientational cross-sections result in stronger anisotropy of the nucleation rates.     

SEMILINEAR HEMIVARIATIONAL INEQUALITIES WITH STRONG RESONANCE AT INFINITY

A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained.     

Routing of single-source and multiple-source queries in static sensor networks

In this paper, we introduce new geometric ad-hoc routing algorithms to route queries in static sensor networks. For single-source-queries routing, we utilise a centralised mechanism to accomplish a query using an asymptotically optimal number of transmissions O(c), where c is the length of the shortest path between the source and the destination. For multiple-source-queries routing, the number of transmissions for each query is bounded by O(clogn), where n is the number of nodes in the network. For both single-source and multiple-source queries, the routing stage is preceded by preprocessing stages requiring O(nD) and O(n²D) transmissions, respectively, where D is the diameter of the network. Our algorithm improves the complexity of the currently best known algorithms in terms of the number of transmissions for each query. The preprocessing is worthwhile if it is followed by frequent queries. We could also imagine that there is an extra initial power (say, batteries) available during the preprocessing stage or alternatively the positions of the sensors are known in advance and the preprocessing can be done before the sensors are deployed in the field. It is also worth mentioning that a lower bound of Ω(c²) transmissions has been proved if preprocessing is not allowed [F. Kuhn, R. Wattenhofer, A. Zollinger, Asymptotically optimal geometric mobile ad-hoc routing, in: Proceedings of the Sixth International Workshop on Discrete Algorithm and Methods for Mobility, Atlanta, GA, September 2002, pp. 24–33].     

Experimental and quantum‐chemical studies of 1H, 13C and 15N NMR coordination shifts in Au(III), Pd(II) and Pt(II) chloride complexes with picolines

¹H, ¹³C and ¹⁵N NMR studies of gold(III), palladium(II) and platinum(II) chloride complexes with picolines, [Au(PIC)Cl₃], trans‐[Pd(PIC)₂Cl₂], trans/cis‐[Pt(PIC)₂Cl₂] and [Pt(PIC)₄]Cl₂, were performed. After complexation, the ¹H and ¹³C signals were shifted to higher frequency, whereas the ¹⁵N ones to lower (by ca 80–110 ppm), with respect to the free ligands. The ¹⁵N shielding phenomenon was enhanced in the series [Au(PIC)Cl₃] < trans‐[Pd(PIC)₂Cl₂] < cis‐[Pt(PIC)₂Cl₂] < trans‐[Pt(PIC)₂Cl₂]; it increased following the Pd(II) → Pt(II) replacement, but decreased upon the trans → cis‐transition. Experimental ¹H, ¹³C and ¹⁵N NMR chemical shifts were compared to those quantum‐chemically calculated by B3LYP/LanL2DZ + 6‐31G**//B3LYP/LanL2DZ + 6‐31G*. Copyright © 2008 John Wiley & Sons, Ltd.     

Existence and multiplicity results for quasilinear hemivariational inequalities at resonance

In this paper we consider quasilinear hemivariational inequality at resonance. We prove existence results for strongly resonant quasilinear problem, resonant problem under a Tang‐type condition as well as two multiplicity results. The method of the proofs is based on the nonsmooth critical point theory for locally Lipschitz functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The existence and regularity of solutions to the non-linear equation of flotating water

The existence of solutions to the nonlinear equations including the equation of flotating water is proved using the subellipticity of an operator in the equation and the contraction argument. Moreover a regularity result is given.