Positive clustered layered solutions for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of RN:

     

Generating functions of multi-symplectic RK methods via DW Hamilton–Jacobi equations

The De Donder–Weyl (DW) Hamilton–Jacobi equation is investigated in this paper, and the connection between the DW Hamilton–Jacobi equation and multi-symplectic Hamiltonian system is established. Based on the DW Hamilton–Jacobi theory, generating functions for multi-symplectic Runge–Kutta (RK) methods and partitioned Runge–Kutta (PRK) methods are presented. The work is supported by the Foundation of ICMSEC, LSEC, AMSS and CAS, the NNSFC (No.10501050, 19971089 and 10371128) and the Special Funds for Major State Basic Research Projects of China (2005CB321701).     

Bounds and monotonicity for the generalized Robin problem

We consider the principal eigenvalue λ ₁^Ω(α) corresponding to Δu = λ (α) u in on ∂Ω, with α a fixed real, and a C ^0,1 bounded domain. If α > 0 and small, we derive bounds for λ ₁^Ω(α) in terms of a Stekloff-type eigenvalue; while for α > 0 large we study the behavior of its growth in terms of maximum curvature. We analyze how domain monotonicity of the principal eigenvalue depends on the geometry of the domain, and prove that domains which exhibit domain monotonicity for every α are calibrable. We conjecture that a domain has the domain monotonicity property for some α if and only if it is calibrable. Robert Smits: This author was partially supported by a grant of the National Security Agency, grant #H98230-05-1-0060.     

Projectively condensed semigroups,generalized completely regular semigroups and projective orthomonoids

The class of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety of . Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of . We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain the structure theorems of various generalized orthogroups. Partially supported by a UGC (HK) grant #2060123 (04-05).     

Comparison of the Electrochemical and Luminescence Properties of Two Carbazole‐Based Phosphine Oxide EuIII Complexes: Effect of Different Bipolar Ligand Structures

The photoluminescence (PL), electrochemical, and electroluminescence (EL) properties of Eu^III complexes, [Eu(cppo)₂(tta)₃] ( 1 ) and [Eu(cpo)₂(tta)₃] ( 2 ; TTA=2‐thenoyltrifluoroacetonate) with two carbazole‐based phosphine oxide ligands, 9‐[4‐(diphenylphosphinoyl)phenyl]‐9H‐carbazole (CPPO) and 9‐(diphenylphosphoryl)‐9H‐carbazole (CPO), which have different bipolar structures, donor–π‐spacer–acceptor (D–π–A) or donor–acceptor (D–A) systems respectively, are investigated. The CPPO with D–π–A architecture has improved PL properties, such as higher PL efficiency and more efficient intramolecular energy transfer, than CPO with the D–A architecture. Gaussian simulation proved the bipolar structures and the double‐carrier injection ability of the ligands. The carrier injection abilities of triphenylphosphine oxide, CPO, and CPPO are gradually improved. Notably, the Gaussian and electrochemical investigations indicate that before and after coordination, the carrier injection ability of the ligands show remarkable changes because of the particularity of the D‐π–A and D–A systems. The electrochemical studies demonstrate that coordination induces the electron cloud to migrate from electron‐rich carbazole to electron‐poor diphenylphosphine oxide, and consequently increases the electron‐cloud density on diphenylphosphine oxide, which weakens its ability for electron affinity and induces the elevation of LUMO energy levels of the complexes. Significantly, the π‐spacer in the D–π–A system exhibits a distinct buffer effect on the variation of the electron‐cloud density distribution of the ligand, which is absent in the D–A system. It is demonstrated that the adaptability of the D–π–A systems, especially for coordination, is stronger than that of D–A systems, which facilitates the modification of the complexes by designing multifunctional ligands purposefully. 1 seems favorable as the most efficient electroluminescent Eu^III complex with greater brightness, higher efficiencies, and more stable EL spectra than 2 . These investigations demonstrate that the phosphine oxide ligands with D–π–A architecture are more appropriate than those with D–A architecture to achieve multifunctional electroluminescent Eu^III complexes.     

The study of the lipophilicity of alpha-(4-phenylpiperazin-1-yl)-gamma-phthalimidobutyramides using chromatographic and computational methods

The lipophilicity of the series of alpha-(4-phenylpiperazin-1-yl)-gamma-phthalimido-butyramides (1-8) has been investigated. Several methods, like reversed-phase thin-layer chromatography and high-performance liquid chromatography using reversed-phase RP18 and IAM.DD2 columns, were applied to determine RMO, log k0 and log k(0IAM) factors. The RP-TLC investigations were performed in mixtures of acetone-water and acetonitrile-water. For RP-HPLC method mixtures of acetonitrile, water and 0.01% TFA were used as the mobile phases while for IAM.DD2 investigations mixtures of acetonitrile and water were applied. The partition coefficients of compounds (1-8) were also calculated with the Pallas and CAChe programs. All the obtained data, both from experimental methods and computational calculations, were compared and a suitable conclusion was reached.