On Weierstrass semigroups and sets: a review with new results

In this work we present a survey of the main results in the theory of Weierstrass semigroups at several points, with special attention to the determination of bounds for the cardinality of its set of gaps. We also review results on applications to the theory of error correcting codes. We then recall a generalization of the concept of Weierstrass semigroup, which is the Weierstrass set associated to a linear system and several points. We finish by presenting new results on this Weierstrass set, including some on the cardinality of its set of gaps.      

Ion–ion interactions of LiPF6 and LiBF4 in propylene carbonate solutions

Self-diffusion coefficients of Li⁺ D_Li⁺, PF₆⁻ D_PF6⁻ and solvent propylene carbonate (PC) D_PC in LiPF₆−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm^– 3). The order of the diffusion coefficients was found to be D_Li⁺ < D_PF6⁻ < D_PC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/Λ_NMR, where Λ and Λ_NMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF₆–PC solutions. Though Λ/Λ_NMR values for LiPF₆-solutions decrease with increasing the salt concentration, they were greater than those for LiBF₄–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF₆^– ion is weaker than that of the BF₄^– ion. The smaller value of the ionic conductivity for the highly concentrated LiPF₆–PC solution (above 2.0 M) than that of the LiBF₄-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF₄-solution. Classic molecular dynamics (MD) simulations for the respective LiPF₆ and LiBF₄-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions g_LiO(r) (for Li⁺–O (PC) pair) and g_LiPF6(r) (for Li⁺–PF₆^– pair) or g_LiBF4(r) (for Li⁺–BF₄^– pair) revealed that the lithium ion weakly forms the contact ion pairs with PF₆^–, whilst strongly with BF₄^–, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase.     

On the residue classes of integer sequences satisfying a linear three term recurrence formula

In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))_n?0 and (U(n))_n?0, which are ultimately periodic modulo m, e.g.

     

Spectroscopy and photophysics of methylphenylsiloxaneand diphenylsiloxane-based molecules and polymers

Spectroscopy and photophysics of various types of methylphenylsiloxane- and diphenylsiloxane-based oligomers and polymers are reviewed. The molecules treated here include homopolymers such as poly(methylphenylsiloxane) and copolymers such as poly(dimethylsiloxane-codiphenylsiloxane) as well as related oligomers or molecules such as diphenyltetramethyldisiloxane. These polymers and oligomers normally exhibit monomer fluorescence in fluid solution at temperatures near room temperature, and the monomer fluorescence and phosphorescence in rigid matrices at 77 K. In addition to these emissions, the excimer fluorescence is often observed depending on the molecular structure of the siloxanes. These emission properties are rationalized based on the molecular structure and kinetics of the excimer formation processes as well as on the flexibility of the Si-O-Si bonds.     

The incorporation of carboxylate groups into temperature‐responsive poly(N‐isopropylacrylamide)‐based hydrogels promotes rapid gel shrinking

Aqueous gel deswelling rates for copolymer hydrogels comprising N‐isopropylacrylamide (IPAAm) and 2‐carboxyisopropylacrylamide (CIPAAm) in response to increasing temperatures were investigated. Compared with pure IPAAm‐based gels, IPAAm–CIPAAm gels shrink very rapidly in response to small temperature increases across their lower critical solution temperature (their volume is reduced by five‐sixths within 60 s). Shrinking rates for these hydrogels increase with increasing CIPAAm content. In contrast, structurally analogous IPAAm–acrylic acid (AAc) copolymer gels lose their temperature sensitivity with the introduction of only a few mole percent of AAc. Additionally, deswelling rates of IPAAm–AAc gels decrease with increasing AAc content. These results indicate that IPAAm–CIPAAm copolymer gels behave distinctly from IPAAm–AAc systems even if both comonomers, CIPAAm and AAc, possess carboxylic acid groups. Thus, we propose that the sensitive deswelling behavior for IPAAm–CIPAAm gels results from strong hydrophobic chain aggregation maintained between network polymer chains due to the similar chemical structures of CIPAAm and IPAAm. This structural homology facilitates aggregation of chain isopropylamide groups for both IPAAm and CIPAAm sequences with increasing temperature. The incorporation of AAc, however, shows no structural homology to IPAAm, inhibiting chain aggregation and limiting collapse. A functionalized temperature‐sensitive poly(N‐isopropylacrylamide) hydrogel containing carboxylic acid groups is possible with CIPAAm, producing rapid and large volume changes in response to smaller temperature changes. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 335–342, 2001     

Theoretical study of endohedral metallofullerenes: Sc3−nLanN@C80 (n=0–3)

To provide theoretical insight into the structures and properties of Sc₃N@C₈₀, which has been isolated in high yield and purity as a new stable endohedral metallofullerene, density functional calculations are carried out for the Sc_3?nLa_nN@C₈₀ (n=0–3) series. Because of electron transfer from Sc₃N to C₈₀, the electronic structure of Sc₃N@C₈₀ is formally described as (Sc₃N)⁶⁺C$_{80}^{6-}$. The encapsulated Sc₃N cluster takes a planar structure with long Sc–Sc distances and is highly stabilized inside the I_h cage of C₈₀, which rotates rapidly. As the number of La atoms increases, the Sc_3?nLa_nN cluster is forced to maintain a pyramidal structure in Sc_3?nLa_nN@C₈₀. In addition, the C₈₀ cage takes an open‐shell electronic structure due to an increase in the number of electrons transferring from Sc_3?nLa_nN. These make the endohedral structure less stable and more reactive. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1353–1358, 2001     

Biosynthetic Conclusions from the Functional Dissection of Oxygenases for Biosynthesis of Actinorhodin and Related Streptomyces Antibiotics

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Highlights? ActVA-ORF5 is a flavin-dependent monooxygenase required for actinorhodin biosynthesis ? ActVA-ORF5 and its three close homologs were functionally dissected ? ActVA-ORF5 and Gra-21 are bifunctional at C-6/C-8, while Med-7 acts only for C-6 ? AlnT exhibits different regiospecificity for oxidation of tricyclic substrates     

Granulation of core particles suitable for film coating by agitation fluidized bed I. Optimum formulation for core particles and development of a novel friability test method

To prepare powdered medicines without bitter taste, film coating is required to cover the surface of core particles. In this study, effect of formulation and operating conditions of agitation fluidized bed on the core particle properties was investigated. In order to prevent breakage of the core particles during coating process, which sometimes causes variation of drug dissolution rate, addition of maltose syrup powder during the formulation process of the core particles was investigated. Also, a method for friability test in which the core particles were subjected to strong impact was proposed to evaluate strength of the core particles. The friability of the core particles determined by this test method correlated well with the actual friability of the particles during the coating process. Based on this result, we confirmed this novel friability test method could predict the core particle endurance during the coating process.     

Preparation and properties of anionic transition metal complexes containing triheterocarbenium ions

Summary Thermally stable anionic tetracarbonylcobalt complexes containing triheterocarbenium ions, [Co(CO)₄]^–[cation]⁺, have been synthesized by the ion exchange reaction of [Co(CO)₄]^–PPN⁺ with the corresponding carbenium ions. Similar molybdenum complexes containing cyclopentadienyl and carbonyl ligands were also prepared. The complexes were characterized by elemental analyses and by i.r. and n.m.r. spectroscopies. The ionic structures of the complexes are confirmed on the basis of their large electric conductivities.     

Structure and dioxygen-reactivity of copper(I) complexes supported by bis(6-methylpyridin-2-ylmethyl)amine tridentate ligands

The structure and dioxygen-reactivity of copper(I) complexes R supported by N,N-bis(6-methylpyridin-2-ylmethyl)amine tridentate ligands L2R[R (N-alkyl substituent)=-CH2Ph (Bn), -CH2CH2Ph (Phe) and -CH2CHPh2(PhePh)] have been examined and compared with those of copper(I) complex (Phe) of N,N-bis[2-(pyridin-2-yl)ethyl]amine tridentate ligand L1(Phe) and copper(I) complex (Phe) of N,N-bis(pyridin-2-ylmethyl)amine tridentate ligand L3(Phe). Copper(I) complexes (Phe) and (PhePh) exhibited a distorted trigonal pyramidal structure involving a d-pi interaction with an eta1-binding mode between the metal ion and one of the ortho-carbon atoms of the phenyl group of the N-alkyl substituent [-CH2CH2Ph (Phe) and -CH2CHPh2(PhePh)]. The strength of the d-pi interaction in (Phe) and (PhePh) was weaker than that of the d-pi interaction with an eta2-binding mode in (Phe) but stronger than that of the eta1 d-pi interaction in (Phe). Existence of a weak d-pi interaction in (Bn) in solution was also explored, but its binding mode was not clear. Redox potentials of the copper(I) complexes (E1/2) were also affected by the supporting ligand; the order of E1/2 was Phe>R>Phe. Thus, the order of electron-donor ability of the ligand is L1Phe相似文献