Banach空间四阶周期边值问题正解的存在性

讨论了Banach空间E中的四阶周期边值问题:( u(4)(t)??u00(t)+′u(t)= f(t; u(t));06 t 61; u(i)(0)= u(i)(1); i =0;1;2;3正解的存在性,其中f :[0;1]￡ P ! P连续, P为E的正元锥,?;′2 R且满足0<′<(?2+2?2)2;?>?2?2;′?4+??2+1>0:通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正解的存在性结果.     

On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.     

The flipped longitudinal polarization sequence

By flipping the longitudinal magnetization with a chain of 180° pulses it is possible to effectively restore the effects of relaxation so that the same longitudinal magnetization is periodically recovered. The pulse sequence for achieving this, called Flipped LOngitudinal Polarization (FLOP), can be incorporated into any pulse sequence whenever it is desired to stop the attenuation in longitudinal magnetization caused by relaxation. We illustrate its use for fast, single-shot measurements of the longitudinal relaxation time and for three-dimensional T₁ mapping.     

Chemical analysis of Gothic mortar from a bridge pier in Roudnice nad Labem (Czech Republic)

In this paper, a Gothic mortar originating from the remains of a bridge pier in Roudnice nad Labem (Czech Republic) was analyzed. The inorganic composition of the mortar showing special mechanical properties was studied using polarizing light microscopy, scanning electron microscopy coupled with energy dispersive X-ray spectrometry, and X-ray diffraction, while the protein content was analyzed by peptide mass mapping using matrix-assisted laser desorption/ionization—time of flight mass spectrometry and nanoliquid chromatography coupled to tandem mass spectrometry. Two types of inorganic binders having a composition similar to mineral wollastonite and hydraulic lime and milk protein additive were detected. We believe that organic and inorganic binders added together to the mortar increase its hardness and firmness in the aquatic environment.     

Heritability and linkage study on heart rates in a Mongolian population

Elevated heart rate has been proposed as an independent risk factor for cardiovascular diseases, but their interrelationships are not well understood. In this study, we performed a genome-wide linkage scan in 1,026 individuals (mean age 30.6 years, 54.5% women) from 73 extended families of Mongolia and determined quantitative trait loci that influence heart rate. The DNA samples were genotyped using deCODE 1,039 microsatellite markers for 3 cM density genome-wide linkage scan. Correlation analysis was carried out to evaluate the correlation of the covariates and the heart rate. T-tests of the heart rate were also performed on sex, smoking and alcohol intake. Consequently, this model was used in a nonparametric genome-wide linkage analysis using variance component model to create a multipoint logarithm of odds (LOD) score and a corresponding P value. In the adjusted model, the heritability of heart rate was estimated as 0.32 (P<.0001) and a maximum multipoint LOD score of 2.03 was observed in 77 cM region at chromosome 18. The second largest LOD score of 1.52 was seen on chromosome 5 at 216 cM. Genes located on the specified locations in chromosomes 5 and 18 may be involved in the regulation of heart rate.     

Synthesis, spectral and biological studies of nitrogen–sulphur donor macrocyclic ligands and their transition metals complexes

Mn(II), Co(II), Ni(II) and Cu(II) complexes have been synthesized with 22 and 24 membered tetramide macrocyclic ligands viz; 1,9,12,20-tetraaza-2,8,13,19-tetraone-5,16-dithiacyclodocosane [L¹] and 1,9,13,21-tetraaza-2,8,14,20-tetraone-5,17-dithiacyclotetracosane [L²] and characterized by elemental analysis, molar conductance, magnetic susceptibility measurements, mass, IR, electronic EPR spectral studies and electrochemical properties. The molar conductance of all the complexes in DMSO solution is corresponding to 1:2 electrolyte. Thus these complexes may be formulated as [M(L′)]Cl₂ [where M = Mn(II), Co(II), Ni(II) and Cu(II) L′ = L¹ and L²]. On the basis of spectral studies a distorted octahedral geometry has been assigned for all the complexes. The ligands and their complexes were also screened in vitro against two pathogenic fungi (F. moniliformae and R. solani) to assess their growth inhibiting potential.     

Synthesis,structure, and spectroscopic characterization of a 2-D organic–inorganic hybrid CuII–ErIII heterometallic arsenotungstate

An organic–inorganic hybrid Cu^II–Er^III heterometallic arsenotungstate Na₃[Cu(en)₂(H₂O)][Cu(en)₂]_1.5[H₃Er(α-AsW₁₁O₃₉)₂]·4H₂O (1) (en = ethylenediamine) has been hydrothermally synthesized and structurally characterized by elemental analyses, IR and UV spectra, X-ray photoelectron spectroscopy (XPS), cyclic voltammetry and single-crystal X-ray diffraction. 1 displays an organic–inorganic 2-D sheet structure constructed by sandwich-type [H₃Er(α-AsW₁₁O₃₉)₂]⁸⁻ fragments and [Cu(en)₂]²⁺ connectors. From the topological viewpoint, if the [H₃Er(α-AsW₁₁O₃₉)₂]⁸⁻ fragments are viewed as 3-connected nodes and [Cu(en)₂]²⁺ connectors are considered as linkers, the 2-D sheet can be simplified into a 2-D (6,3)-network topology.     

Studies on ruthenium(III) chalcone thiosemicarbazone complexes as catalysts for carbon–carbon coupling

New six-coordinate ruthenium(III) complexes [RuX(EPh₃)₂(L)] (X = Cl or Br; E = P or As; L = chalcone thiosemicarbazone) have been prepared by reacting [RuX₃(EPh₃)₃] (X = Cl or Br; E = P or As) with chalcone thiosemicarbazones in benzene under reflux. The new complexes have been characterized by analytical and spectroscopic (IR, electronic, mass, and EPR) data. The redox behavior of the complexes has also been studied. Based on the above data, an octahedral structure has been assigned for all the complexes. The new complexes exhibit catalytic activity for carbon–carbon coupling reactions.     

Synthesis and characterization of a Cu(II) complex of 2-benzylmercapto-5-methyl-1,3,4-thiadiazole (C10H10N2S2)

A Cu(II) complex of 2-benzylmercapto-5-methyl-1,3,4-thiadiazole was synthesized and characterized. The crystal structure of the copper complex and the free ligand were determined by single-crystal X-ray diffraction at room temperature: {[Cu(C₁₀H₁₀N₂S₂)₂(Cl)₂], P 1 triclinic, a = 8.1450(2) Å, b = 8.1690(2) Å, c = 10.8180(3) Å, α = 97.4040(12)°, β = 101.6270(11)°, γ = 116.1431(14)°; C₁₀H₁₀N₂S₂ ligand, Pbca orthorhombic, a = 8.7938(7) Å, b = 9.6491(7) Å, c = 25.3552(18) Å}. The metal complex framework consists of discrete units that provide crystalline stability through a network of van der Waals contacts. The Cu(II) is coordinated by two chloride ions and two 2-benzylmercapto-5-methyl-1,3,4-thiadiazole monodentate ligands showing a distorted square planar configuration. Both thiadiazole ligands coordinate through the N atom bonded to the benzylthio substituted C atom.

The FTIR spectroscopic data are consistent with this structural model. Analysis of the magnetic susceptibility from 5 K to room temperature indicates the presence of paramagnetic Cu(II), confirmed by the EPR spectrum.     

A systematic theoretical investigation of the valence excited states of the diatomic molecules B2, C2, N2 and O2

A quantitative survey on the performance of multireference (MR), configuration interaction with all singles and doubles (CISD), MRCISD with the Davidson correction and MR-average quadratic coupled cluster (AQCC) methods for a wide range of excited states of the diatomic molecules B₂, C₂, N₂ and O₂ is presented. The spectroscopic constants r _e, ω_e, T _e and D _e for a total of 60 states have been evaluated and critically compared with available experimental data. Basis set extrapolations and size-extensivity corrections are essential for highly accurate results: MR-AQCC mean-errors of 0.001 ?, 10 cm⁻¹, 300 cm⁻¹ and 300 cm⁻¹ have been obtained for r _e, ω_e, T _e and D _e, respectively. Owing to the very systematic behavior of the results depending on the basis set and the choice of method, shortcomings of the calculations, such as Rydberg state coupling or insufficient configuration spaces, can be identified independently of experimental data. On the other hand, significant discrepancies with experiment for states which indicate no shortcomings whatsoever in the theoretical treatment suggest the re-evaluation of experimental results. The broad variety of states included in our survey and the uniform quality of the results indicate that the observed systematics is a general feature of the methods and, hence, is molecule-independent. Received: 12 June 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000