Noncommutative maximal ergodic theorems for positive contractions

Let M be a von Neumann algebra equipped with a normal semifinite faithful trace τ. Let T be a positive linear contraction on M such that τ○T?τ and such that the numerical range of T as an operator on L₂(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on Lp(M), 1<p?∞. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations.     

Copper(II) complexes derived from substituted 2,2′-bis-(4-isopropyl-4-methyl-4,5-dihydro-1H-imidazol-5-one) ligands: Synthesis,structure and catalytic activity

New chiral N,N-bidentate 2,2′-bis-(4-isopropyl-4-methyl-4,5-dihydro-1H-imidazol-5-one) ligands have been prepared and characterised by their ¹H and ¹³C NMR spectra and/or optical rotation. The ligands prepared were then tested for their ability to form complexes with copper(II) salts. It was found that the most stable complex is formed from the 2,2′-bis-(4-isopropyl-1,4-dimethyl-4,5-dihydro-1H-imidazol-5-one) ligand and copper(II) chloride. The structure of this complex was determined by means of quantum-chemical computations at the B3LYP or UB3LYP/6-31G(d,p) level. According to the computations, the geometry of the copper atom most resembles a tetrahedral arrangement, which was also confirmed by means of X-ray structural analysis. It was found that the structure of this copper(II) complex does not allow the copper atom to coordinate to additional ligands; therefore, it is catalytically inactive in the asymmetric Henry reaction.     

Comparative study of degree-based molecular descriptors of cyclodextrins through M-polynomial and NM-polynomial

Cyclodextrins are natural oligosaccharides used to increase the solubility of drugs. It has numerous applications in drug discovery, food storage and other fields. Loftsson et al. explained about applications of Cyclodextrins(CDs) in administrating the drugs through various ways. Jansook et al. has given insights into the structure, physicochemical properties and pharmaceutical applications of CDs. In the present work, cyclodextrin and its derivatives such as α, β, γ CDs are studied for which various degree and neighborhood degree-based topological indices are computed through M-polynomial and NM-polynomial respectively and the comparison of the indices for all three types of cyclodextrins are presented which are of great importance in QSPR/QSAR studies.     

Characterizing the round sphere by mean distance

We discuss the measure theoretic metric invariants extent, rendezvous number and mean distance of a general compact metric space X and relate these to classical metric invariants such as diameter and radius. In the final section we focus attention to the category of Riemannian manifolds. The main result of this paper is Theorem 4 stating that the round sphere of constant curvature 1 has maximal mean distance among Riemannian n-manifolds with Ricci curvature Ric?n−1, and that such a manifold is diffeomorphic to a sphere if the mean distance is close to .     

On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption

The aim of this paper is to study, for L ¹-data, the absorption problem of parabolic type : with Dirichlet boundary conditions and initial conditions. Here a satisfies the classical Leray-Lions hypotheses and β(x, ·) is the subdifferential ∂j(x, ·), where j is a convex function such that j(·, 0) = 0. Existence and uniqueness of an entropy solution is established.      

Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems

Let m ≥ 1 be an integer and N > 2m. Let μ be a positive Radon measure on 317x56/32_2008_Article_90_TeX2GIFIEq1.gif" alt="$${\mathbf{R}}^N$$" align="middle" border="0">. We study necessary and sufficient conditions on possible distributional solutions of 317x56/32_2008_Article_90_TeX2GIFIEq2.gif" alt="$$(-\Delta)^{m}u = \mu\,{\rm on}\,{\mathbf{R}}^N$$" align="middle" border="0">, that guarantee the validity of the representation formula 317x56/32_2008_Article_90_TeX2GIFIEq3.gif" alt="$$u(x) = l + c(2m) \int_{{\mathbf R}^{N}} {\frac {d\mu(y)} {|x - y|^{N-2m}}}$$" align="middle" border="0"> a.e. on 317x56/32_2008_Article_90_TeX2GIFIEq4.gif" alt="$${\mathbf{R}}^N$$" align="middle" border="0">, where 317x56/32_2008_Article_90_TeX2GIFIEq5.gif" alt="$$l\,\in\,{\mathbf{R}}$$" align="middle" border="0"> and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities and weighted form of Hardy-Littlewood-Sobolev systems of integral equations. Received: March 2008     

Predicting the NMR spectra of nucleotides by DFT calculations: cyclic uridine monophosphate

We present an experimental and quantum chemical NMR study of the mononucleotide cyclic uridine monophosphate in water. Spectral parameters ((1)H and (13)C chemical shifts and (1)H--(1)H, (13)C--(1)H, (31)P--(13)C and (31)P--(1)H spin-spin coupling constants) have been carefully obtained experimentally and calculated using DFT methods including the solvent effect and the conformational flexibility of the solute. This study confirms that the (1)H and (13)C spectra of polar, flexible molecules in aqueous solution can be predicted with a high level of accuracy, comparable to that obtained for less complex systems.     

Applications of P NMR spectroscopy in development of M(Duphos)-catalyzed asymmetric synthesis of P-stereogenic phosphines (M = Pt or Pd)

This perspective describes the use of ³¹P NMR spectroscopy in an ongoing research project on enantioselective P−C bond formation catalyzed by platinum and palladium Duphos complexes. This technique was used to characterize catalyst precursors, intermediates and products, to determine equilibrium and rate constants, and to measure the enantiomeric excess (ee) of the P-stereogenic phosphine products. Applications of ³¹P NMR spectroscopy in problem-solving and identifying unexpected products, as well as the analysis of an unusual and esthetically pleasing spectrum, are also discussed.     

大鼠脑组织含磷代谢物随年龄变化的NMR研究

随着人口老龄化的不断加剧,衰老相关疾病已成为全球关注的问题.神经系统功能的退行性改变居于衰老相关疾病的首位,其机制尚不明了.该文旨在通过核磁共振磷谱(~(31)P NMR)检测不同月龄大鼠脑组织中小分子物质的改变,明确能量相关的含磷化合物随大鼠年龄增长的变化,从而揭示脑组织中年龄相关代谢物的变化规律.该研究萃取了不同年龄(幼年、中年及老年)Sprague-Dawley(SD)大鼠脑组织中的小分子物质,进行了~(31)P NMR检测分析.结果显示:老年大鼠脑组织中能量代谢相关物质——磷酸肌酸的含量显著升高,而磷脂酰胆碱及磷酸肌醇含量显著降低,并且出现了磷酸化葡萄糖.这一发现有助于理解衰老相关的脑结构和功能下调,为神经退行性疾病的发生提供依据.     

Synthesis of lariat organochalcogenoethers based on azacalix[3]arenes for the potentiometric detection of [UO2] ions

The syntheses of organochalcogen-supported azacalix[3]arenes are described in a one-pot manner in satisfactory yields. A remarkably selective potentiometric response was accomplished for uranyl ions over a variety of other metal ions, including alkali (Na⁺, K⁺), alkaline-earth (Mg²⁺, Ca²⁺, Ba²⁺), transition and heavy metal ions (Co²⁺, Ni²⁺, Cu²⁺, Ag⁺, Fe³⁺, Zn²⁺, Cd²⁺ and Pb²⁺) using an ion-selective electrode based on compound 3 incorporated into a polymeric (PVC) membrane.