Some properties of the riesz charge associated with a δ-subharmonic function

The first property is a refinement of earlier results of Ch. de la Vallée Poussin, M. Brelot, and A. F. Grishin. Let w=u–v with u, v superharmonic on a suitable harmonic space (for example an open subset of R ⁿ ), and let [w]=[u]–[v] denote the associated Riesz charge. If w0, and if E denotes the set of those points of at which the lim inf of w in thefine topology is 0, then the restriction of [w] to E is 0. Another property states that, if e denotes a polar subset of such that the fine lim inf of |w| at each point of e is finite, then the restriction of [w] to e is 0.     

Problème inverse de la théorie du potentiel logarithmique pour les lemniscates

The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D ₁ and D ₂ producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D₁D₂)_c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.

     

Dirichlet norms,capacities and generalized isoperimetric inequalities for Markov operators

We define the notion of p-capacity for a reversible Markov operator on a general measure space and prove that uniform estimates for the ratio of capacity and measure are equivalent to certain imbedding theorems for the Orlicz and Dirichlet norms. As a corollary we get results on connections between embedding theorems and isoperimetric properties for general Markov operators and, particularly, a generalization of the Kesten theorem on the spectral radius of random walks on amenable groups for the case of arbitrary graphs with non-finitely supported transition probabilities.     

Investigation of the metal binding site in methionine aminopeptidase by density functional theory

All methionine aminopeptidases exhibit the same conserved metal binding site. The structure of this site with either Co²⁺ions or Zn²⁺ions was investigated using density functional theory. The calculations showed that the structure of the site was not influenced by the identity of the metal ions. This was the case for both of the systems studied; one based on the X-ray structure of the human methionine aminopeptidase type 2 (hMetAP-2) and the other based on the X-ray structure of the E. colimethionine aminopeptidase type 1 (eMetAP-1). Another important structural issue is the identity of the bridging oxygen, which is part of either a water molecule or a hydroxide ion. Within the site of hMetAP-2 the results strongly indicate that a hydroxide ion bridges the metal ions. By contrast, the nature of the oxygen bridging the metal ions within the metal binding site of eMetAP-1 cannot be determined based on the results here, due to the similar structural results obtained with a bridging water molecule and a bridging hydroxide ion.     

Asymmetric Hydroformylation of Vinylfurans Catalyzed by {(11bS)‐4‐{[(1R)‐2′‐Phosphino[1,1′‐binaphthalen]‐2‐yl]oxy}dinaphtho[2,1‐d:1′,2′‐f]‐ [1,3,2]dioxaphosphepin}rhodium(I) [RhI{(R,S)‐binaphos}] Derivatives

The asymmetric hydroformylation of 2‐ and 3‐vinylfurans ( 2a and 2b , resp.) was investigated by using [Rh{(R,S)‐binaphos}] complexes as catalysts ((R,S)‐binaphos = (11bS)‐4‐{[1R)‐2′‐phosphino[1,1′‐binaphthalen]‐2‐yl]oxy}dinaphtho[2,1‐d:1′,2′‐f][1,3,2]dioxaphosphepin; 1 ). Hydroformylation of 2 gave isoaldehydes 3 in high regio‐ and enantioselectivities (Scheme 2 and Table). Reduction of the aldehydes 3 with NaBH₄ successfully afforded the corresponding alcohols 5 without loss of enantiomeric purity (Scheme 3).     

MnIII2 (5-Rsaltmen)2NiII(pao)2(L)]2+: an S(T)=3 building block for a single-chain magnet that behaves as a single-molecule magnet

Mn(III)-Ni(II)-Mn(III) linear-type trinuclear complexes bridged by oximate groups were selectively synthesized by the assembly reaction of [Mn2(5-Rsaltmen)2(H2O)2](ClO4)2 (5-Rsaltmen2-=N,N'-(1,1,2,2-tetramethylethylene) bis(5-R-salicylideneiminate); R=Cl, Br) with [Ni(pao)2(phen)] (pao-=pyridine-2-aldoximate; phen=1,10-phenanthroline) in methanol/water: [Mn2(5-Rsaltmen)2Ni(pao)2(phen)](ClO4)2 (R=Cl, 1; R=Br, 2). Structural analysis revealed that the [Mn(III)-ON-Ni(II)-NO-Mn(III)] skeleton of these trimers is in every respect similar to the repeating unit found in the previously reported series of 1D materials [Mn2(saltmen)2Ni(pao)2(L1)2](A)(2) (L(1)=pyridine, 4-picoline, 4-tert-butylpyridine, N-methylimidazole; A=ClO4-, BF4-, PF6-, ReO4-). Recently, these 1D compounds have attracted a great deal of attention for their magnetic properties, since they exhibit slow relaxation of the magnetization (also called single-chain magnet (SCM) behavior). This unique magnetic behavior was explained in the framework of Glauber's theory, generalized for chains of ferromagnetically coupled anisotropic spins. Thus, in these 1D compounds, the [Mn(III)-ON-Ni(II)-NO-Mn(III)] unit was considered as an S(T)=3 anisotropic spin. Direct-current magnetic measurements on 1 and 2 confirm their S(T)=3 ground state and strong uniaxial anisotropy (D/k(B) approximately -2.4 K), in excellent agreement with the magnetic characteristic deduced in the study on the SCM series. The ac magnetic susceptibility of these trimers is strongly frequency-dependent and characteristic of single-molecule magnet (SMM) behavior. The relaxation time tau shows a thermally activated (Arrhenius) behavior with tau0 approximately 1x10(-7) s and Delta(eff)/k(B) approximately 18 K. The effective energy barrier for reversal of the magnetization Delta(eff) is consistent with the theoretical value (21 K) estimated from |D| S2T. The present results reinforce consistently the interpretation of the SCM behavior observed in the [Mn2(saltmen)2Ni(pao)2(L1)2](A)2 series and opens new perspectives to design single-chain magnets.     

NMR study of some diastereomeric nucleoside-3′-thiophosphate derivatives in solution

The conformational properties of diastereomeric P-modified nucleotides are reported as reflected by different NMR parameters. Some conformational trends can be rationalized by consideration of the ³J(C4,P) and ³J(C2,P) coupling values of the isomers and the nature of the substituent on the phosphorus. Configurational assessment of the phosphorus is inferred from NOE experiments. The effects of temperature, solvent and size of substituents are presented.     

Phosphan-, Phosphit- und Phosphido-Komplexe des Vanadiums(V)

Phosphane, Phosphite, Phosphido, Complexes of Vanadium(V) Complex formation of tert-butylimidovanadium(V)trichloride ( 1 ) with phosphanes und phosphites has been studied. Syntheses of phosphidovanadium(V) compounds ^tC₄H₉N?VCp(NH^tC₄H₉)[P(SiMe₃)₂] and ^tC₄H₉N?VCp(NⁱProp₂)(PR₂) (R?SiMe₃, Ph) are described starting from the corresponding chlorovanadium(V) complexes. The reaction of 1 with silver hexafluorophosphate yields a bis(fluoro)phosphidovanadium(IV complex [(μ-PF₂)₂V₂Cl₂)(N^tC₄H₉)₂]; as primary intermediate product of the unknown redox reaction a cationic vanadium(V) complex [^tC₄H₉N?VCl₂ · PPh₃]⁺PF₆^? has been isolated. 1 reacts with an excess of diisopropylamine forming ^tC₄H₉N?V(NⁱProp₂)Cl₂ ( 16 ); in addition the following diisopropylamido-tert-butylimidovanadium(V) compounds ^tC₄H₉N?VCp(NⁱProp₂)Cl ( 3 ) and ^tC₄H₉N?V(NⁱProp₂)X₂ (X?CH₂CMe₃, O^tC₄H₉, CH₃COO) has been prepared. All compounds obtained are characterized by ¹H, ⁵¹V, ³¹P NMR spectroscopy. The X-ray diffraction analysis of 16 and 3 indicate a planar coordination sphere of the amido nitrogen atom.     

Energetic and topological analyses of the oxidation reaction between Mo(n) (n = 1, 2) and N2O

The interaction between molybdenum, atom, and dimer, with nitrous oxide has been investigated using density functional theory. The analysis of the potential energy surfaces for both reactions has revealed that a single molybdenum atom can activate the N--O bond of N2O requiring a small activation energy. However, the presence of several intersystem crossings between three different spin states, namely, septet, quintet and triplet states, seems to be the major constraint to the Mo + N2O reaction. Contrarily, the low-lying excited states (triplet and quintet) do not participate in the reaction between the molybdenum dimer and N2O. The latter reaction fully evolves on the singlet spin surface. Three different regions have been distinguished along the pathway: formation of an adduct complex, formation of an inserted compound, and the N2 detachment. The connection between the two first regions has been characterized by the formation of a special complex in which the N--O bond is so weakened that it could be considered as a first step in the insertion process. It has been shown that the topological changes along the pathways provide a clear explanation for the geometrical changes that occur along the reaction pathway. In summary, the detachment of the N2 molecule is found to be kinetically an effective process for both reactions, owing to the high exothermicity and consequently to the high internal energy of the insertion intermediates. However, in the case of Mo atom, the reaction should be a slow process due to the presence of spin-forbidden transitions. These results fully agree with previous experimental works.     

Ein Neues,tricyclisches schwefelreiches Phosphan

A New Tricyclic Sulfur-rich Phosphane From the products of the reaction of P₄S₃ with tert-Butyliodide the compound (t-Bu(S)P)₂P₄S₃ was isolated in low yield. The compound is stable and has a structure related to the hydrocarbon brexane. By reaction with triphenylphosphin the compounds (t-BuP)(t-Bu(S)P)P₄S₃ and (t-BuP)₂P₄S₃ were obtained. The ³¹P-nmr spectra of all compounds were solved and used to determine the structure of the molecules. A complete set of ³¹P-nmr data is given.