Template-directed synthesis of mechanically interlocked molecular bundles using dynamic covalent chemistry

Mixing the dipyrido[24]crown-8 derivatives carrying one or two formyl group(s) on the 4 position(s) of their pyridine ring(s) with a 3-fold symmetrical trisammonium ion template in a 3:1 ratio in CD3NO2 results in the formation of thermodynamically stable [4]pseudorotaxanes which, upon addition of a 1,3,5-trisaminobenzene cap, form mechanically interlocked molecular bundles with one and two caps, respectively, by virtue of dynamic imine bond formation.     

Thermal collapse of spin polarization in half-metallic ferromagnets

We propose two novel approaches to study the temperature dependence of the magnetization and the spin polarization at the Fermi level in magnetic compounds, and apply them to half-metallic ferromagnets. We reveal a new mechanism, where the hybridization of states forming the half-metallic gap depends on thermal spin fluctuations and the polarization can drop abruptly at temperatures much lower than the Curie point. We verify this for NiMnSb by ab initio calculations. The thermal properties are studied by mapping ab initio results to an extended Heisenberg model which includes longitudinal fluctuations and is solved by a Monte Carlo method.     

On Li’s coefficients for the Rankin–Selberg <Emphasis Type="Italic">L</Emphasis>-functions

We define a generalized Li coefficient for the L-functions attached to the Rankin–Selberg convolution of two cuspidal unitary automorphic representations π and π ^′ of GL_m(\mathbbA_F)GL_{m}(\mathbb{A}_{F}) and GL_m^￠(\mathbbA_F)GL_{m^{\prime }}(\mathbb{A}_{F}) . Using the explicit formula, we obtain an arithmetic representation of the n th Li coefficient l_p,p^￠(n)\lambda _{\pi ,\pi ^{\prime }}(n) attached to L(s,p_f×[(p)\tilde]_f^￠)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime }) . Then, we deduce a full asymptotic expansion of the archimedean contribution to l_p,p^￠(n)\lambda _{\pi ,\pi ^{\prime }}(n) and investigate the contribution of the finite (non-archimedean) term. Under the generalized Riemann hypothesis (GRH) on non-trivial zeros of L(s,p_f×[(p)\tilde]_f^￠)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime }) , the nth Li coefficient l_p,p^￠(n)\lambda _{\pi ,\pi ^{\prime }}(n) is evaluated in a different way and it is shown that GRH implies the bound towards a generalized Ramanujan conjecture for the archimedean Langlands parameters μ _π (v,j) of π. Namely, we prove that under GRH for L(s,p_f×[(p)\tilde]_f)L(s,\pi _{f}\times \widetilde{\pi}_{f}) one has |Rem_p(v,j)| ￡ \frac14|\mathop {\mathrm {Re}}\mu_{\pi}(v,j)|\leq \frac{1}{4} for all archimedean places v at which π is unramified and all j=1,…,m.     

Dynamic graphs and continuous Boolean networks,II: Large-scale organic structures

In this paper, we propose a new method for constructing large-scale dynamic graphs. The procedure is based on the notion of graph entanglement, and involves “organic” operations such as self-replication and random mutations. Graphs obtained in this manner are globally asymptotically stable, and the simulation of their dynamics requires only a modest computational effort. As a result, they provide a suitable mathematical framework for studying the behavior of large-scale continuous Boolean networks.     

The isomorphism relation between tree-automatic Structures

An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is neither a Σ₂¹-set nor a Π₂¹-set.     

Distribution of stable isotopes in surface water along the Danube River in Serbia†

Stable hydrogen and oxygen isotopes were analysed in water samples from the River Danube and its tributaries during a longitudinal survey performed in August 2005 on Serbian territory. Danube river water data ranged from?80‰ to?66‰ for δ²H, and from?11.2‰ to?9.3‰ for δ¹⁸O with δ values increasing downstream. The isotopic signatures of the adjacent tributaries (the Tisza, the Sava and the Velika Morava) sampled at the locations close to their confluence with the Danube (Titel, Ostru?nica and Ljubi?evski most, respectively) just about the time of the campaign were enriched (?67‰ and?63‰ for δ²H, and?9.3‰ and?8.9‰ for δ¹⁸O) with respect to the Danube water because of their catchment effects. Hydrogen and oxygen stable isotope values were used in combination with measured physico-chemical and biological parameters to trace hydrological and transport processes in these river systems. The mixing relationships between the Danube main stream and its tributaries were estimated using the mass balance for isotopic composition and electrical conductivity as conservative parameters. Evidence of an incomplete mixing process at the ?enta location, 8 km below the confluence of the Tisza river, with its participation of 88% was shown by its oxygen-18 content. The correlations between river water isotope composition and physico-chemical and biological parameters are discussed.     

Partie 1: La nouvelle enceinte destinée à Ia production de I'or colloidal radioactif 198 Au

Une nouvelle enceinte destinée à la production de l,or colloïdal radioactif¹⁹⁸Au à usage thérapeutique et diagnostique est construite dans le Laboratoire de Chimie de Haute Activité à l'Institut des Sciences Nucléaires ?Boris Kidri?”. L'enceinte comporte deux appareils pour la préparation des colloïdes de l'or radioactif, permettant une production permanente méme au cas où l'un des appareils est accidenté. C'est grâce à une conception originale de la protection en plomb que l'accès aus appareils et aux stocks des effluents est rendu facile et ainsi que les systèmes de commande des processus des processus chimiques et la manipulation dans l,enceinte sont bien simplifiés