SBV REGULARITY OF GENUINELY NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN ONE SPACE DIMENSION

The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered.An overview of the techniques involved in the proof is given,and a c...     

Capping [H<Subscript>8−n</Subscript>Ni<Subscript>42</Subscript>C<Subscript>8</Subscript>(CO)<Subscript>44</Subscript>]<Superscript>n−</Superscript> (n = 6, 7, 8) Octa-carbide Carbonyl Nanoclusters with [Ni(CO)] and [CuCl] Fragments

The reactions of [Ni₁₆(C₂)₂(CO)₂₃]^4? and [Ni₃₈C₆(CO)₄₂]^6? with CuCl afforded mixtures of the previously reported [HNi₄₂C₈(CO)₄₄(CuCl)]^7? bimetallic octa-carbide cluster and the new [HNi₄₃C₈(CO)₄₅]^7? and [HNi₄₄C₈(CO)₄₆]^7? homo-metallic octa-carbides. The three species have very similar properties resulting always in co-crystals such as [NMe₄]₇[HNi_42+2xC₈(CO)_44+2x(CuCl)_1?x]·6.5MeCN (x = 0.14) (86% [HNi₄₂C₈(CO)₄₄(CuCl)]^7?, 14%[HNi₄₃C₈(CO)₄₅]^7?/[HNi₄₄C₈(CO)₄₆]^7?) and [NMe₄]₇[HNi_42+2xC₈(CO)_44+2x(CuCl)_1?x]·5.5MeCN (x = 0.30) (70% [HNi₄₂C₈(CO)₄₄(CuCl)]^7?, 30% [HNi₄₃C₈(CO)₄₅]^7?/[HNi₄₄C₈(CO)₄₆]^7?). The new homo-metallic octa-carbides can be obtained free from the Ni–Cu octa-carbido cluster by reacting [Ni₁₀(C₂)(CO)₁₆]^2? in thf with a stoichiometric amount of CuCl, and crystals of [NMe₄]₆[H₂Ni_43+xC₈(CO)_45+x]·6MeCN (x = 0.72), which contain [H₂Ni₄₄C₈(CO)₄₆]^6? (72%) and [H₂Ni₄₃C₈(CO)₄₅]^6? (28%), have been obtained. Despite the different charges and compositions, these anions display almost identical structures, which are also closely related to those previously reported for the bimetallic Ni–Cd octa-carbido clusters [Ni_42+xC₈(CO)_44+x(CdCl)]^7? and [HNi_42+xC₈(CO)_44+x(CdBr)]^6?. Indeed, all these clusters are based on the same Ni₄₂C₈ cage decorated by miscellaneous [CdX]⁺ (X = Cl, Br), [CuCl] and [Ni(CO)] fragments.     

Coherent transfer by adiabatic passage in two-dimensional lattices

Coherent tunneling by adiabatic passage (CTAP) is a well-established technique for robust spatial transport of quantum particles in linear chains. Here we introduce two exactly-solvable models where the CTAP protocol can be extended to two-dimensional lattice geometries. Such bi-dimensional lattice models are synthesized from time-dependent second-quantization Hamiltonians, in which the bosonic field operators evolve adiabatically like in an ordinary three-level CTAP scheme thus ensuring adiabatic passage in Fock space.     

Ergodicity of a Single Particle Confined in a Nanopore

We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of the phase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.     

Gold catalysed Suzuki-Miyaura coupling of arenediazonium o-benzenedisulfonimides

Arenediazonium o-benzenedisulfonimides have been used as efficient electrophilic partners in Au(I) catalysed Suzuki coupling reactions. The synthetic protocol is general, easy and produced either biaryls or heteroaryl arenes in good yields (51 positive examples, average yield 80%). o-Benzenedisulfonimide was recovered at the end of the reactions and was reused to prepare the starting salts for further reactions. Mechanistic insights suggest that the o-benzenedisulfonimide anion act as an electron transfer agent and promotes a catalytic cycle which does not require the presence of photocatalysts or external oxidants.     

On the integrability of Degasperis–Procesi equation: Control of the Sobolev norms and Birkhoff resonances

We consider the dispersive Degasperis–Procesi equation $u_t?u_{xxt}?\mathtt{c}{u}_{xxx}+4\mathtt{c}{u}_x?u{u}_{xxx}?3u_x{u}_{xx}+4u{u}_x=0$ with $\mathtt{c}\in \mathbb{R}?\{0\}$. In [15] the authors proved that this equation possesses infinitely many conserved quantities. We prove that there are infinitely many of such constants of motion which control the Sobolev norms and which are analytic in a neighborhood of the origin of the Sobolev space $H^s$ with $s\ge 2$, both on $\mathbb{R}$ and $\mathbb{T}$. By the analysis of these conserved quantities we deduce a result of global well-posedness for solutions with small initial data and we show that, on the circle, the formal Birkhoff normal form of the Degasperis–Procesi at any order is action-preserving.     

Differences in Salivary Proteins as a Function of PROP Taster Status and Gender in Normal Weight and Obese Subjects

Taste plays an important role in processes such as food choices, nutrition status and health. Salivary proteins contribute to taste sensitivity. Taste reduction has been associated with obesity. Gender influences the obesity predisposition and the genetic ability to perceive the bitterness of 6-n-propylthiouracil (PROP), oral marker for food preferences and consumption. We investigated variations in the profile of salivary proteome, analyzed by HPLC-ESI-MS, between sixty-one normal weight subjects (NW) and fifty-seven subjects with obesity (OB), based on gender and PROP sensitivity. Results showed variations of taste-related salivary proteins between NW and OB, which were differently associated with gender and PROP sensitivity. High levels of Ps-1, II-2 and IB-1 proteins belonging to basic proline rich proteins (bPRPs) and PRP-1 protein belonging to acid proline rich proteins (aPRPs) were found in OB males, who showed a lower body mass index (BMI) than OB females. High levels of Ps-1 protein and Cystatin SN (Cyst SN) were found in OB non-tasters, who had lower BMI than OB super-tasters. These new insights on the role of salivary proteins as a factor driving the specific weight gain of OB females and super-tasters, suggest the use of specific proteins as a strategic tool modifying taste responses related to eating behavior.