On the Large-Distance Behavior of Correlations for a Hierarchical N-Component Classical Vector Model in Three Dimensions

We consider the correlation functions for a hierarchical N-component classical vector model in three dimensions. For N = , we find explicitly the eigenvalues and global eigenfunctions of the linearized renormalization group transformation. In a very direct way, this yields the correlation functions for the N = model. In particular, we check that the two-point function has canonical decay.     

Attracting properties for one dimensional flows of a general barotropic viscous fluid. Periodic flows

Summary We consider the motion of a barotropic compressible fluid in a one dimensional bounded region with impermeable boundary, see equation (1.1). Here, u(t, q) denotes the velocity and v(t, q) the specific volume. The quantity log v(t, q) measures the displacement of v(t, q) with respect to the equilibrium v 1. For the sake of brevity we denote here different norms by the simbol . We show that there is a positive constant r₀=r₀(), a small ball B₁ (r) (with radius R₁ (r), ), and a large ball B(r) (with radius R(r), ) such that the following holds, for each r [0, r₀ [(i) If f(t) < r for all t 0, and if (u(0), log v(0))R(r) (i.e. (u(0), log v(0)) B(r)) then, for sufficiently large values of t, (u(t), log v(t))R₁ (r); (ii) The solutions starting at time t=0 from the large ball B(r) have all the same asymptotic behaviour (see (1.11)); (iii) If f is T-periodic then there is a (unique) T-periodic solution (u(t), log v(t)) inside the small ball B₁ (r). This periodic solution atracts all solutions which intersect the large ball B(r). Periodic solutions had been previously studied only for very specific pressure laws, namely p(v)-log v and p(v)-v^–1.     

Long time behavior for one-dimensional motion of a general barotropic viscous fluid

Communicated byJ. Serrin     

N‐[Tris(hydroxymethyl)methyl]glycine (tricine)

The title compound, C₆H₁₃NO₅, adopts a zwitterionic form where the carboxylic acid H atom is transferred to the amino group. The methyl–glycine backbone is planar. The tris(hydroxy­methyl)­methyl group is rotated as a rigid group around the amino–methyl bond by 22 (1)° and the carboxylic acid plane is rotated by 19.76 (12)° from the plane of the main skeleton. Apart from their H atoms, the three hydroxy­methyl groups adopt a propeller‐like conformation around the amino–methyl bond, close to C₃ symmetry.     

Strong hydrogen‐bonded amino acid dimers in l‐alanine alaninium nitrate

The title compound, C₃H₇NO₂·C₃H₈NO₂⁺·NO₃^?, contains l ‐alanine–alaninium dimers bonded via the carboxyl groups by a strong asymmetric hydrogen bond with an O?O distance of 2.4547 (19) Å. The neutral alanine mol­ecule exists as a zwitterion, where the carboxyl group is dissociated and the amino group is protonated. The alaninium cation has both groups in their acidic form. The alanine mol­ecule and the alaninium cation differ only slightly in their conformation, having an N—C_α—C=O torsion angle close to ?25°. The dimers and the nitrate anion are joined through a three‐dimensional hydrogen‐bond network, in which the full hydrogen‐bonding capabilities of the amino groups of the two alanine moieties are realised.     

Navier-Stokes equations under slip boundary conditions: Lower bounds to the minimal amplitude of possible time-discontinuities of solutions with two components in L∞(L3)

Science China Mathematics - The main purpose of this paper is to extend the result obtained by Beirão da Veiga (2000) from the whole-space case to slip boundary cases. Denote by ū two...     

Excited State Properties and Energy Transfer within Dipyrrin‐Based Binuclear Iridium/Platinum Dyads: The Effect of ortho‐Methylation on the Spacer

Luminescent cyclometalated iridium complexes based on pyridyl appended dipyrrin ligands were prepared and characterized both in the solid state and in solution. The functionalization of the peripheral pyridyl moiety causes dramatic changes on the emission properties of both mono‐ and hetero‐ binuclear complexes. A detailed photophysical investigation of the two mononuclear derivatives of the [(Ppy)₂Ir(dpm‐py)] family (Ppy=2‐phenylpyridine, dpm‐py=5‐(4‐pyridyl)dipyrrin) was carried out. Introduction of methyl groups at the 3 and 5 positions on the pyridyl unit diminishes the non‐radiative rate constant by locking the peripheral pyridyl group orthogonally to the dipyrrinato plane. Thus, they limit the rotational degree of freedom, as well as the charge‐transfer character of the excited state. The coordination of these two complexes to a cyclometalated [(dppy)Pt] fragment (dppy=2,6‐diphenylpyridine) led to the formation of binuclear species in which the iridium and platinum complexes behave as acceptors and donors, respectively. In these heterobinuclear compounds, the methyl groups do not influence the energy transfer efficiency, which is estimated to be above 90 %. However, they do limit the charge‐transfer character of the acceptor’s excited state, as well as its rotational degree of freedom, thus avoiding the detrimental effect upon the photophysical performance.     

A posteriori boundary control for FEM approximation of elliptic eigenvalue problems

We derive new a posteriori error estimates for the finite element solution of an elliptic eigenvalue problem, which take into account also the effects of the polygonal approximation of the domain. This suggests local error indicators that can be used to drive a procedure handling the mesh refinement together with the approximation of the domain. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 369–388, 2012     

Excited state properties and energy transfer within dipyrrin-based binuclear iridium/platinum dyads: the effect of ortho-methylation on the spacer

Luminescent cyclometalated iridium complexes based on pyridyl appended dipyrrin ligands were prepared and characterized both in the solid state and in solution. The functionalization of the peripheral pyridyl moiety causes dramatic changes on the emission properties of both mono- and hetero- binuclear complexes. A detailed photophysical investigation of the two mononuclear derivatives of the [(Ppy)(2)Ir(dpm-py)] family (Ppy=2-phenylpyridine, dpm-py=5-(4-pyridyl)dipyrrin) was carried out. Introduction of methyl groups at the 3 and 5?positions on the pyridyl unit diminishes the non-radiative rate constant by locking the peripheral pyridyl group orthogonally to the dipyrrinato plane. Thus, they limit the rotational degree of freedom, as well as the charge-transfer character of the excited state. The coordination of these two complexes to a cyclometalated [(dppy)Pt] fragment (dppy=2,6-diphenylpyridine) led to the formation of binuclear species in which the iridium and platinum complexes behave as acceptors and donors, respectively. In these heterobinuclear compounds, the methyl groups do not influence the energy transfer efficiency, which is estimated to be above 90?%. However, they do limit the charge-transfer character of the acceptor's excited state, as well as its rotational degree of freedom, thus avoiding the detrimental effect upon the photophysical performance.     

Concerning the W k,p -Inviscid Limit for 3-D Flows Under a Slip Boundary Condition

We consider the 3-D evolutionary Navier–Stokes equations with a Navier slip-type boundary condition, see (1.2), and study the problem of the strong convergence of the solutions, as the viscosity goes to zero, to the solution of the Euler equations under the zero-flux boundary condition. We prove here, in the flat boundary case, convergence in Sobolev spaces W ^k, p (Ω), for arbitrarily large k and p (for previous results see Xiao and Xin in Comm Pure Appl Math 60:1027–1055, 2007 and Beir?o da Veiga and Crispo in J Math Fluid Mech, 2009, doi:). However this problem is still open for non-flat, arbitrarily smooth, boundaries. The main obstacle consists in some boundary integrals, which vanish on flat portions of the boundary. However, if we drop the convective terms (Stokes problem), the inviscid, strong limit result holds, as shown below. The cause of this different behavior is quite subtle. As a by-product, we set up a very elementary approach to the regularity theory, in L ^p -spaces, for solutions to the Navier–Stokes equations under slip type boundary conditions.