Nanoporous carbon allotropes by septupling map operations

Spongy carbon nanostructures, also called schwarzites, have been synthesized. They consist of highly connected covalent networks, periodic in the three dimensions of Euclidean space. The intimate structure of schwarzites has a topology of triply periodic minimal surfaces. They can be tessellated by some geometric operations on maps, including the newly proposed septupling operations. Formulas for calculating the lattice parameters of iteratively transformed maps are presented. Examples are given for both finite/closed cages and infinite/open all-sp2 carbon structures. Strain energy calculations for structures, consisting of thousands of atoms, show that such carbon allotropes are very relaxed and approach to the non-strained graphite sheet.     

Novel type of CPT violation for correlated Einstein-Podolsky-Rosen states of neutral mesons

We discuss modifications to the concept of an "antiparticle," induced by a breakdown of the CPT symmetry at a fundamental level, realized within an extended class of quantum gravity models. The resulting loss of particle-antiparticle identity in the neutral-meson system induces a breaking of the Einstein-Podolsky-Rosen correlation imposed by Bose statistics. This is parametrized by a complex parameter associated with the contamination by the "wrong symmetry" state. The physical consequences are studied, and novel observables of CPT violation in phi factories are proposed.     

Proprieétés du degré des morphismes de Belyi

Properties of the degree of Belyi functions. A famous theorem of Belyi characterizes the curves defined over a number field by the existence of an element of its function field with certain ramification properties. In this article we are interested in the degree of these functions. We define the Belyi degree of a curve defined over a number field and the Belyi degree of a point on such a curve. We prove finiteness results concerning these invariants. We give an explicit upper bound for the Belyi degree of a point on the projective line, depending on the height and on the degree of its field of definition.     

Capillary instabilities by fluctuation induced forces

The spontaneous break-up of thin films is commonly attributed to the destabilizing effect of van der Waals forces. Dispersion forces can be considered in terms of the confinement of the electromagnetic fluctuation spectrum. The principle of confinement is more general than the usual argument of interacting dipole fluctuations. It includes also disjoining pressures that are caused by thermal fluctuations. In this context, we review recent publications on the dewetting of thin polymer films, and argue that the presence of an acoustic disjoining pressure is necessary to adequately describe some of these experimental results.Received: 1 August 2003PACS: 47.20.Ma Interfacial instability - 68.15. + e Liquid thin films - 43.25.Qp Radiation pressure     

Aperiodic metal–organic frameworks

Metal–organic frameworks (MOFs) represent one of the most diverse structural classes among solid state materials, yet few of them exhibit aperiodicity, or the existence of long-range order in the absence of translational symmetry. From this apparent conflict, a paradox has emerged: even though aperiodicity frequently arises in materials that contain the same bonding motifs as MOFs, aperiodic structures and MOFs appear to be nearly disjoint classes. In this perspective, we highlight a subset of the known aperiodic coordination polymers, including both incommensurate and quasicrystalline structures. We further comment upon possible reasons for the absence of such structures and propose routes to potentially access aperiodic MOFs.

This perspective discusses progress and future directions in metal–organic frameworks with aperiodic structures. Reported quasicrystalline and incommensurate materials are presented, and pathways towards designing new such materials are provided.     

Invariance for stochastic differential systems with time-dependent constraining sets

The first part of this article presents invariance criteria for a stochastic differential equation whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain.     

α‐Amino Acid‐Isosteric α‐Amino Tetrazoles

The synthesis of all 20 common natural proteinogenic and 4 otherα‐amino acid‐isosteric α‐amino tetrazoles has been accomplished, whereby the carboxyl group is replaced by the isosteric 5‐tetrazolyl group. The short process involves the use of the key Ugi tetrazole reaction followed by deprotection chemistries. The tetrazole group is bioisosteric to the carboxylic acid and is widely used in medicinal chemistry and drug design. Surprisingly, several of the common α‐amino acid‐isosteric α‐amino tetrazoles are unknown up to now. Therefore a rapid synthetic access to this compound class and non‐natural derivatives is of high interest to advance the field.     

On the Superlinear Convergence of the Successive Approximations Method

The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations x _k+1 = G(x _k ) near a fixed point x*. Different conditions [ultimately on the magnitude of G(x*)] provide lower bounds for the convergence order of the process as a whole. In this paper, we consider only one such sequence and we characterize its high convergence orders in terms of some spectral elements of G(x*); we obtain that the set of trajectories with high convergence orders is restricted to some affine subspaces, regardless of the nonlinearity of G. We analyze also the stability of the successive approximations under perturbation assumptions.     

An existence result for a nonhomogeneous problem in R2 related to nonlinear Hencky-type materials

This paper investigates a nonlinear and non-homogeneous system of partial differential equations. The motivation comes from the fact that in a particular case the problem discussed here can be used in modeling the behavior of nonlinear Hencky-type materials. The main result of the paper establishes the existence of a nontrivial solution in an adequate functional space of Orlicz–Sobolev type by using Schauder’s fixed point theorem combined with adequate variational techniques.