Synthesis and characterization of photosensitive cinnamate-modified cellulose acetate butyrate spin-coated or network derivatives

The photochemical behavior of photosensitive materials obtained by spin-coating or network synthesis of a cellulosic polymer bearing photo-cross-linkable cinnamate groups was investigated. First, cinnamate groups were grafted on a cellulose acetate butyrate polymer, with different grafting densities. The photochemical properties of the polymers were studied in solution by UV–visible and ¹H NMR spectroscopy. Then spin-coated films and networks were prepared and characterized as a function of the number of cinnamate groups per cellulosic unit. The water-wetting properties of both surfaces were studied by dynamic contact angle measurements, before and after photoirradiation, and subsequent heating. The surfaces obtained by the two methods have significantly different behaviors that can be assigned to the distinct photochemical pathways of the cinnamate groups upon irradiation depending on the sample preparation. Indeed, dimerization reaction is evidenced as the main process in the spin-coated films while the expected isomerization is predominant at the surface of the polymer networks.     

Chiral single-molecule magnet with a 35 K energy barrier for relaxation of the magnetization

The reaction of [Mn^II(S-mandelato)₂] complexes with 5-Methyl-salicylaldoxim (5-Me-saloxH₂) leads to the chiral hexanuclear manganese(III) complex [Mn₆(μ₃-O)₂(5-Me-salox)₆(S-mandelato)₂(EtOH)₆]. The structure can be viewed as two neutral stacked {Mn₃(μ₃-O)(5-Me-salox)₃(S-mandelato)(EtOH)₃} triangular subunits linked together in a head-to-tail manner by two phenoxo and two oximato μ₃-oxygen atoms of the deprotonated oxime groups of the ligands. The magnetic study of this chiral hexanuclear manganese(III) complex reveals a SMM behaviour with an energy barrier of the slow relaxation of the magnetisation equal to 35 K. Considering the structural features, the fitting of the temperature dependence of the magnetic susceptibility gives a good agreement with the experimental data considering two sets of interactions: J₁ = +0.37 cm⁻¹ and J₂ = −0.70 cm⁻¹ within (ferromagnetic) and between (antiferromagnetic), respectively, the {Mn₃(μ₃-O)(5-Me-salox)₃(S-mandelato)(EtOH)₃} triangular subunits.     

Magnetic ordering of Ni4 Cubane complexes through hydrogen bonds

The serendipity synthesis of the 2-hydroxy-3-methoxy-benzaldehyde or o-vanillin nickel(II) cubane complex, obtained by ourselves and other workers, can be rationalized to give the cubane in a high yield by direct use of 2-hydroxy-3-methoxy-benzaldehyde (H-ovan). The structural determinations of crystals obtained according to the two experimental processes show that the complex formulated [(MeOH)Ni(μ₃-OMe)(ovan)]₄ (ovan = deprotonated form of o-vanillin) is characterized in the two cases. Ni-Ni ferromagnetic interactions (J_NiNi = 5.8 cm⁻¹) giving an S = 4 ground state are active in the Ni₄ cubane. Replacement of methanol molecules coordinated to the Ni ions by a diol, an amino-alcohol or an amino-ether allows self-association of these Ni₄ units according to two different ways: by direct coordination bonds through the diol ligand or by hydrogen bonds involving the OMe groups of o-vanillin located at the periphery of the cubane and the hydrogen atoms of the primary amine functions. This association is suggested in the two cases by the presence of out-of-phase signals (χ”) when ac susceptibility measurements are performed at different frequencies. These molecules do not behave as SMM for these χ” signals, that are not frequency-dependent, correspond to the establishment of a three-dimensional ordering.     

New serinolic amino-<Emphasis Type="Italic">s</Emphasis>-triazines by chemoselective amination of cyanuric chloride and their (pro)diastereomerism in restricted rotational phenomena

The highly chemoselective preparation of new elaborated N-unsymmetrically substituted chlorodiamino-s-triazines and melamines, seen as building-blocks for iterative synthesis, is reported. It consisted of amination of cyanuric chloride with commercial C-2-substituted 2-aminopropane-1,3-diols (“serinols”), playing the role as “open-chain” unit and enantiopure (1S,2S)-2-amino-1-(4-nitrophenyl)propane-1,3-diols (“p-nitrophenylserinols”) based amino-1,3-dioxanes (“closed-chain” unit). Issued from the restricted rotation about C(s-triazine)-N(exocyclic) partial double bonds, seen as axes of (pro)diastereomerism, a global four-component rotational equilibrium involving the title compounds is discussed based on DFT computation and (VT) NMR data. Depending on π-deficiency of the s-triazine core, an (un)synchronised deblocking of the generated rotational diastereomers was observed. They are discussed as influence of intra-vs. intermolecular NH...OH (dynamic) interactions occurring in the “open-chain” unit and the anancomeric, axial vs. equatorial, amino-anchorage of the “closed-chain” unit.      

Renormalized solutions of nonlinear parabolic equations with diffuse measure data

Given a parabolic cylinder Ω × (0, T), where Ω is a bounded domain of ${\mathbb{R}^N}$ , we consider IBV problems involving equations of the type $$b(u)_{t} - \Delta_{p} u = \mu$$ where b is a increasing C ¹-function and μ is a diffuse measure. We prove the existence and uniqueness of a renormalized solution for this class of nonlinear parabolic equations.     

Breaks or long memory behavior: An empirical investigation

Are structural break models true switching models or long memory processes? The answer to this question remains ambiguous. In recent years, many papers have dealt with this problem. Some studies have shown that, under specific conditions, switching models and long memory processes can easily be confused. In this paper, using several generating models (the mean-plus-noise model, the stochastic permanent break model, the Markov switching model, the threshold autoregressive (TAR) model, the sign model, and the structural change model) and several estimation techniques (the Geweke–Porter–Hudak (GPH) technique, detrended fluctuation analysis (DFA), the exact local Whittle (ELW) method, and wavelet methods) we show that, even if the answer is quite simple in some cases, it can be mitigated in other cases. Using French and American inflation rates, we found that the most appropriate process that takes into account the important features of these series is a model that simultaneously combines changes in regimes and long memory behavior. The main result of this study indicates that estimating a long memory parameter without taking into account the presence of breaks in the data sets may lead to misspecification and hence to overestimating the true parameter.     

Monte Carlo analysis of polymer translocation with deterministic and noisy electric fields

Polymer translocation through the nanochannel is studied by means of a Monte Carlo approach, in the presence of a static or oscillating external electric voltage. The polymer is described as a chain molecule according to the two-dimensional “bond fluctuation model”. It moves through a piecewise linear channel, which mimics a nanopore in a biological membrane. The monomers of the chain interact with the walls of the channel, modelled as a reflecting barrier. We analyze the polymer dynamics, concentrating on the translocation time through the channel, when an external electric field is applied. By introducing a source of coloured noise, we analyze the effect of correlated random fluctuations on the polymer translocation dynamics.     

Vietoris–Rips complexes also provide topologically correct reconstructions of sampled shapes

Given a point set that samples a shape, we formulate conditions under which the Rips complex of the point set at some scale reflects the homotopy type of the shape. For this, we associate with each compact set X of ${\mathbb{R}}^n$ two real-valued functions $c_X$ and $h_X$ defined on ${\mathbb{R}}_{+}$ which provide two measures of how much the set X fails to be convex at a given scale. First, we show that, when P is a finite point set, an upper bound on $c_P(t)$ entails that the Rips complex of P at scale r collapses to the ?ech complex of P at scale r for some suitable values of the parameters t and r. Second, we prove that, when P samples a compact set X, an upper bound on $h_X$ over some interval guarantees a topologically correct reconstruction of the shape X either with a ?ech complex of P or with a Rips complex of P. Regarding the reconstruction with ?ech complexes, our work compares well with previous approaches when X is a smooth set and surprisingly enough, even improves constants when X has a positive μ-reach. Most importantly, our work shows that Rips complexes can also be used to provide shape reconstructions having the correct homotopy type. This may be of some computational interest in high dimensions.     

An omnibus test to detect time-heterogeneity in time series

This paper focuses on a procedure to test for structural changes in the first two moments of a time series, when no information about the process driving the breaks is available. We model the series as a finite-order auto-regressive process plus an orthogonal Bernstein polynomial to capture heterogeneity. Testing for the null of time-invariance is then achieved by testing the order of the polynomial, using either an information criterion, or a restriction test. The procedure is an omnibus test in the sense that it covers both the pure discrete structural changes and some continuous changes models. To some extent, our paper can be seen as an extension of Heracleous et al. (Econom Rev 27:363–384, 2008).