Scalar conservation laws with fractional stochastic forcing: Existence,uniqueness and invariant measure

We study a fractional stochastic perturbation of a first-order hyperbolic equation of nonlinear type. The existence and uniqueness of the solution are investigated via a Lax–Ole?nik formula. To construct the invariant measure we use two main ingredients. The first one is the notion of a generalized characteristic in the sense of Dafermos. The second one is the fact that the oscillations of the fractional Brownian motion are arbitrarily small for an infinite number of intervals of arbitrary length.     

Synthesis,characterization and energetic properties of novel 1-methyl-1,2,4-triazolium N-aryl/N-pyridinyl ylids

Synthesis, characterization and energetic properties of novel, nitrogen-rich 1-methyl-1,2,4-triazolium N-aryl/N-pyridinyl ylids 3a–m are reported.     

Highly Efficient Copper(II) Ion Sorbents Obtained by Calcium Carbonate Mineralization on Functionalized Cross‐Linked Copolymers

A new type of Cu^II ion sorbents is presented. These are obtained by CaCO₃ mineralization from supersaturated solutions on gel‐like cross‐linked polymeric beads as insoluble templates. A divinylbenzene–ethylacrylate–acrylonitrile cross‐linked copolymer functionalized with weakly acidic, basic, or amphoteric functional groups has been used, as well as different initial inorganic concentrations and addition procedures for CaCO₃ crystal growth. The morphology of the new composites was investigated by SEM and compared to that of the unmodified beads, and the polymorph content was established by X‐ray diffraction. The beads, before and after CaCO₃ mineralization, were tested as sorbents for Cu^II ions. The newly formed patterns on the bead surface after Cu^II sorption were observed by SEM, and the elemental distribution on the composites and the chemical structure of crystals after interaction with Cu^II were investigated by EDAX elemental mapping and by FTIR‐ATR spectroscopy, respectively. The sorption capacity increased significantly after CaCO₃ crystals growth on the weak anionic bead surface (up to 1041.5 mg Cu^II/g sample) compared to that of unmodified beads (491.5 mg Cu^II/g sample).     

The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Let ${\left(Z_n\right)}_{n\ge 0}$ be a branching process in a random environment defined by a Markov chain ${\left(X_n\right)}_{n\ge 0}$ with values in a finite state space $\mathbb{X}$. Let ${\mathbb{P}}_i$ be the probability law generated by the trajectories of ${\left(X_n\right)}_{n\ge 0}$ starting at $X_0=i\in \mathbb{X}.$ We study the asymptotic behaviour of the joint survival probability ${\mathbb{P}}_i\left(Z_n>0,X_n=j\right)$, $j\in \mathbb{X}$ as $n\to +\infty$ in the critical and strongly, intermediate and weakly subcritical cases.     

Kinetics of the Copolymerization of Methyl Vinyl Ketone and Acrylamide Initiated by the Adduct of Methyl Vinyl Ketone and Imidazole

N-(Butyl-3-one)imidazole acts as an initiating adduct which is formed in the anionic polymerization of methyl vinyl ketone (MVK) induced by imidazole (Im) and is directly formed from Im and the MVK monomer. The kinetics of the anionic homopolymerization of MVK and acrylamide (AAm) under argon in the presence of the adduct were investigated in tetrahydrofuran (THF). The rate of polymerization for the MVK system is expressed as R_p = k[Adduct] [MVK], where k = 3.1 × 10^?6 L/(mol·s)in THF at 30°C. The overall activation energy, E_a , was found to be 5.34 kcal/mol. The R_p for the AAm system is expressed as R_p = k[Adduct] [AAm], where k = 6.8 × 10^?6 L/(mol·s) in THF at 30°C, with E_a 7.78 kcal/mol. The mechanism of the polymerization induced by the initiator adduct is discussed on the basis of these results.     

Polymerization of N,N-Dimethylaminopropyl-Acrylamide Through Hydrogen Transfer Induced by the Propagation of the Polyacrolein Anion

The anionic polymerization of acrolein (AL) with N, N-dimethylamino-propylacrylamide (DMAPA) in the presence of water was investigated in tetrahydrofuran, benzene, and ethanol at 0°C in a nitrogen atmosphere. The resulting polymers were found to be essentially vinyl polymers with one DMAPA attached and an aldehyde side chain. From observations of the polymerization process by ¹H NMR, we find that polymerization was initiated by the hydroxyl anion formed in the thermodynamic equilibrium between the amine of DMAPA and water. The hydrogen transfer reaction of DMAPA was caused by the propagating poly-AL anion. On the other hand, the monomer reactivity ratios and the Q₂-e₂values of DMAPA were determined by the free-radical copolymerization of styrene (St, M₁) with DMAPA and AIBN as initiator.     

The Mitsunobu Reaction: An Alternative Synthesis of 1-(Primary Alkyl)benzotriazoles

1-(Primary alkyl)benzotriazoles are obtained in convenient yields by treating the corresponding alcohol with triphenylphosphine, N-bromosuccinimide and benzotriazole. Under these conditions, the alcohols gave exclusively the corresponding 1-alkyl-benzotriazoles. Allyl and propargyl alcohols also reacted regiospecifically in a typical Sn2 manner, and no products derived from prototropic rearrangement were found.     

In Vitro Cytotoxic Protective Effect of Alginate-Encapsulated Capsaicin Might Improve Skin Side Effects Associated with the Topical Application of Capsaicin

Chronic neuropathic pain, particularly peripheral pain, is a cause of great concern for diabetic patients. Current treatments include numerous agents such as capsaicinoids, a known deterrent of neuropathic pain despite the inconvenience associated with local side effects. In this context, the current work aims to elucidate the potential mechanisms involved in cytotoxicity by capsaicin and proposes an efficient formulation of capsaicin in alginate microcapsules, which significantly reduces side effects from capsaicin topical administration. For this, human dermal fibroblast cells were treated with alginate-microencapsulated capsaicin extracts and screened for potential cytotoxic effects produced by the treatment. Cell viability and morphology were examined, as well as oxidative stress status and anti-inflammatory potential. Our results show that the alginate encapsulated formulation of capsaicin exerted lower cytotoxic effects on human dermal fibroblasts as measured by cell viability and reactive oxygen species (ROS) production. Furthermore, the expression profiles of inflammatory cytokines were significantly altered by the treatment as compared with the control culture.