Strongly anisotropic diffusion problems; asymptotic analysis

The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrices have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them and establish convergence results. The analysis relies on averaging techniques, which have been used previously for studying transport equations whose advection fields have disparate components.     

Editorial Board: Electrophoresis 18'14

Electrophoresis 2014, 35, 2673–2680. DOI: 10.1002/elps.201400210 pH‐responsive microcapsules manufactured by combining electrostatic droplets (ESD) and microfluidic droplets (MFD) techniques to produce mono‐disperse core (alginate) ‐ shell (chitosan) structure with controlled drug release behavior. The fabricated core‐shell microcapsules have a pH‐controlled drug delivery function according to acidic and alkaline environment, and present positive biocompatibility, indicating their potential use in biological and biomedical applications, such as pH‐responsive drug‐delivery systems, scaffolding for bone tissues, and as an oral drug‐delivery vehicle.

     

Chemical Investigation on Various Aromatic Compounds Polymerization in Low Pressure Helium Plasma

Remarkable properties of plasma polymer films are greatly dependent not only on the chemical structure of precursor but also on the reactor design and the deposition conditions. In many industrial applications it is a challenge to control the plasma polymer structure. In this paper we investigate the chemical transformation of various aromatic compounds, such as activation and fragmentation of substituent-part, aromatic ring opening, during plasma polymerization process. Polymerized films are deposited in a low-frequency capacitively coupled plasma-enhanced chemical vapour deposition reactor, working at low pressure. The chemical composition of plasma-polymerized films is elucidated by Fourier-transform infrared spectroscopy, solid-state carbon-13 nuclear magnetic resonance spectroscopy, and X-ray photoelectron spectroscopy. Based on spectroscopic measurements, the intermediary reactions during film growth may be presumed.     

Birkhoff Completeness in Institutions

We develop an abstract proof calculus for logics whose sentences are ‘Horn sentences’ of the form: and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the ‘Horn fragment’ of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants. the restriction of a logic to Horn sentences     

Viability for Differential Inclusions on Graphs

Let X be a Banach space, I a nonempty, bounded interval and let $K:I\leadsto X$ be a given multi-valued function. We rephrase the concept of tangent set introduced by Cârj? et al. (Trans Amer Math Soc, 2008; Viability, Invariance and Applications. North-Holland Mathematics Studies, vol. 207. Elsevier, 2007) by saying that a bounded set $E\subseteq X$ is right tangent to at if $\liminf_{h\downarrow0}{1}/{h}\,\text{\rm dist}(\xi+hE;K(\tau+h))=0$ . Next, by using a tangency condition expressed in the terms of this concept, we establish several necessary and sufficient conditions for viability referring to differential inclusions on graphs.     

Necessary and Sufficient Conditions for Viability for Nonlinear Evolution Inclusions

We consider the viability problem for nonlinear evolutions inclusions of the form u′(t)?∈?Au(t)?+?F(u(t)), where A is an m-dissipative (possible nonlinear and multi-valued) operator acting in a Banach space X, K?X is a nonempty, locally closed set and $F:K{\user1{ \rightsquigarrow }}X$ is with nonempty, convex, closed and bounded values. We define the concept of A-quasi-tangent set to K at a given point ξ?∈?K and we prove a necessary condition for C ⁰-viability expressed in terms of this new tangency concept. We next show that, under various natural extra-assumptions, the necessary condition is also sufficient. We extend the results to the quasi-autonomous case, we deal with the existence of noncontinuable or even global C ⁰-solutions and, as applications, we deduce a comparison result and a sufficient condition for null controllability.     

Taylor dispersion analysis discloses the impairment of Aβ peptide aggregation by the presence of a fluorescent tag

The use of fluorescently tagged amyloid peptides, implicated in Alzheimer's disease, to study their aggregation at low concentrations is a common method; however, the fluorescent tag should not introduce a bias in the aggregation process. In this work, native amyloid peptides Aβ(1–40) and Aβ(1–42) and fluorescein-5-isothiocyanate (FITC), tagged ones, were studied using Taylor dispersion analysis coupled with a simultaneous UV and light-emitting diode-induced fluorescence detection, to unravel the effect of FITC on the aggregation process. For that, a total concentration of 100 µM of peptides consisting of a mixture of native and tagged ones (up to 10% in moles) was applied. Results demonstrated that FITC had a strong inhibition effect upon the aggregation behaviour of Aβ(1–42), whereas for Aβ(1–40), only a retardation in kinetics was observed. It was also shown that when mixed solutions of Aβ(1–40) and Aβ(1–42) are used, the Aβ(1–42) alloform was the leading peptide in the aggregation process, and when the latter was tagged, the aggregation kinetics decreased but the lifetime of potentially toxic oligomers was drastically increased. These results confirmed that the hydrophilicity of the N-terminus part of the peptide plays a major role in the aggregation process.     

Continuity of the first eigenvalue for a family of degenerate eigenvalue problems

For each \({\alpha\in[0,2)}\) we consider the eigenvalue problem \({-{\rm div}(|x|^\alpha \nabla u)=\lambda u}\) in a bounded domain \({\Omega\subset \mathbb{R}^N}\) (\({N\geq 2}\)) with smooth boundary and \({0\in \Omega}\) subject to the homogeneous Dirichlet boundary condition. Denote by \({\lambda_1(\alpha)}\) the first eigenvalue of this problem. Using \({\Gamma}\)-convergence arguments we prove the continuity of the function \({\lambda_1}\) with respect to \({\alpha}\) on the interval \({[0,2)}\).     

Kinetic studies for the esterification of acetic acid with epichlorohydrin over an anion exchange resin catalyst

The kinetics of the esterification reaction between acetic acid and epichlorohydrin catalysed by Purolite A-520E strong basic anion exchange resin was studied. The effects of certain parameters such as stirring speed, particle diameter, temperature, catalyst amount and molar ratio between reactants were experimentally determined. It was found that the overall reaction rate is intrinsically kinetically controlled. The partial orders of reaction with respect to catalyst, acetic acid and epichlorohydrin were determined. A reaction mechanism is proposed. Based on chromatographic data and taking into account the partial orders of reaction, a more detailed kinetic model is suggested.      

Extremal Problems for Mappings with Generalized Parametric Representation in $${{\mathbb {C}}}^{n}$$

In this paper we are concerned with the family \(\widetilde{S}^t_A(\mathbb {B}^n)\) (\(t\ge 0\)) of normalized biholomorphic mappings on the Euclidean unit ball \(\mathbb {B}^n\) in \({\mathbb {C}}^n\) that can be embedded in normal Loewner chains whose normalizations are given by time-dependent operators \(A\in \widetilde{\mathcal {A}}\), where \(\widetilde{\mathcal {A}}\) is a family of measurable mappings from \([0,\infty )\) into \(L({\mathbb {C}}^n)\) which satisfy certain natural assumptions. In particular, we consider extreme points and support points associated with the compact family \(\widetilde{S}^t_A(\mathbb {B}^n)\), where \(A\in \widetilde{\mathcal {A}}\). We prove that if \(f(z,t)=V(t)^{-1}z+\cdots \) is a normal Loewner chain such that \(V(s)f(\cdot ,s)\in \mathrm{ex}\,\widetilde{S}^s_A(\mathbb {B}^n)\) (resp. \(V(s)f(\cdot ,s)\in \mathrm{supp}\,\widetilde{S}^s_A(\mathbb {B}^n)\)), then \(V(t)f(\cdot ,t)\in \mathrm{ex}\, \widetilde{S}^t_A(\mathbb {B}^n)\), for all \(t\ge s\) (resp. \(V(t)f(\cdot ,t)\in \mathrm{supp}\,\widetilde{S}^t_A(\mathbb {B}^n)\), for all \(t\ge s\)), where V(t) is the unique solution on \([0,\infty )\) of the initial value problem: \(\frac{d V}{d t}(t)=-A(t)V(t)\), a.e. \(t\ge 0\), \(V(0)=I_n\). Also, we obtain an example of a bounded support point for the family \(\widetilde{S}_A^t(\mathbb {B}^2)\), where \(A\in \widetilde{\mathcal {A}}\) is a certain time-dependent operator. We also consider the notion of a reachable family with respect to time-dependent linear operators \(A\in \widetilde{\mathcal {A}}\), and obtain characterizations of extreme/support points associated with these families of bounded biholomorphic mappings on \(\mathbb {B}^n\). Useful examples and applications yield that the study of the family \(\widetilde{S}^t_A(\mathbb {B}^n)\) for time-dependent operators \(A\in \widetilde{\mathcal {A}}\) is basically different from that in the case of constant time-dependent linear operators.