Exponential trichotomy and p-admissibility for evolution families on the real line

The aim of this paper is to obtain necessary and sufficient conditions for uniform exponential trichotomy of evolution families on the real line. We prove that if p ∈ (1,∞) and the pair (C_b(R,X),C_c(R,X)) is uniformly p-admissible for an evolution family ={U(t,s)}_t≥_s then is uniformly exponentially trichotomic. After that we analyze when the uniform p-admissibility of the pair (C_b(R, X), C_c(R, X)) becomes a necessary condition for uniform exponential trichotomy. As applications of these results we study the uniform exponential dichotomy of evolution families. We obtain that in certain conditions, the admissibility of the pair (C_b(R,X),L^p(R,X)) for an evolution family ={U(t,s)}_t≥_s is equivalent with its uniform exponential dichotomy.     

Preparation of aqueous crosslinked dispersions of functionalized poly(d,l-lactic acid) with a thermomechanical method

Aqueous crosslinked microparticle dispersions were prepared from a copolymer of d,l-lactic acid, 1,4-butanediol, and itaconic acid with a thermomechanical method. The copolymer was prepared in one step polycondensation reaction using Sn(Oct)₂ as a catalyst. A polymer with M_n of 2800 g mol^?1 and a molecular weight distribution of 1.41 was obtained (as determined by SEC), that contained double bonds introduced by the itaconic acid monomer units (6 mol-%, as determined by NMR). Crosslinking ability of the prepared copolymer was demonstrated in bulk by adding a thermal initiator and altering amounts of ethylene glycol dimethacrylate (EGDMA) crosslinking agent into molten polymer at 60–150 °C. A crosslinked gel was formed in less than 15 min at 80 °C when 10 wt.% of EGDMA was added and benzoyl peroxide (BPO) was used as the initiator. Aqueous dispersions were prepared of the non-crosslinked copolymer with a thermomechanical method that involved slow addition of aqueous polyvinyl alcohol (PVA) solution into molten copolymer at 60 °C under shear. Dispersions were prepared with 10 wt.% of EGDMA and 2 wt.% of BPO. Crosslinking of the dispersed microparticles was achieved by heating the dispersions at 80 °C for 30 or 60 min. The dispersions were characterized by SEM, DSC, TGA, FT-IR, solid state NMR, and gel content measurements. The effect of crosslinking was clearly seen in SEM images of films cast from the dispersions. The films cast from non-crosslinked dispersions had smooth morphology whereas in films cast from crosslinked dispersions separate spherical particles were observed. During the crosslinking reactions, glass transition temperatures increased (as determined by DSC), thermal stability of the samples increased (as determined by TGA), and the gel content of the samples increased.     

Lipschitz regularity of solutions for mixed integro-differential equations

We establish new Hölder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii–Lions?s method. We thus extend the Hölder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local–nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one.     

View factors in a finite length axysymmetric cylindrical annulus enclosure

View factor – defined as fraction of total outgoing radiation from surface 1 intercepted by surface 2 – is a key concept in solving the radiative heat transfer in systems of surfaces. Analytical forms of the view factor have been developed by means of integration for many conventional systems of 2D and 3D surfaces in various spatial positions. However, little investigation has been carried out for situations in which there is no complete visibility between the surfaces involved in radiative exchange due to configuration of 3D surfaces or due to presence of interposing object that obstruct partially the mutual visibility.Radiative heat exchange was modeled in a finite length cylindrical annulus consisting of non-isothermal diffusely-emitting surfaces. The canonical definition of the view factor was extended by means of an analytical approach to both 3D and 2D surfaces with shading effects (incomplete mutual visibility) and numerical algorithms were developed in order to calculate view factors values and test view factor algebra rules. The system considered in this paper was an axysymmetric cylindrical annulus – frequently used in many heat transfer applications. View factor values for various surface elements were calculated by means of numerical integration. View factor algebra rules – summation and reciprocity – were verified.     

Biharmonic hypersurfaces in 4‐dimensional space forms

We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4‐dimensional space forms (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability and geometric properties of constant weighted mean curvature hypersurfaces in gradient Ricci solitons

In this paper, we study stability properties of hypersurfaces with constant weighted mean curvature (CWMC) in gradient Ricci solitons. The CWMC hypersurfaces generalize the f-minimal hypersurfaces and appear naturally in the isoperimetric problems in smooth metric measure spaces. We obtain a result about the relationship between the properness and extrinsic volume growth under the assumption of a limitation for the weighted mean curvature of the immersion. Moreover, we estimate Morse index for CWMC hypersurfaces in terms of the dimension of the space of parallel vector fields restricted to hypersurface.     

A convenient and simple procedure for the preparation of nitrate esters from alcohols employing LiNO3/(CF3CO)2O

Alcohols in small peptides, monosaccharides and steroids (12 examples) are conveniently transformed to their corresponding nitrate esters upon treatment with an acetonitrile solution of LiNO₃ and trifluoroacetic anhydride. The in situ formed mixed anhydride (CF₃COONO₂) is proposed to be the reactive nitration reagent.     

Distribution and Excretion of Radiolabeled Temoporfin in a Murine Tumor Model

The biodistribution and excretion of temoporfin (tetra[ m -hydroxyphenyl]chlorin, m -THPC), a recently developed photosensitizer, was investigated in BALB/c mice. [¹⁴C]temoporfin was administered intravenously (0.73 μmol/kg) to tumor-free mice or to mice implanted with the Colo 26 colorectal carcinoma. Blood, tissue and fecal samples were collected for 35 days and 10 days postdose from tumor-free mice and tumor-bearing mice, respectively. Blood concentrations fell rapidly such that at later time points they were indistinguishable from background counts. Tumor concentrations rose to a peak of 0.34 μg temoporfin equivalents/mL at 2 days and then declined in parallel (log plot) with the blood concentrations. Tumor : tissue ratios at 2 days for skin, adipose tissue and skeletal muscle underlying the tumor were 1.5, 2.3 and 3.8, respectively. By 4 days the corresponding values were 1.6, 3.4 and 4.0. Nearly 40% of the administered radioactivity was excreted in the feces in the first 24 h and more than 80% had been excreted by 20 days. Less than 0.2 % of the dose was recovered from the urine. An elimination half-life of 10–12 days was calculated from the excretion data.