Perturbation theorems for linear hyperbolic mixed problems and applications to the compressible euler equations

The main result of this paper (which is completely new, apart from our previous and less general result proved in reference [9]) states that the nonlinear system of equations (1.11) (or, equivalently, (1.10)) that describes the motion of an inviscid, compressible (barotropic) fluid in a bounded domain Ω, gives rise to a strongly well-posed problem (in the Hadamard classical sense) in spaces H^k(Ω), k ≧ 3; see Theorem 1.4 below. Roughly speaking, if (a_n, ?_n) → (a, ?) in H^k × H^k and if f_n → f in ??²(0, T;H^k), then (v_n, g_n) → (v, g) in ?? (0, T; H^k × H^k). The method followed here (see also [8]) also applies to the non-barotropic case p = p(ρ, s) (see [10]) and to other nonlinear problems. These results are based upon an improvement of the structural-stability theorem for linear hyperbolic equations. See Theorem 1.2 below. Added in proof: The reader is referred to [29], Part I, for a concise explanation of some fundamental points in the method followed here. © 1993 John Wiley & Sons, Inc.     

Avoiding infeasibility in DEA models with weight restrictions

The flexibility of weights assigned to inputs and outputs is a key aspect of DEA modeling. However, excessive weight variability and implausible weight values have led to the development of DEA models that incorporate weight restrictions, reflecting expert judgment. This in turn has created problems of infeasibility of the corresponding linear programs. We provide an existence theorem that establishes feasibility conditions for DEA multiplier programs with weight restrictions. We then propose a linear model that tests for feasibility and a nonlinear model that provides minimally acceptable adjustments to the original restrictions that render the program feasible. The analysis can be applied to restrictions on weight ratios, or to restrictions on virtual inputs or outputs.     

Statistical Properties of Unimodal Maps

We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition into topological conjugacy classes, see [ALM]) is not transversely absolutely continuous. As an intermediate step in the proof of the formula, we show that the distribution of the critical orbit is described by the physical measure supported in the chaotic attractor.     

Pre-relaxation Processes in a Radiating Relativistic Sphere

The influence of processes occurring before the system relaxes into diffusion, on the evolution of a radiating sphere, is exhibited in a specific example. The luminosity profiles, and consequently the general evolution of the object, are shown to be quite sensitive to the value of relaxation time.     

Thermal Analysis of Ionizing Radiation Effects on Recycled Polyamide-6

The aim of this work is to study the ionizing radiation effects on thermal properties of there cycled polyamide-6. This polymer was irradiated with an electron beam of 1.5 MeV with different doses. The thermal properties of the samples were determined by TG, DSC and DMA measurements. It was observed that the irradiated samples of recycled polyamide-6undergo a crosslinking process. This revised version was published online in July 2006 with corrections to the Cover Date.     

Natural convection in a vertical strip immersed in a porous medium

In this work, the conjugated heat transfer characteristics of a thin vertical strip of finite length, placed in a porous medium has been studied using numerical and asymptotic techniques. The nondimensional temperature distribution in the strip and the reduced Nusselt number at the top of the strip are obtained as a function of the thermal penetration parameter s, which measures the thermal region where the temperature of the strip decays to the ambient temperature of the surrounding fluid. The numerical values of this nondimensional parameter permits to classify the different physical regimes, showing different solutions: a thermally long behaviour, an intermediate transition and a short strip limit.     

Phase coexistence in annealed CaMn7O12

The structural phase transition in annealed CaMn₇O₁₂ has been investigated by using high resolution synchrotron radiation powder diffraction. There is a phase coexistence phenomenon: two different crystallographic phases coexist in the material between 410 and 458 K. The first one is trigonal and it has a charge ordering (CO) of the Mn³⁺ and Mn⁴⁺ ions, while the second one is cubic and charge delocalized (CD). The volume fraction of the CD phase increases with temperature from 22% at 418 K up to 100% at 468 K. Both phases have domains of at least 150 nm at each temperature. The annealing of CaMn₇O₁₂ relaxed a part of the strains in the lattice, but did not influence the phase coexistence phenomenon.     

Investigations into the utility of high-surface area silica pellets as potential solid-phase synthesis supports

Grace-Davidson silica pellets (SMR-057-015) are found to be optimal for surface grafting of (RO)₃Si(CH₂)₃FG reagents. While loadings of up to 2.1 mmol g⁻¹ can be attained (ca. 0.05 mmol per pellet) access of further reagents to the graft sites is problematic above loadings of 0.8 mmol g⁻¹. ¹³C CPMAS NMR studies may be carried out on individual pellets (using natural abundance substrates) and the resulting spectra are diagnostic in identifying successful subsequent coupling reactions.