The extended Graetz problem with Dirichlet wall boundary conditions

The extension of the Graetz problem to include axial conduction has been of interest in view of its application to a number of low Peclet number heat or mass transfer situations. Past efforts in dealing with this problem have been plagued with uncertainties arising from expansion in terms of “eigenfunctions” and “eigenvalues” belonging to a nonselfadjoint operator. The uncertainties spring from a lack of basis for the assumptions that no complex eigenvalues exist and that the calculated eigenvectors originate from a complete set. Other methods have been entirely numerical. The present work produces an entirelyanalytical solution to the Graetz problem for the Dirichlet boundary condition based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. Physically, the decomposition views the convective diffusion process as a pair of stipulations on how the temperature (or concentration) and theaxial energy (or mass) flow through a partial tube cross-section vary with radial and axial distances. The solution obtained is simple, and readily computed. To whom correspondence may be addressed     

Liquid chromatography techniques for characterizing poly(Vinyl Alcohol)

Poly(vinyl alcohol) (PVOH) samples may contain several heterogeneities requiring the development of chromatographic techniques for characterization. Size exclusion separations have been carried out using a number of aqueous eluents, incorporating electrolyte, or electrolyte/organic modifier, or surfactant. The most favourable molecular size separation was obtained using 0.25% w/v sodium lauryl sulfate as eluent. Reasonable values for molecular weights of PVOH samples have been determined. Compositional distributions in copolymer systems can be assessed using high-performance liquid chromatography employing a reversed-phase separation mechanism. For poly(vinyl alcohol), gradient elution with water/tetrahydrofuran (THF) with a wide pore polystyrene-based packing produced separations dependent on degree of hydrolysis and sequence length distribution. The elution results were verified with a column packed with non-porous beads. Partially hydrolysed PVOH samples appeared to have a broad distribution of composition.     

Non‐constructive Properties of the Real Numbers

We study the relationship between various properties of the real numbers and weak choice principles.     

On vector spaces over specific fields without choice

We investigate the deductive strength of statements concerning vector spaces over specific fields in the hierarchy of various choice principles.     

Improvement of image quality using BLADE sequences in brain MR imaging

The purpose of this study is to compare two types of sequences in brain magnetic resonance (MR) examinations of uncooperative and cooperative patients. For each group of patients, the pairs of sequences that were compared were two T2-weighted (T2-W) fluid attenuated inversion recovery sequences with different k-space trajectories (conventional Cartesian and BLADE) and two T2-TSE weighted with different k-space trajectories (conventional Cartesian and BLADE). Twenty-three consecutive uncooperative patients and 44 cooperative patients, who routinely underwent brain MR imaging examination, participated in the study. Both qualitative and quantitative analyses were performed based on the signal-to-noise ratio, contrast-to-noise ratio (CNR), and relative contrast (ReCon) measures of normal anatomic structures. The qualitative analysis was performed by experienced radiologists. Also, the presence of motion, other (e.g., Gibbs, susceptibility artifacts, phase encoding from vessels) artifacts and pulsatile flow artifacts was evaluated.     

Evaluation of Different Turbulent Combustion Models Based on Tabulated Chemistry Using DNS of Heterogeneous Mixtures Under Multi-injection Diesel Engine-Relevant Conditions

Flow, Turbulence and Combustion - This paper assesses the accuracy of partially-premixed turbulent combustion models based on the tabulation of chemical kinetics, under multi-injection diesel...     

A new class of exact hairy black hole solutions

We present a new class of black hole solutions with a minimally coupled scalar field in the presence of a negative cosmological constant. We consider an one-parameter family of self-interaction potentials parametrized by a dimensionless parameter g. When g = 0, we recover the conformally invariant solution of the Martinez–Troncoso–Zanelli (MTZ) black hole. A non-vanishing g signals the departure from conformal invariance. Thermodynamically, there is a critical temperature at vanishing black hole mass, where a higher-order phase transition occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch of hairy solutions which undergo a first-order phase transition at a second critical temperature which depends on g and it is higher than the MTZ critical temperature. As g → 0, this second critical temperature diverges.     

Swelling Induced Finite Strain Flexure in a Rectangular Block of an Isotropic Elastic Material

The deformation of a rectangular block into an annular wedge is studied with respect to the state of swelling interior to the block. Nonuniform swelling fields are shown to generate these flexure deformations in the absence of resultant forces and bending moments. Analytical expressions for the deformation fields demonstrate these effects for both incompressible and compressible generalizations of conventional hyperelastic materials. Existing results in the absence of a swelling agent are recovered as special cases.     

Properties of the real line and weak forms of the Axiom of Choice

We investigate, within the framework of Zermelo‐Fraenkel set theory ZF, the interrelations between weak forms of the Axiom of Choice AC restricted to sets of reals. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interactive bicriterion decision support for a large scale industrial scheduling system

In this paper we develop an interactive decision analysis approach to treat a large scale bicriterion integer programming problem, addressing a real world assembly line scheduling problem of a manufacturing company. This company receives periodically a set of orders for the production of specific items (jobs) through a number of specialised production (assembly) lines. The paper presents a non compensatory approach based on an interactive implementation of the ε-constraint method that enables the decision maker to achieve a satisfactory goal for each objective separately. In fact, the method generates and evaluates a large number of non dominated solutions that constitute a representative sample of the criteria ranges. The experience with a specific numerical example shows the efficiency and usefulness of the proposed model in solving large scale bicriterion industrial integer programming problems, highlighting at the same time the modelling limitations.