Rank-one completions of partial matrices and completely rank-nonincreasing linear functionals

We obtain necessary and sufficient conditions for the existence and the uniqueness of rank-one completions of a partial matrix, and we verify a conjecture of Hadwin and Larson concerning the nature of completely rank-nonincreasing linear functionals defined on pattern subspaces.

     

Anisotropic field of background internal waves on a sea shelf and its effect on low-frequency sound propagation

The space-time spectral characteristics of the field of background internal waves (IW) are obtained for two oceanic shelf regions (the Atlantic shelf of the United States and the Kamchatka shelf) and analyzed. Within the framework of a numerical experiment, it is shown that the observed anisotropy of the IW field may considerably affect the low-frequency sound fluctuations in the aforementioned regions and, in particular, may change the interference invariant of the sound field.     

Markov processes associated with L p -resolvents and applications to stochastic differential equations on Hilbert space

We give general conditions on a generator of a C₀-semigroup (resp. of a C₀-resolvent) on L^p(E,μ), p ≥ 1, where E is an arbitrary (Lusin) topological space and μ a σ-finite measure on its Borel σ-algebra, so that it generates a sufficiently regular Markov process on E. We present a general method how these conditions can be checked in many situations. Applications to solve stochastic differential equations on Hilbert space in the sense of a martingale problem are given. Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday     

Far-infrared signature of animal tissues characterized by terahertz time-domain spectroscopy

We present terahertz time-domain spectroscopy characterization of various animal tissues obtained from pork and rats. As the sensitivity of terahertz radiation to polar molecules of water is very high, biological tissues with high level of hydration show strong absorption at terahertz frequencies. The experimental data indicate that skin, fat and lean pork tissues have different frequency-dependent response to terahertz radiation due to the variation in water content. The same type tissue from different animals, however, is observed to show very similar water absorption.     

Route stability in vehicle routing decisions: a bi-objective approach using metaheuristics

In this paper, we argue that vehicle routing solutions are often tactical decisions, that should not be changed too often or too much. For marketing or other reasons, vehicle routing solutions should be stable, i.e. a new solution (when e.g. new customers require service) should be as similar as possible to a solution already in use. Simultaneously however, this new solution should still have a good quality in the traditional sense (e.g. small total travel cost). In this paper, we develop a way to measure the difference between two vehicle routing solutions. We use this distance measure to create a metaheuristic approach that will find solutions that are “close” (in the solution space) to a given baseline solution and at the same time have a high quality in the sense that their total distance traveled is small. By using this approach, the dispatcher is offered a choice of Pareto-optimal solutions, allowing him to make a trade-off between changing his existing solution and allowing a longer travel distance. Some experiments are performed to show the effectiveness of the approach.     

On Subgroups of Prime Order in a Finite Group

We study finite groups with generalized normality condition for subgroups of prime order.     

Modeling of the microwave drying process of aqueous dielectrics

We propose a thermodynamic framework for describing the microwave drying process of aqueous dielectrics based on Maxwell-Lorentz Field equations and mixture theory. Several issues are discussed such as the form of entropy equation; the constitutive relations for the macroscopic electric polarization vectors, Cauchy stresses, heat fluxes, internal momentum supplies, etc., for each component of the mixture: porous solid, water and gas in different regions; and the interfacial jump conditions between different regions in the mixture. A brief examination of the status of material frame indifference within the context of our framework is presented.     

MULTI-MODE TRIMMING OF IMPERFECT THIN RINGS USING MASSES AT PRE-SELECTED LOCATIONS

This paper presents a practical method for trimming the natural frequencies of an initially imperfect ring to simultaneously eliminate certain of the frequency splits present. Compared with previous work, the novel feature of this method is that the trimming masses are positioned at pre-selected locations on the ring. The basis for the proposed method is the concept of equivalent imperfection mass, which allows any imperfect ring to be considered as a perfect ring with equivalent imperfection masses attached. By considering this trimming problem it is deduced that it is possible to trim N pairs of modes simultaneously by removing (a minimum of) 2 N trimming masses at particular locations around the ring. By positioning the trimming masses at pre-selected locations, it is shown that a simple set of trimming masses can be calculated easily, and from this set an infinite number of solution sets can be found. Methods for generating these sets are outlined for the trimming of both a single and a dual pair of modes. In practice, it is likely that the trimming masses will be spaced regularly. For this special case, it is found that it is not possible to trim all single- and dual-mode pairs with any arrangement of masses. Validation of the derived simple solution set and the proposed procedure to generate further sets is achieved by studying a number of theoretical examples.     

The Effect of Boundary Conditions on Gas-phase Synthesised Silver Nanoparticles

We have prepared spherical non-agglomerated silver nanoparticles by an evaporation–condensation–dilution/cooling technique. Silver was evaporated from a crucible in a tubular flow reactor. A porous tube diluter was used to quench the carrier gas at the outlet of the reactor to enhance the formation of small particles and to suppress agglomeration and other particle growth mechanisms. The number size distribution of the prepared particles was measured with a differential mobility analyser–condensation nucleus counter combination and the size and the shape of the particles were analysed with transmission electron microscope. The system was modelled using a sectional aerosol dynamics computer code to estimate the importance of different aerosol processes. In all conditions the particles obtained were non-agglomerated and spherical. The mean particle diameter varied from 4 to 10-nm depending on boundary conditions. From the modelling studies it can be concluded that the nucleation rate is the most important parameter controlling the final particle size.