Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

Dynamic Strategic Pricing and Speed of Diffusion

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.     

Uniformity in Computable Structure Theory

We investigate the effects of adding uniformity requirements to concepts in computable structure theory such as computable categoricity (of a structure) and intrinsic computability (of a relation on a computable structure). We consider and compare two different notions of uniformity, previously studied by Kudinov and by Ventsov. We discuss some of their results and establish new ones, while also exploring the connections with the relative computable structure theory of Ash, Knight, Manasse, and Slaman and Chisholm and with previous work of Ash, Knight, and Slaman on uniformity in a general computable structure-theoretical setting.     

The evolution of a truncated gaussian probability density through time—modelling animal liveweights after selection

The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal Liveweights is of interest in animal husbandry. Truncated frequency distributions arise when the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs, the resulting density is practically indistinguishable from Gaussian.     

Elastic wave scattering around cavities in inhomogeneous continua by the BEM

This work examines elastic wave scattering around cavities embedded in a continuum with depth-dependent shear modulus and under conditions of plane strain. A restricted case of inhomogeneity is considered, where the Poisson ratio is fixed at 0.25 and where the density profile also varies, but proportionally to the shear modulus. For this specific case, the wave speeds remain macroscopically constant and it becomes possible to recover the exact Green functions by using an algebraic transformation method. These functions are subsequently used as kernels in a standard 2D boundary element formulation defined in the Laplace transform domain. The final step involves an inverse Laplace transformation, whereby the transient behavior of cavities in the aforementioned inhomogeneous continuum can be recovered. Two basic examples are solved, namely the circular cylindrical cavity under sudden internal explosion and under a pressure wave sweep. In the latter case, it is possible to investigate the effect that the angle of wave incidence has on the displacement and stress that develop along the cavity's perimeter, given the fact that the shear modulus is changing along the vertical direction. These examples serve to illustrate the present approach and to reveal some interesting differences that are observed in transient wave scattering phenomena between homogeneous and continuously inhomogeneous models, where the latter models yield a more realistic representation of geological formations.     

Calculation of the vibrational spectra of copper crystals with vacancies

The local vibrational spectra of copper crystals containing vacancies are calculated using the pair atomic potential derived in the framework of the resonance pseudopotential theory. The calculations are performed by a recursive method with due regard for the symmetry of the defect region. The frequencies of the vacancy-induced resonance vibrations of different symmetries are determined.     

The use of an ultrasonic Doppler velocimeter in turbulent pipe flow

An ultrasonic Doppler velocimeter (UDV) is used for an experimental investigation of turbulent pipe flow at eight different Reynolds numbers (22,300–854,900). The UDV is a multipoint probe in the sense that it takes instantaneous measurements of fluid velocities at different locations simultaneously, with remarkable resolutions in space and time. The performances of the instrument with respect to the properties of the overlap layer of the turbulent flow field are investigated; the experimental results are compared with both already existing and more recently proposed scaling laws, and with other data of experimental nature.     

Crossover from high-temperature vortex-liquid to low-temperature vortex-glass behavior in single phase HgBa2Ca2Cu3O8+δ superconductor

The ρ-T curves in our single phase HgBa₂Ca₂Cu₃O_8+δ superconductor were measured as a function of temperature and magnetic field, ρ=ρ₀exp(−U_eff/κ_BT). It can be transformed to another form d(lnρ)/d(1/T)=−U_eff+TdU_eff/dT, then this becomes a plot of the activation energy U_eff as a function of temperature. Our data plotted in these ways show a clear crossover from high-temperature two-dimensional vortex-liquid to a critical region associated with the low-temperature three-dimensional vortex-glass phase transition. The critical exponents v(z−1)=3.9±1.9 in this system are little different with previous measurements in BSCCO and YBCO systems.     

Propagation of magnetostatic waves in unsaturated ferrite films with a strip domain structure

The propagation of surface and volume magnetostatic waves in unsaturated films of yttrium iron garnet is studied experimentally for the case when the wavelength greatly exceeds the domain width, while the domain width is comparable to the film thickness. The characteristics of these waves are examined for symmetric linear, asymmetric linear, and symmetric zigzag strip domain structures in the films. These characteristics cannot be explained by a theory based on averaging the magnetization over all the domains. Zh. éksp. Teor. Fiz. 111, 1016–1031 (March 1997)