On interpolatory divergence-free wavelets

We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct compactly supported divergence-free interpolatory wavelets.

     

Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.

     

Does the beam width affect the generalized M factor of hard-edged diffracted beams?

A detailed study of the generalized M² factor of hard-edged diffracted beams based on the truncated second-order moments method, asymptotic analysis and self-convergent beam width approach is performed. The dependence of the generalized M² factor on the parameters characterizing the spatial profile, and beam truncation, etc. is analyzed.     

Capture of an Ensemble of Microparticles in the Field of Laser Multibeam Interference

Capture of an ensemble of polymeric microspheres in a water suspension under the action of optical gradient forces in the field of interfering laser beams has been investigated for the case of two-, three-, and four-beam interference. The self-diffraction and diffraction of radiation on induced ordered spatial distribution of particles have been obtained.     

On the role of the interface charge in non-ideal metal–semiconductor contacts

The bias dependent interface charge is considered as the origin of the observed non-ideality in current–voltage and capacitance–voltage characteristics. Using the simplified model for the interface electronic structure based on defects interacting with the continuum of interface states, the microscopic origin of empirical parameters describing the bias dependent interface charge function is investigated. The results show that in non-ideal metal–semiconductor contacts the interface charge function depends on the interface disorder parameter, density of defects, barrier pinning parameter and the effective gap center. The theoretical predictions are tested against several sets of published experimental data on bias dependent ideality factor and excess capacitance in various metal–semicoductor systems.     

Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

Social action is situated in fields that are simultaneously composed of interpersonal ties and relations among organizations, which are both usefully characterized as social networks. We introduce a novel approach to distinguishing different network macro-structures in terms of cohesive subsets and their overlaps. We develop a vocabulary that relates different forms of network cohesion to field properties as opposed to organizational constraints on ties and structures. We illustrate differences in probabilistic attachment processes in network evolution that link on the one hand to organizational constraints versus field properties and to cohesive network topologies on the other. This allows us to identify a set of important new micro-macro linkages between local behavior in networks and global network properties. The analytic strategy thus puts in place a methodology for Predictive Social Cohesion theory to be developed and tested in the context of informal and formal organizations and organizational fields. We also show how organizations and fields combine at different scales of cohesive depth and cohesive breadth. Operational measures and results are illustrated for three organizational examples, and analysis of these cases suggests that different structures of cohesive subsets and overlaps may be predictive in organizational contexts and similarly for the larger fields in which they are embedded. Useful predictions may also be based on feedback from level of cohesion in the larger field back to organizations, conditioned on the level of multiconnectivity to the field.     

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-P_N) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μ_a/μ_s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.     

Sub-bundles of the complexified tangent bundle

We study embeddings of complex vector bundles, especially line bundles, in the complexification of the tangent bundle of a manifold. The aim is to understand implications of properties of interest in partial differential equations.

     

Analysis of Two-Dimensional Optical Fields Using an Additional Shift

A solution to the phase problem in optics is considered within the context of registration and analysis of two-dimensional stationary optical fields transformed by the object under study or fields forming an image. To obtain information on amplitude and phase distributions of the light field analyzed, a method of registration of two intensity distributions is used. The first distribution corresponds directly to the amplitude distribution. The other is formed for the sum of the initial field and the field shifted along a certain direction. The intensity distributions obtained allow one to calculate the two-dimensional structure of the field under study. It is noteworthy that the method requires no iteration procedures in solving the problem. This leads to speeding up of the processing and analysis of the information. Two variants of optical schemes for the analysis of light fields are considered. The first one corresponds to registration of the image of the analyzed plane and the second to registration of the spectrum of the spatial frequencies.