Effect of selected signals of interest on ultrasonic backscattering measurement in cancellous bones

This study examined how the signals of interest (SOI) effect on the backscattering measurement numerically based on 3-D finite-difference time-domain (FDTD) method. High resolution microstructure mappings of bovine cancellous bones provided by micro-CT were used as the input geometry for simulations. Backscatter coefficient (BSC), integrated backscatter coefficient (IBC) and apparent integrated backscatter (AIB) were calculated with changing the start (L1) and duration (L2) of the SOI. The results demonstrated that BSC and IBC decrease as L1 increases, and AIB decreases more rapidly as L1 increases. The backscattering parameters increase with fluctuations as a function of L2 when L2 is less than 6 mm. However, BSC and IBC change little as L2 continues to increase, while AIB slowly decreases as L2 continues to increase. The results showed how the selections of the SOI effect on the backscattering measurement. An explicit standard for SOI selection was proposed in this study and short L1 (about 1.5 mm) and appropriate L2 (6 mm-12 mm) were recommended for the calculations of backscattering parameters.     

Cellular properties and population asymptotics in the population balance equation

Proliferating cell populations at steady-state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by asymptotic analysis of the population balance equation. We show that the steady-state distribution tail is determined by a combination of protein production and cell division and is insensitive to other model details. Under general conditions this tail is exponential with a dependence on parameters consistent with experiment. We discuss the conditions for this effect to be dominant over other sources of variation and the relation to experiments.     

Cohomology of bifunctors

We initiate the study of the cohomology of (strict polynomial)bifunctors by introducing the foundational formalism, establishingnumerous properties in analogy with the cohomology of functors,and providing computational techniques. Since one of the initialmotivations for the study of functor cohomology was the determinationof H *(GL (k), S*(g) *(g)), we keep this challenging examplein mind as we achieve numerous computations which illustrateour methods.     

Generic and maximal Jordan types

For a finite group scheme G over a field k of characteristic p>0, we associate new invariants to a finite dimensional kG-module M. Namely, for each generic point of the projectivized cohomological variety we exhibit a “generic Jordan type” of M. In the very special case in which G=E is an elementary abelian p-group, our construction specializes to the non-trivial observation that the Jordan type obtained by restricting M via a generic cyclic shifted subgroup does not depend upon a choice of generators for E. Furthermore, we construct the non-maximal support variety Γ(G) _M , a closed subset of which is proper even when the dimension of M is not divisible by p.     

Solution of a General Linear Complementarity Problem Using Smooth Optimization and Its Application to Bilinear Programming and LCP

This paper addresses a General Linear Complementarity Problem (GLCP) that has found applications in global optimization. It is shown that a solution of the GLCP can be computed by finding a stationary point of a differentiable function over a set defined by simple bounds on the variables. The application of this result to the solution of bilinear programs and LCPs is discussed. Some computational evidence of its usefulness is included in the last part of the paper. Accepted 28 June 1999. Online publication 4 December 2000.