Scaling Features of Two Special Markov Chains Involving Total Disasters

Journal of Statistical Physics - Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving...     

Intensive 2-phenylethanol production in a hybrid system combined of a stirred tank reactor and an immersed extraction membrane module

Bioconversion of l-phenylalanine to 2-phenylethanol using Saccharomyces cerevisiae is connected with the growth of biomass strongly limited by product inhibition. Therefore, fermentation can proceed only at low conversions of l-phenylalanine with very low yield of the desired product, which allows reaching the maximum concentration of 2-phenylethanol, 4 g L^?1, in an ordinary batch, fed-batch, or chemostat bioreactor. To minimize capital and operating costs in the bioproduction of chemical specialties where the product inhibits the bioreaction, using a hybrid system based on the application of membrane extraction integrated in the bioreactor to remove the product is a suitable solution. Integration can be done by an external module for membrane extraction or, as a more efficient solution, by an extraction membrane module immersed directly in the bioreactor. Such a hybrid system can be used to remove 2-phenylethanol from the fermentation media and thus to overcome the product inhibition of the biotransformation process. In this paper, a hybrid system consisting of a stirred tank bioreactor (3.5 L) and an immersed extraction hollow fiber membrane module was studied. In the proposed system, the kinetics of 2-phenylethanol extraction from a water solution with and without biomass in the bioreactor to alkanes at different operational conditions was measured. Extraction kinetics was compared with the predictions obtained by a mathematical model. In the hybrid system, two extractive biotransformation experiments were performed and compared with that without product removal. Experimental data were also mathematically predicted with good accuracy between the simulation and the experiment.     

Some experiments on γ-scattering between 122 and 145 keV at small angles

Differential cross section for scattering of 145.4 keV gamma rays by B, C, Al, Cu and Cd have been measured from 5–25°. For angles <10° it was not possible to separate Rayleigh and Compton scattering; therefore, the sum of the cross sections is given. Rayleigh cross sections have been measured for Pb at 122.1 and 136.5 keV at angles between 20° and 70°. The experimental results are compared with the form factor theory for Rayleigh scattering and the incoherent scattering factor theory for Compton scattering.     

Generalizations of Fox Homotopy Groups,Whitehead Products,and Gottlieb Groups

In this paper, we redefine the Fox torus homotopy groups and give a proof of the split exact sequence of these groups. Evaluation subgroups are defined and are related to the classical Gottlieb subgroups. With our constructions, we recover the Abe groups and prove some results of Gottlieb for the evaluation subgroups of Fox homotopy groups. We further generalize Fox groups and define a group τ = [Σ(V×W⋃ *), X] in which the generalized Whitehead product of Arkowitz is again a commutator. Finally, we show that the generalized Gottlieb group lies in the center of τ, thereby improving a result of Varadarajan. __________ Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 3, pp. 320–328, March, 2005.     

BODIPY: A Highly Versatile Platform for the Design of Bimodal Imaging Probes

In molecular imaging, multimodal imaging agents can provide complementary information, for improving the accuracy of disease diagnosis or enhancing patient management. In particular, optical/nuclear imaging may find important preclinical and clinical applications. To simplify the preparation of dual‐labeled imaging agents, we prepared versatile monomolecular multimodal imaging probe (MOMIP) platforms containing both a fluorescent dye (BODIPY) and a metal chelator (polyazamacrocycle). One of the MOMIP was conjugated to a cyclopeptide (i.e., octreotide) and radiolabeled with ¹¹¹In. In vitro and in vivo studies of the resulting bioconjugate were conducted, highlighting the potential of these BODIPY‐based bimodal probes. This work also confirmed that the biovector and/or the bimodal probes must be chosen carefully, due to the impact of the MOMIP on the overall properties of the resulting imaging agent.     

Free groups in a normal subgroup of the field of fractions of a skew polynomial ring

Let k(t) be the field of rational functions over the field k, let σ be a k-automorphism of K = k(t), let D = K(X;σ) be the ring of fractions of the skew polynomial ring K[X;σ], and let D^? be the multiplicative group of D. We show that if N is a noncentral normal subgroup of D^?, then N contains a free subgroup. We also prove that when k is algebraically closed and σ has infinite order, there exists a specialization from D to a quaternion algebra. This allows us to explicitly present free subgroups in D^?.     

Vectors with a prescribed minimal polynomial

Let V be a finite dimensional vector space over the field Fand φ (x)∈F[x].LetxV → V be a linear operator. Let S_φbe the set consisting of the vectors whose minimal polynomial φ(x)together with the zero vector We give necessary and sufficieni condition for S _φ to be a subspace.     

Basic Feasible Solutions and the Dantzig-Wolfe Decomposition Algorithm

The relationship between solutions of the full master program of the Dantzig-Wolfe decomposition routine and the originally given problem is considered, and a criterion is established which states whether a basic feasible solution of the former corresponds to one of the latter.