Adjoints of rationally induced composition operators

We give an elementary proof of a formula recently obtained by Hammond, Moorhouse, and Robbins for the adjoint of a rationally induced composition operator on the Hardy space H^2. We discuss some variants and implications of this formula, and use it to provide a sufficient condition for a rationally induced composition operator adjoint to be a compact perturbation of a weighted composition operator.Comment: 21 pages, Published Versio

Diagnostic and corrective measures in addition

This item was digitized by the Internet Archive. Thesis (Ed. M.)--Boston Universityhttps://archive.org/details/diagnosticcorrec00sol

Remedial program for 100% mastery of the four fundamental processes of arithmetic in grades five, six and eight.

Thesis (M.A.)--Boston Universit

A computational model of the line-1 retrotransposon life cycle and visualization of metabolic networks in 3-dimensions.

Computational modeling of metabolic reactions and cellular systems is evolving as a tool for quantitative prediction of metabolic parameters and reaction pathway analysis. In this work, the basics of computational cell biology are presented as well as a summary of physical processes within the cell, and the algorithmic methods used to find time dependent solutions. Protein-protein and enzyme-substrate interactions are mathematically represented via mass action kinetics to construct sets of linear differential equations that describe reaction rates and formation of protein complexes. Using mass action methods, examples of reaction networks and their solutions are presented within the Virtual Cell simulation package. A computational model capturing the life cycle of an ancient (typically dormant) parasitic genetic element called the long interspersed nuclear element type 1 (LINE-1) is developed and refined. When activated, the proteins encoded by LINE-1 function to produce copies of itself that are reinserted into the genome. Thus, activation of LINE-1 is associated with genomic instability, tumorigenesis, and cancer. The model tracks the copy number of LINE-1 associated proteins, mRNA, and DNA under conditions that simulate carcinogenic insults to the element’s epigenetic silencing mechanisms. Results show that proliferation of LINE-1 has a distinct threshold as a function of mRNA copy number and transcription rate. Above the threshold, the retrotransposon copy number enters a positive feedback loop that allows the cDNA copy number to grow exponentially. We also found that most of the LINE-1 RNA was degraded via the RNAase pathway and that neither ORF0 RNAi, nor the sequestration of LINE-1 products into granules and multivesicular structures, played a significant role in regulating the retrotransposon’s life cycle. Most systems in computational cell biology are represented as 2-dimensional graphs of nodes symbolizing reactions and chemical species. At even moderate complexity, however, these network maps become difficult to read and understand. Thus, a Python interface was developed which maps biological networks generated using the free Virtual Cell simulation package onto an impressive open source 3-D network visualization system called OpenGraphiti. By interfacing these two packages the software allows one to view reaction networks and solutions of simulations in a more intuitive way

Much Ado About Zero

41-43A look at how Indian ingenuity resulted in the invention of the ‘Zero’ and how the idea spread to other parts of the world gaining widespread acceptability