Hydrothermal reactions of simple molecules by real-time infrared spectroscopy

Abstract

The relative roles of the materials of construction of the reactor (stainless steel or titanium) and the effects of Group 1 cations are discussed in terms of their effect on the rate of decarboxylation of acetic acid derivatives, RCO₂H. Past work indicates that the reaction container composition has a very large effect when R is CH3—. A smaller but significant effect is seen when R is electron neutral (i.e., R=H). When R is electron Withdrawing the rate depends less on the reactor type than the nature of R. The effect of the counter ion M on the rate of decarboxylation of monovalent malonate salts, HC&CHzC02M, is discussed for M=Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺. The rate generally increases with the ionic radius except that the Rb⁺ salt exhibits the fastest rate. Preliminary explanations are given.     

Discrete approximations to real-valued leaf sequencing problems in radiation therapy

For a given m×n nonnegative real matrix A, a segmentation with 1-norm relative error e is a set of pairs (α,S)={(α₁,S₁),(α₂,S₂),…,(α_k,S_k)}, where each α_i is a positive number and S_i is an m×n binary matrix, and , where |A|₁ is the 1-norm of a vector which consists of all the entries of the matrix A. In certain radiation therapy applications, given A and positive scalars γ,δ, we consider the optimization problem of finding a segmentation (α,S) that minimizes subject to certain constraints on S_i. This problem poses a major challenge in preparing a clinically acceptable treatment plan for Intensity Modulated Radiation Therapy (IMRT) and is known to be NP-hard. Known discrete IMRT algorithms use alternative objectives for this problem and an L-level entrywise approximation (i.e. each entry in A is approximated by the closest entry in a set of L equally-spaced integers), and produce a segmentation that satisfies . In this paper we present two algorithms that focus on the original non-discretized intensity matrix and consider measures of delivery quality and complexity (∑α_i+γk) as well as approximation error e. The first algorithm uses a set partitioning approach to approximate A by a matrix that leads to segmentations with smaller k for a given e. The second algorithm uses a constrained least square approach to post-process a segmentation of to replace with real-valued α_i in order to reduce k and e.     

On incidence structures of nonsingular points and hyperbolic lines of ovoids in finite orthogonal spaces

We study the point-line incidence structures of nonsingular points and hyperbolic secant lines associated with ovoids in finite orthogonal spaces. We show that these incidence structures frequently produce partial linear spaces and the parameters of the bipartite graphs (called ovoidal graphs) associated with these structures produce simple and effective isomorphism invariants to distinguish non-isomorphic ovoids. We prove explicit formulas for these isomorphism invariants for a number of infinite families of 2-transitive ovoids.