Sturm-Liouville Estimates for the Spectrum and Cheeger Constant

Buser's inequality gives an upper bound on the first non-zero eigenvalue of the Laplacian of a closed manifold M in terms of the Cheeger constant h(M). Agol later gave a quantitative improvement of Buser's inequality. Agol's result is less transparent since it is given implicitly by a set of equations, one of which is a differential equation Agol could not solve except when M is three-dimensional. We show that a substitution transforms Agol's differential equation into the Riemann differential equation. Then, we give a proof of Agol's result and also generalize it using Sturm-Liouville theory. Under the same assumptions on M, we are able to give upper bounds on the higher eigenvalues of M, \lambda_k(M), in terms of the eigenvalues of a Sturm-Liouville problem which depends on h(M). We then compare the Weyl asymptotic of \lambda_k(M) given by the works of Cheng, Gromov, and B\'erard-Besson-Gallot to the asymptotics of our Sturm-Liouville problems given by Atkinson-Mingarelli.Comment: 41 pages, 7 figures. Answered the question from v1 in the negative; see Example 1.5. Some changes in numbering conventions of equations and examples to avoid confusion that occurred in v1. Improvements to the writing of the proof of Proposition 2.1. Lemma 3.5 now references the slicing lemma, which was omitted in v1. Some typos were fixed and references added from v

Inhibition and nucleic acid binding studies of the carboxyltransferase component of bacterial acetyl-CoA carboxylase

Acetyl-CoA carboxylase is an essential enzyme, as it catalyzes the first committed and regulated step in fatty-acid biosynthesis in all organisms excepting few Archaea and Eubacteria. Acetyl-CoA carboxylase from gram-negative and gram-positive bacteria is a multifunctional enzyme composed of three separate proteins. The carboxyltransferase subunit catalyzes the transfer of a carboxyl group from carboxybiotin to acetyl-CoA, forming malonyl-CoA. The crystal structure of the Escherichia coli (E. coli) carboxyltransferase component of acetyl-CoA carboxylase revealed a unique Zn-domain, presumed to mediate nucleic acid binding, that is absent in the eukaryotic enzyme. Notably, the Zn-domain, adjacent to the active site of carboxyltransferase, makes for a unique target in the development of novel antibiotics capable of highly specific binding. Utilizing an Electrophoretic Mobility Shift Assay as part of this study, we investigated the nonspecific nucleic-acid binding and substrate (malonyl-CoA and biocytin) inhibition of DNA:carboxyltransferase complex formation. Inhibition of carboxyltransferase activity by single-stranded DNA, double-stranded DNA, RNA, and heparin was measured in the reverse direction with a spectrophotometric assay in which the production of acetyl-CoA was coupled with the combined citrate synthase-malate dehydrogenase reaction requiring NAD+ reduction (Blanchard and Waldrop, 1998). NADH formation was followed spectrophotometrically at 340 nm. We then determined and characterized the mechanism of inhibition by tetracycline (and derivatives) on carboxyltransferase from E. coli and Staphylococcus aureus. The tetracyclines are broad-spectrum antibiotics that inhibit translation by binding to the 30S ribosomal subunit and preventing the binding of the acylated-tRNA to the A-site. Tetracycline exhibited competitive inhibition with respect to both malonyl-CoA and biocytin. Multiple inhibition analyses with a bisubstrate analog showed that tetracycline and the substrates can bind to the enzyme simultaneously. Surprisingly, tetracycline did not interfere with the DNA-binding properties of carboxyltransferase. This introduction begins with a historical perspective of carboxylation reactions. Next biotin and the structure, function and practical applications of acetyl-CoA carboxylase are described. Subsequently a review of moonlighting enzymes, or those capable of catalyzing reactions in basic metabolism while acting as regulators of gene expression, is provided, as are the functions and structures of several types of zinc finger

Methods development for total organic carbon accountability

This report describes the efforts completed during the contract period beginning November 1, 1990 and ending April 30, 1991. Samples of product hygiene and potable water from WRT 3A were supplied by NASA/MSFC prior to contract award on July 24, 1990. Humidity condensate samples were supplied on August 3, 1990. During the course of this contract chemical analyses were performed on these samples to qualitatively determine specific components comprising, the measured organic carbon concentration. In addition, these samples and known standard solutions were used to identify and develop methodology useful to future comprehensive characterization of similar samples. Standard analyses including pH, conductivity, and total organic carbon (TOC) were conducted. Colorimetric and enzyme linked assays for total protein, bile acid, B-hydroxybutyric acid, methylene blue active substances (MBAS), urea nitrogen, ammonia, and glucose were also performed. Gas chromatographic procedures for non-volatile fatty acids and EPA priority pollutants were also performed. Liquid chromatography was used to screen for non-volatile, water soluble compounds not amenable to GC techniques. Methods development efforts were initiated to separate and quantitate certain chemical classes not classically analyzed in water and wastewater samples. These included carbohydrates, organic acids, and amino acids. Finally, efforts were initiated to identify useful concentration techniques to enhance detection limits and recovery of non-volatile, water soluble compounds

The Structure of a Bernoulli Process Variation of the Fibonacci Sequence

We consider the structure of a variation of the Fibonacci sequence which is determined by a Bernoulli process. The associated structure of all Bernoulli variations of the Fibonacci sequence can be represented by a directed binary tree, which we denote X, with vertex labels representing the specific state of the recurrence variation. Since X is a binary tree, we can consider the term of a sequence variation given by a finite traversal of X represented by a binary code t. We then prove that the traversal of X that is the reflection of the digits of t gives exactly the integer term corresponding to t. We consider how to further this result with the statement of an additional conjecture. Finally, we give connections to Fibonacci expansions, the Stern-Brocot tree, and we apply our methods to the Three Hat Problem as seen in ``Puzzle Corner'' of the ``Technology Review'' magazine.Comment: 22 pages, 1 figur

Torsion and ground state maxima: close but not the same

Could the location of the maximum point for a positive solution of a semilinear Poisson equation on a convex domain be independent of the form of the nonlinearity? Cima and Derrick found certain evidence for this surprising conjecture. We construct counterexamples on the half-disk, by working with the torsion function and first Dirichlet eigenfunction. On an isosceles right triangle the conjecture fails again. Yet the conjecture has merit, since the maxima of the torsion function and eigenfunction are unexpectedly close together. It is an open problem to quantify this closeness in terms of the domain and the nonlinearity

Spectroscopy and multivariate analyses applications related to solid rocket nozzle bondline

Chemical composition and molecular orientation define the properties of materials. Information related to chemical composition and molecular configuration is obtained by various forms of spectroscopy. Software algorithms developed for multivariate analyses, expert systems, and Artificial Intelligence (AI) are used to conduct repetitive operations. The techniques are believed to be of particular significance toward achieving TQM objectives. The objective was to obtain information related to the quality of the bondline in the solid rocket motor, SRM, nozzle. Hysol 934 NA, a room temperature curing epoxide resin, is used as the bonding agent. A good bond requires that the adhesive be placed on a properly prepared metal surface, the adhesives Part A and B be mixed in appropriate ratio from material within shelf life specifications. Spectroscopic data was obtained for surfaces prepared according to specifications, contaminated metal surfaces, samples of the epoxide adhesive at times that represent shelf aging from 3 months to 2 years, several mix ratio of A to B, and curing material. Temperature was found to be a significant factor. The study concentrated on pot life and mix ratio

Server-based and server-less BYOD solutions to support electronic learning

Over the past 10 years, bring your own device has become an emerging practice across the commercial landscape and has empowered employees to conduct work-related business from the comfort of their own phone, tablet, or other personal electronic device. Currently in the Department of Defense, and specifically the Department of the Navy, no viable solution exists for the delivery of eLearning content to a service member's personal device that satisfy existing policies. The purpose of this thesis is to explore two potential solutions: a server-based method and a server-less method, both of which would allow Marines and Sailors to access eLearning course material by way of their personal devices. This thesis will test the feasibility and functionality of our server-based and server-less solutions by implementing a basic proof of concept for each. The intent is to provide a baseline from which further research and development can be conducted, and to demonstrate how these solutions present a low-risk environment that preserves government network security while still serving as a professional military education force multiplier. Both solutions, while demonstrated with limited prototypes, have the potential to finally introduce bring your own device into the Department of the Navy's eLearning realm.http://archive.org/details/serverbasedndser1094549343Captain, United States Marine CorpsCaptain, United States Marine CorpsApproved for public release; distribution is unlimited