Equivalence of inverse Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter

Three inverse problems for a Sturm-Liouville boundary value problem −y″+qy=λy, y(0)cosα=y′(0)sinα and y′(1)=f(λ)y(1) are considered for rational f. It is shown that the Weyl m-function uniquely determines α, f, and q, and is in turn uniquely determined by either two spectra from different values of α or by the Prüfer angle. For this it is necessary to produce direct results, of independent interest, on asymptotics and oscillation.     

Construction of best Bregman approximations in reflexive Banach spaces

An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.

     

Photothermal microanalysis of thermal discontinuities in metallic samples

Modeling the behavior of a protective coating during a thermal shock not only requires the knowledge of its own thermophysical characteristics, but also those of the coating–substrate discontinuity. According to its nature, this discontinuity can be modeled as a zero-thickness interface (thermal contact resistance) or a finite thickness layer (thermal third body). This paper presents an experimental device and two associated thermal transfer models developed in view of the microscale characterization of such discontinuities.     

A Reality Proof in PT-Symmetric Quantum Mechanics

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral equivalences inspired by the correspondence are also discussed.     

Tabu search applied to the general fixed charge problem

Recent successes in applying tabu search to a wide variety of classical optimization problems have motivated the investigation of applying tabu search to the well-known general fixed charge problem (GFCP). In this paper, an adaptation of tabu search to GFCP is described and computational results are given. In addition, the computational results are compared with those obtained from SWIFT-2, the most well-known and frequently used heuristic method for GFCP. As will be shown, the results are very encouraging.     

Effect of stoichiometry on liquid crystalline supramolecular polymers formed with complementary nucleobase pair interactions

We report herein studies on the liquid crystalline behavior of a series of supramolecular materials that contain different ratios of two complementary symmetrically-substituted alkoxy-bis(phenylethynyl)benzene AA- and BB-type monomers. One monomer has thymine units placed at either end of the rigid mesogenic core, while the other has N⁶-(4-methoxybenzoyl)-adenine units placed on the ends. Differential scanning calorimetric and polarized optical microscopy studies have been carried out on these systems. These studies show that the material's behavior is strongly dependent on its thermal history. As a result, the materials can exhibit, on heating, either a liquid crystalline phase, a crystalline phase, or the coexistence of crystalline and liquid crystalline regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5049–5059, 2006     

Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]     

Action of photoreactivating light on pyrimidine heteroadduct in bacteria

Abstract— In stationary-phase Escherichia coli B/r, photoreactivation (PR) at 313 nm of ultraviolet (u.v.) killing is inefficient compared with PR at 405 nm, and can be explained solely by photoenzymatic reversal of pyrimidine dimers. In Staphylococcus epidermidis, PR shows a maximum at 313 nm, suggesting that this organism shows the Type III PR proposed by Jagger et al.[5] for Streptomyces strains. Reversal of pyrimidine dimers is not sufficient to explain this PR. The mechanism of Type III PR remains unknown. With both S. epidermidis and E. coli B/r, the amount of uracil–thymine heteroadduct in DNA hydrolysates decreases if the cells are given a post-u.v. treatment at 313 nm, but no decrease is observed if the post-u.v. treatment is at 405 nm. The biological significance of this adduct and of its removal is not clear. It may play a role in Type III PR.     

THE EFFECTS OF HOST-CELL REACTIVATION ON ASSAY OF U.V.-IRRADIATED HAEMOPHILUS INFLUENZAE TRANSFORMING DNA

Abstract— The host cell reactivation (HCR) mechanism in Haemophilus influenzae cells is inhibited by sub-microgram concentrations of acriflavine (as is already known to be true for Escherichia coli ). Exposure of these cells to similar concentrations of the drug during bacterial transformation increases the apparent ultraviolet light (u.v.) sensitivity of previously irradiated transforming DNA, indicating a repair of this DNA after uptake by the cells under normal conditions. Repair is inhibited by applying acriflavine at any time up to one hour after competent cells contact the irradiated transforming DNA. The fraction of the u.v. damage repaired by HCR is very different for different genetic markers. Those markers which are most u.v. sensitive when assayed in the absence of acriflavine are most poorly repaired, suggesting that this is the reason for their higher sensitivity. For all markers the fraction of the damage repairable by in vitro photoreactivation is approximately constant, and strongly overlaps the damage repairable by HCR. The degree of HCR achieved can be altered by experimental treatment of the H. influenzae DNA prior to transformation. Thus treatment of irradiated DNA with an enzyme from Micrococcus lysodeikticus –known to attack u.v. damaged, but not undamaged DNA–prevents subsequent intracellular repair of the same u.v. lesions whose repair is inhibited by acriflavine. Similarly, partial replacement of the thymine in transforming DNA by 5-bromouracil (BU) strongly inhibits repair of subsequent u.v. damage. As in bacteriophage, the BU effect is relieved if the u.v. exposure occurs in the presence of cysteamine. It is clear that intracellular repair must be considered in interpreting experiments with u.v.-irradiated transforming DNA.     

Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Probability densities that are not uniquely determined by their moments are said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison with standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.