Solving Bertolami's equations for Brans-Dicke cosmological models

Solutions are developed for Berman and Som's formulation of Bertolami's equations for a Brans-Dicke cosmology with time-dependent cosmological term. Physical constraints are applied to these solutions to deduce conditions necessary for constructing plausible cosmological models in this theory.     

Self-adjunctions and matrices

It is shown that the multiplicative monoids of Temperley-Lieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronecker product of matrices. This self-adjunction underlies the orthogonal group case of Brauer's representation of the Brauer centralizer algebras.     

Concurrent restructuring and oxidation of the surface of n-hexane plasma polymers during aging in air

Angle-dependent XPS and air/water contact angle (CA) measurements were performed on specimens of n-hexane plasma polymers at various times after fabrication in order to monitor the aging of the surfaces in contact with air. XPS revealed incorporation of oxygen over extended periods of time. The depth distribution of O changed in the course of aging. CAs decreased over the first 3 weeks, then increased again, and finally stabilized at 5 weeks. These results were interpreted in terms of two concurrent processes: spontaneous oxidation (initiated by trapped radicals), which increased the surface polarity, and surface restructuring, which caused the partial removal of polar groups from the interface with air. The former process made a larger contribution to the overall aging of the surfaces but the latter process also contributed measurably. Over the first 3 weeks, oxidation was rapid and surface restructuring was not competitive. Subsequently, the oxygen uptake slowed down markedly, and the outermost surface layers became oxygen depleted relative to the deeper layers, due to partial surface reorientation. The surface topography, assessed by STM, did not change on aging. The aging of n-hexane plasma polymer surfaces thus is due to superimposed effects arising from post-deposition oxidative processes and partial surface reorientation.     

Sub-Coulomb deuteron break-up and the neutron-nucleus interaction

Low-energy deuteron break-up on heavy nuclei is treated paying special attention to the neutron-nucleus interaction. The neutron-nucleus elastic scattering phase shift, the only quantity through which the neutron-nucleus interaction enters into our calculations, is split into an energy-averaged part described by the optical model and a fluctuating part. Some calculations are given in order to illustrate the effects of the neutron-nucleus interaction, along with a comparison with recent experimental results, which shows very good agreement.     

Analysis of electrophoretic patterns of arbitrarily primed PCR profiling

We present a mathematical algorithm for the analysis of electrophoretic patterns resulting from arbitrarily primed PCR profiling. The algorithm is based on the established mathematical procedures applied to the analysis of digital images of gel patterns. The algorithm includes (a) transformation of the image into a matrix form, (b) identification of every electrophoretic lane as a set of matrix columns that are further mathematically processed, (c) averaging of matrix columns corresponding to electrophoretic lanes that define lane representatives, (d) elimination of "smiling" bands, (e) solving the problem of a lane offset, and (f) removal of the background. Representation of individual electrophoretic lanes in the form of functions allows interlane comparisons and further mathematical analysis. Direct comparison of selected lanes was obtained by employing correlation analysis. Gel images were those obtained after arbitrarily primed PCR analysis of DNA that underwent damage induced by gamma radiation from a (60)Co source. The applied method proved to be useful for elimination of subjectivity of visual inspection. It offers the possibility to avoid overlooking important differences in case of suboptimal electrophoretic resolution. In addition, higher precision is achieved in the assessment of quantitative differences due to better insight into experimental artifacts. These simple mathematical methods offer an open-type algorithm, i.e., this algorithm enables easy implementation of different parameters that may be useful for other analytical needs.     

Spike detection using the continuous wavelet transform

This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution.     

Influence of alkali metal cations upon the Kolbe-Schmitt reaction mechanism

The mechanisms of the carboxylations of lithium, potassium, rubidium, and cesium phenoxides are investigated by means of the DFT method with the LANL2DZ basis set. It is shown that the reactions of all alkali metal phenoxides with carbon dioxide occur via very similar reaction mechanisms. The reactions can proceed in the ortho and para positions. The exception is lithium phenoxide which yields only salicylic acid in the Kolbe-Schmitt reaction. It is found that the yield of the para substituted product increases with increasing the ionic radius of the alkali metal used. An explanation for this experimental and theoretical observation is proposed.     

A fixed point theorem of Jungck in $$b_v(s)$$-metric spaces

In this paper, we prove the common fixed point theorem of Jungck in \(b_v(s)\)-metric spaces. As a corollary, a common fixed point theorem in the rectangular b-metric space and the well known common fixed point theorem in b-metric spaces are obtained.     

Surface states of titanium dioxide nanoparticles modified with enediol ligands

Control of surface states of titanium dioxide nanoparticles using 2-(3,4-dihydroxyphenyl)ethylamine (dopamine) and 3,4-dihydrophenylacetic acid, which act as ligands to the undercoordinated surface sites (carrier traps), is demonstrated by electrochemical techniques. The deepest traps were found to be most reactive and are selectively removed by the addition of the ligands which enhances the kinetics of electron accumulation in the film. Furthermore, a shift in the Fermi level to more positive potentials was detected for electrodes modified with the negatively charged ligand (3,4-dihydrophenylacetic acid) compared to that of electrodes modified with the positively charged ligand (dopamine). The presence of the negative charge on the ligand also contributed to the underpotential of hydrogen evolution on 3,4-dihydrophenylacetic acid-modified electrodes.