Automated antenna positioning algorithms for wireless fixed-access networks

This article addresses a real-life problem - obtaining communication links between multiple base station sites, by positioning a minimal set of fixed-access relay antenna sites on a given terrain. Reducing the number of relay antenna sites is considered critical due to substantial installation and maintenance costs. Despite the significant cost saved by eliminating even a single antenna site, an inefficient manual approach is employed due to the computational complexity of the problem. From the theoretical point of view we show that this problem is not only NP hard, but also does not have a constant approximation. In this paper we suggest several alternative automated heuristics, relying on terrain preprocessing to find educated potential points for positioning relay stations. A large-scale computer-based experiment consisting of approximately 7,000 different scenarios was conducted. The quality of alternative solutions was compared by isolating and displaying factors that were found to affect the standard deviation of the solutions supplied by the tested heuristics. The results of the simulation based experiments show that the saving potential increases when more base stations are needed to be interconnected. The designs of a human expert were compared to the automatically generated solutions for a small subset of the experiment scenarios. Our studies indicate that for small networks (e.g., connecting up to ten base stations), the results obtained by human experts are adequate although they rarely exceed the quality of automated alternatives. However, the process of obtaining these results in comparison to automated heuristics is longer. In addition, when more base station sites need to be interconnected, the human approach is easily outperformed by our heuristics, both in terms of better results (fewer antennas) and in significant shorter calculation times.     

A Liouville-type Theorem for Schrödinger Operators

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P ₁, such that a nonzero subsolution of a symmetric nonnegative operator P ₀ is a ground state. Particularly, if P _j : = ?Δ + V _j , for j = 0,1, are two nonnegative Schrödinger operators defined on \(\Omega\subseteq \mathbb{R}^d\) such that P ₁ is critical in Ω with a ground state φ, the function \(\psi\nleq 0\) is a subsolution of the equation P ₀ u = 0 in Ω and satisfies \(\psi_+\leq C\varphi\) in Ω, then P ₀ is critical in Ω and \(\psi\) is its ground state. In particular, \(\psi\) is (up to a multiplicative constant) the unique positive supersolution of the equation P ₀ u = 0 in Ω. Similar results hold for general symmetric operators, and also on Riemannian manifolds.     

A scale-dependent equation for solute transport in porous media

The governing equation describing solute transport in porous media is reformulated using standard volume averaging techniques. The alternative formulation is based on a modified definition of the deviation, which allows for variation of macroscopic velocity across the REV. The new equation contains additional scale-dependent terms which are functions of the size of the averaging volume (REV). This result indicates that the scale-dependent nature of the dispersion phenomenon is inherent even at the scale of the REV.     

A model for slug frequency during gas-liquid flow in horizontal and near horizontal pipes

Slug formation is an entry region phenomena. Waves form on a growing stratified film eventually blocking the gas to form a slug. The liquid level drops when the slug is swept away and the waves disappear. Then the film rebuilds its level in a time equal to the inverse frequency. The process is modelled and the results shown to be in agreement with experiment.     

Matrix problems in the determination of lithium by flameless (HGA) atomic-absorption spectrometry, and their solution

Flameless atomic-absorption analyses for Li in geological materials (limestones, carbonate-bearing cherts, calcium containing subsurface brines and sweet waters) result in low values, which may amount to less than 10% of the real lithium concentration in the sample. The observed signal decrease is caused by the reaction between gaseous Li and Cl and the consequent formation of LiCl (b.p. = 1325-1360 degrees ). The Cl vapour is produced by the dissociation of CaCl(2) molecules in the graphite-tube cavity. The interfering capacity of CaCl(2) is marked because of its survival in the graphite tube at temperatures above the boiling points of both LiCl and Li metal (= 1317 degrees ). Hydrochloric acid represses the Li signal in a similar manner but to a lesser extent because most of it is removed during the pre-atomizing drying and ashing stages. The addition of Ca(2+) to the analytical solution lowers the absorption signal only if chloride is present. This interference of Cl has been completely overcome by addition of sulphuric acid in moderate excess relative to the quantity of chloride present. The release from interference is in strict accord with the stoichiometry of the reaction: H(2)SO(4) + CaCl(2) --> 2HCl + CaSO(4). The same remedy overcomes Cl interference introduced by the presence of hydrochloric acid in the analytical solution. The addition of sulphuric acid itself has no effect on the intensity of the atomic-absorption signal of lithium. An analogous reaction with phosphoric acid takes place, but the Li signal is weaker and less reproducible. Solutions in which the Na/Li ratio exceeds 3 x 10(4) cannot be analysed for Li by the method described since a molecular sodium peak is superimposed on the major Li peak.     

Kitungolides A, B, and C, new diterpenes from a soft coral of a new genus

Three novel compounds, designated kitungolides A (1), B (2), and C (3), were isolated from a soft coral of a new genus collected at Kitungamwe, Kenya. The three new compounds are of a unique heterotricyclic skeleton. The structures and relative stereochemistry of the compounds were elucidated by interpretation of MS, COSY, HMQC, HMBC, and NOESY experiments. [structure: see text]     

Callynormine A, a new marine cyclic peptide of a novel class

[structure: see text] A novel cyclic peptide, callynormine A, was isolated from the Kenyan marine sponge Callyspongia abnormis and its structure elucidated by interpretation of its NMR data and X-ray diffraction analysis. Callynormine A represents a new class of heterodetic cyclic peptides (designated endiamino peptides) possessing an alpha-amido-beta-aminoacrylamide cyclization functionality.     

Novel electronic transitions within excited doublets of dimers

We consider the electronic transition between the split components of the excited electronic doublet of a dimer species when the monomer species have permanent dipole moments. We show that the transition moment is given in terms of the permanent dipole moments of the ground and excited states of the monomers. Extension to ionic dimers and transitions between exciton bands in molecular crystals are suggested.     

Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity

The paper establishes a substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s. New results in the structure theory of totally disconnected groups are established along the way and are of independent interest. Other ideas in the argument motivate a sweeping conjecture, presented in the last section of the paper, which naturally unifies in an adelic setting deep results and fundamental conjectures in the rigidity theory of arithmetic groups.