Constraint classification in mathematical programming

Consider a set of algebraic inequality constraints defining either an empty or a nonempty feasible region. It is known that each constraint can be classified as either absolutely strongly redundant, relatively strongly redundant, absolutely weakly redundant, relatively weakly redundant, or necessary. We show that is is worth making a distinction between weakly necessary constraints and strongly necessary constraints. We also present afeasible set cover method which can detect both weakly and strongly necessary constraints.The main interest in constraint classification is due to the advantages gained by the removal of redundant constraints. Since classification errors are likely to occur, we examine how the removal of a single constraint can affect the classification of the remaining constraints.     

A Distributed and Collaborative Beamforming algorithm for a self-organizing Wireless Sensor Network

In this paper the scenario where sensors of a Wireless Sensor Network (WSN) are able to process and transmit monitored data to a far collector is considered. The far collector may be a Base Station (BS) that gathers data from a certain number of deployed WSNs, in applications such as earthquake, tsunami, or pollution monitoring. In this paper, the possible use of Distributed and Collaborative BeaMForming (DC-BMF) technique is analyzed, with the goal of enhancing the capability of a single sensor to communicate its data to the far collector. This technique considers nodes as elements of a phased array, where the phases of the signals at each antenna node are linearly combined in order to adjust the directional gain of the whole array. In particular, a novel self-localization technique for WSNs performing DC-BMF is studied, a closed form solution for beamforming gain degradation is derived and the evaluation of the power consumption of the proposed DC-BMF algorithm is provided.     

Band gap of carbon-sulfur [N]helicenes

Asymmetric synthesis of (-)-[9]helicene, as well as preparation of its lower homologues, completes the series of carbon-sulfur [5]-, [7]-, [9]-, and [11]helicenes. Spectroscopic and electrochemical studies of this series provide an absorption onset-based band gap, E(g) = 3.40 eV, for a cross-conjugated (C(2)S)(n) helix; this value may be compared to E(g) = 3.59 eV obtained from TD-DFT computed excitation energies for a series of dimethyl-substituted [n]helicenes (n ≤ 31).     

Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution: II

In a previous publication (part I) it has been shown that for an arbitrary statistically isotropic and homogeneous medium the parabolic equation for the two-frequency mutual coherence function can be separated and thereby expressed as a superposition of modes. A parameterization based on the longitudinal part of this representation has also been treated. This paper explores the transverse structure and parameterization of the field solution by employing dimensional, variational and the modified WKB procedures for solving the eigenfunction/eigenvalue problem. General expressions are derived first for a general structure function and then specialized for a power-law structure function with emphasis on quadratic and Kolmogorov media.     

Qualitative Analyse

Ohne Zusammenfassung     

Generalized Dickson invariants

The action of the Steenrod Algebra on the Dickson invariants is studied in a certain ‘localized’ context. In this context one can define a completed version of the Steenrod Algebra which acts on the local Dickson invariants in a manner which extends the action of the Steenrod Algebra on the usual invariants. One can also construct an infinite Dickson Algebra which carries a left and a right action of the completed Steenrod Algebra and a nondegenerate bilinear form which makes those actions dual. Supported in part by the Alfred P. Sloan Foundation and the Edmund Landau Center for Research in Mathematical Analysis, sponsored by the Minerva Foundation (Germany).