Localization from Incomplete Noisy Distance Measurements

We consider the problem of positioning a cloud of points in the Euclidean space ? ^d , using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and reconstruction of protein conformations from NMR measurements. It is also closely related to dimensionality reduction problems and manifold learning, where the goal is to learn the underlying global geometry of a data set using local (or partial) metric information. Here we propose a reconstruction algorithm based on semidefinite programming. For a random geometric graph model and uniformly bounded noise, we provide a precise characterization of the algorithm’s performance: in the noiseless case, we find a radius r ₀ beyond which the algorithm reconstructs the exact positions (up to rigid transformations). In the presence of noise, we obtain upper and lower bounds on the reconstruction error that match up to a factor that depends only on the dimension d, and the average degree of the nodes in the graph.     

A Characterization of Generalized Derivations on Prime Rings

Let R be a noncommutative prime ring, U be the left Utumi quotient ring of R, and k, m, n, r be fixed positive integers. If there exist a generalized derivation G and a derivation g (which is independent of G) of R such that [G(x^m)xⁿ + xⁿg(x^m), x^r]_k = 0, for all x ∈ R, then there exists a ∈ U such that G(x) = ax, for all x ∈ R. As a consequence of the result in the present article, one may obtain Theorem 1 in Demir and Argaç [10 Demir, Ç., Argaç, N. (2010). A result on generalized derivations with Engel conditions on one-sided ideals. J. Korean Math. Soc. 47(3):483–494.[Crossref], [Web of Science ®] , [Google Scholar]].     

On the Simplicity of the Lie Algebra of a Leavitt Path Algebra

For a field F and a row-finite directed graph Γ, let L(Γ) be the associated Leavitt path algebra. We find necessary and sufficient conditions for the Lie algebra [L(Γ), L(Γ)] to be simple.     

Finite difference approach to trigonometry

Two interrelated, finite difference and graph theoretic, approaches to trigonometry are developed by combining a generalization of the finite difference method first employed by Viète, with solution techniques, based on signal flow graphs, for finite difference equations with variable coefficients, and a scaling approach to trigonometry, based on the polygonometric identities.     

The generalized Gompertz distribution

This paper deals with a new generalization of the exponential, Gompertz, and generalized exponential distributions. This distribution is called the generalized Gompertz distribution (GGD). The main advantage of this new distribution is that it has increasing or constant or decreasing or bathtub curve failure rate depending upon the shape parameter. This property makes GGD is very useful in survival analysis. Some statistical properties such as moments, mode, and quantiles are derived. The failure rate function is also derived. The maximum likelihood estimators of the parameters are derived using a simulations study. Real data set is used to determine whether the GGD is better than other well-known distributions in modeling lifetime data or not.     

Can Anyon Statistics Explain High Temperature Superconductivity?

In this paper, we find a reasonable explanation of high temperature superconductivity phenomena using Anyon statistics.

     

Synthesis of Some Benzimidazole‐based Heterocycles and their Application as Copper Corrosion Inhibitors

A series of new substituted benzimidazoles embedded with a variety of function groups has been synthesized from N‐methyl‐2‐bromoacetylbenzimidazole. The synthesized compounds were fully characterized, and their structures were elucidated based on elemental analysis, spectral data, and alternative synthetic pathways, whenever possible. Some of benzimidazole derivatives were tested as corrosion inhibitors.     

Textural,structural and catalytic behavior of low specific area silica-supported copper catalysts: effect of preparation method

Supported copper catalysts on low surface area silica were prepared by several methods and characterized by AAS, XRD, N₂ adsorption, SEM, H₂-TPR, N₂O titration, TGA-DTA, UV–Vis techniques. Their hydrogenating properties were examined in the gas-phase hydrogenation of benzaldehyde. The analysis of characterization results revealed that the choice of preparation method affected the texture, composition, and structure of the calcined and reduced Cu/SiO₂ catalysts. The dispersion and size distribution of copper species was present in different forms in the catalysts that exhibited low specific surface areas. In gas-phase hydrogenation of benzaldehyde to benzyl alcohol, the catalysts tested at the reaction temperatures of 160 and 200 °C were stable and conducted to a good catalytic activity and benzyl alcohol selectivity ranging between 5 and 39 µmol min^?1 g^?1 and 0–95%, respectively. The activity of the catalysts in gas-phase hydrogenation also depended on the particle size and the nature of copper species formed on low surface area silica.