A new first-principles approach for the catenary

This paper reports on findings relating to catenaries since the publication in Expositiones Mathematicae of Denzler and Hinz’s pioneering 1999 paper, Catenaria Vera – the True Catenary. New governing differential equations and explicit solutions are derived for the catenary in positive and negative radial potentials with physical constants incorporated in the derivations. In keeping with precedent by Denzler and Hinz, a measure of historical perspective is offered as homage to Gottfried Wilhelm Leibniz, Christiaan Huygens and Johann Bernoulli, the original first-solvers of the catenary.     

Estimating the Positive and Negative Jumps of Asset Returns Via Kalman Filtering. The Case of Nasdaq Index

The daily asset (log) return is considered to consist of two parts, the positive and negative jump. These jumps are determined by the arrival of positive and negative news in the market, are not observable and their differences define the asset returns. In order to estimate the jumps, the basic discrete time-homogeneous linear Kalman filter is applied, in which all the noises are assumed to be normally distributed. Then, under the assumption that the estimated jumps have to be non-negative, the method of their pdfs’ truncation, according to the non-negativity constraints, is used, and it is accompanied by appropriate scaling. The fitting of the model is justified by examining the fitting of the estimated returns to the empirical ones. For that purpose, the daily Nasdaq returns during the three year period 2006-2008 are used.     

Lattice tolerances and congruences

We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.     

Recent Progress on Electrode Design for Efficient Electrochemical Valorisation of CO2, O2, and N2

CO₂ reduction, two-electron O₂ reduction, and N₂ reduction are sustainable technologies to valorise common molecules. Their further development requires working electrode design to promote the multistep electrochemical processes from gas reactants to value-added products at the device level. This review proposes critical features of a desirable electrode based on the fundamental electrochemical processes and the development of scalable devices. A detailed discussion is made to approach such a desirable electrode, addressing the recent progress on critical electrode components, assembly strategies, and reaction interface engineering. Further, we highlight the electrode design tailored to reaction properties (e.g., its thermodynamics and kinetics) for performance optimisation. Finally, the opportunities and remaining challenges are presented, providing a framework for rational electrode design to push these gas reduction reactions towards an improved technology readiness level (TRL).     

Ion recognition by 1,2,3-triazole moieties synthesized via “click chemistry”

1,2,3-Triazole-based ligands obtained through copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC) have been exploited in vast array of research domains owing to the stitching of simpler molecules through a needle of Cu(I) catalyst. The numerous reports on ion(s) detection capabilities of synthesized 1,4-disubstituted 1,2,3-triazole ligands using absorption and fluorescence spectroscopy are accessible. This review enlists substituted 1,2,3-triazole-based sensor probes, since 2010, synthesized selectively by CuAAC, having the ability to sense either a single ion or multiple ions under specific set of conditions along with their detection limits. The review also apprehends the different techniques and sensing mechanisms involved in the detection of ions by chemosensor probes.     

Stochastic matrices over cones

The notion of a stochastic operator in an ordered Banach space is specialized to a finite dimensional ordered real vector space. The classical limit theorems are obtained, and an application is made to non-homogeneous Markov chains. Finally, groups of nonnegative matrices are discussed.     

Propagation of waves from spherical and cylindrical cavities

Résumé L'auteur examine la propagation des ondes d'une cavité sphérique ou cylindrique dans une substance avec une isotropie transversale et curviligne. Il traite d'une manière assez détaillée le cas particulier d'un solide infini dans lequel existe un trou sphérique ou cylindrique, et les résultats numériques sont donnés sous une forme graphique pour le trou cylindrique avec un démarrage à fonction type unitaire.     

Large molecular aggregates: From atmospheric aerosols to drug nanoparticles

Large molecular aggregates with sizes ranging from subnanometers to microns are ubiquitous. As atmospheric aerosols they influence our climate, in interstellar space they are discussed as reactive sites, and in medicine small particles are considered as promising candidates to achieve a targeted drug delivery. The present contribution is focused on the characterization of the physical-chemical properties of these particles and on their targeted generation. One of the greatest challenges is to understand the properties of these aggregates on a molecular level. The latter point is discussed in detail focussing on the vibrational dynamics of these particles.     

On-resin native chemical ligation for cyclic peptide synthesis

A novel cysteine derivative, N(alpha)-trityl-S-(9H-xanthen-9-yl)-l-cysteine [Trt-Cys(Xan)-OH] has been introduced for peptide synthesis, specifically for application to a new strategy for the preparation of cyclic peptides. The following steps were carried out to synthesize the cyclic model peptide cyclo(Cys-Thr-Abu-Gly-Gly-Ala-Arg-Pro-Asp-Phe): (i). side-chain anchoring of Fmoc-Asp-OAl via its free beta-carboxyl as a p-alkoxybenzyl ester to a solid support; (ii). stepwise chain elongation of the peptide by standard Fmoc/tBu solid-phase chemistry; (iii). removal of the N-terminal Fmoc group; (iv). coupling of Trt-Cys(Xan)-OH; (v). selective Pd(0)-promoted cleavage of the C-terminal allyl ester; (vi). coupling of the C-terminal residue, i.e., H-Phe-SBzl, preactivated as a thioester; (vii). selective removal of the N(alpha)-Trt and S-Xan protecting groups under very mild acid conditions; (viii). on-resin cyclization by native chemical ligation in an aqueous milieu; and (ix). final acidolytic cleavage of the cyclic peptide from the resin. The strategy was evaluated for three supports: poly[N,N-dimethacrylamide-co-poly(ethylene glycol)] (PEGA), cross-linked ethoxylate acrylate resin (CLEAR), and poly(ethylene glycol)-polystyrene (PEG-PS) graft resin supports. For PEGA and CLEAR, the desired cyclic product was obtained in 76-86% overall yield with initial purities of approximately 70%, whereas for PEG-PS (which does not swell nearly as well in water), results were inferior. Solid-phase native chemical ligation/cyclization methodology appears to have advantages of convenience and specificity, which make it promising for further generalization.