Geometry of Coadjoint Orbits and Multiplicity-one Branching Laws for Symmetric Pairs

Consider the restriction of an irreducible unitary representation π of a Lie group G to its subgroup H. Kirillov’s revolutionary idea on the orbit method suggests that the multiplicity of an irreducible H-module ν occurring in the restriction π|_H could be read from the coadjoint action of H on \(\mathcal {O}^{G} \cap \text {pr}^{-1}({\mathcal {O}}^{H})\), provided π and ν are ‘geometric quantizations’ of a G-coadjoint orbit \(\mathcal {O}^{G}\) and an H-coadjoint orbit \(\mathcal {O}^{H}\), respectively, where \(\text {pr} \colon \sqrt {-1}\mathfrak {g}^{\ast } \to \sqrt {-1}\mathfrak {h}^{\ast }\) is the projection dual to the inclusion \(\mathfrak {h} \subset \mathfrak {g}\) of Lie algebras. Such results were previously established by Kirillov, Corwin and Greenleaf for nilpotent Lie groups. In this article, we highlight specific elliptic orbits \(\mathcal {O}^{G}\) of a semisimple Lie group G corresponding to highest weight modules of scalar type. We prove that the Corwin–Greenleaf number \(\sharp (\mathcal {O}^{G} \cap \text {pr}^{-1}({\mathcal {O}}^{H}))/H\) is either zero or one for any H-coadjoint orbit \(\mathcal {O}^{H}\), whenever (G,H) is a symmetric pair of holomorphic type. Furthermore, we determine the coadjoint orbits \(\mathcal {O}^{H}\) with nonzero Corwin–Greenleaf number. Our results coincide with the prediction of the orbit philosophy, and can be seen as ‘classical limits’ of the multiplicity-free branching laws of holomorphic discrete series representations (Kobayashi [Progr. Math. 2007]).     

Essential Spectra, Matrix Operator and Applications

This paper gives a survey on some recent results on the spectral theory of block operator matrices. We study the closeness in the product space and we give some conditions to characterize the essential spectra in the Browder resolvent set case. Furthermore, we apply the obtained results to several models such as delay equations, Sturm–Liouville problem and transport equations.     

Facile one-pot synthesis,butyrylcholinesterase and α-glucosidase inhibitory activities,structure–activity relationship,molecular docking and DNA–drug binding analysis of Meldrum’s acid derivatives

Research on Chemical Intermediates - Meldrum’s acid derivatives were facile synthesized by one-pot condensation process and characterized by NMR (1H, 13C, DEPT-90 and DEPT-135) and EI-MS. The...     

An eco-friendly multi-analyte high-performance thin layer chromatographic densitometric determination of amoxicillin,metronidazole, and famotidine in their ternary mixtures and simulated gastric juice: A promising protocol for eradicating Helicobacter pylori

Gastrointestinal tract disorders constitute a heavy burden to healthcare providers. To eradicate Helicobacter pylori infection, different triple therapy protocols have been proposed. Among which are combinations of proton pump inhibitors (e.g., omeprazole), histamine-2 receptor antagonists (e.g., famotidine), along with antibiotics (e.g., amoxicillin). In this work, a sensitive and accurate high-performance thin-layer chromatographic method was developed for the simultaneous determination of amoxicillin, metronidazole, and famotidine in bulk powder and laboratory-prepared combined-tablet mixtures. Complete separation of the cited compounds was achieved using pre-coated silica gel plates with a mixture of methanol:chloroform:toluene:water:glacial acetic acid (5:2:1.5:0.5:0.1 v/v/v/v/v) as the mobile phase. The method was fully validated as per the international conference of harmonization guidelines. Good linearity, a correlation coefficient of 0.9991, was obtained in the concentration ranges 0.1–1.6 μg/band (amoxicillin), 0.1–0.9 μg/band (metronidazole), and 0.1–0.9 μg/band (famotidine). Since the method allowed the determination of the three compounds in combined tablets with a high degree of selectivity, accuracy, precision, with cost-effectiveness, it could be used for regular quality control. Moreover, the applicability of the proposed method was extended to the determination of the ternary mixture in simulated gastric juice. Method greenness was assessed using different green metrics.     

Intramolecular Path Determination of Active Electrons on Push-Pull Oligocarbazole Dyes-Sensitized Solar Cells

Several push-pull oligocarbazole dye-sensitizers have been studied using theoretical methods in order to better understand the relationship between structural electronic or optical properties and intramolecular path of active electrons during the ionization and injection processes. DFT/TD-DFT calculations were performed on a series of five dye sensitizers. They differ by the presence of electron donating group (EDG) by inductive effect (noted+I) or electron releasing group (ERG) by mesomeric effect (noted+M) or electron withdrawing group by inductive effect (noted-I) on the pushed part of the dyes studied. Our work focused on the internal distribution of electrons in the different parts of dye that are the push/pull moieties and the π -bridge. The study concerned the ground state, the electronic transition process and the excited state. In each situation, the fragment acting in the ionization or transition phenomena were identified. In the ground state, the electrons of the push part appear to be the least bound because they have the highest probabilities of ionization. In the excited state, the ionized atoms are essentially positioned in the pushing part and some neighboring atoms of the bridge. In the electronic transition, the active atoms are located in the π -conjugated part but only on the side adjacent to the acceptor group. To arrive to this conclusion, we optimized the structures of the five dyes in their ground and excited states. We calculated the atomic charges, the wavelengths and intensities of electronic transitions in the visible domain, the reorganization energies as well as the oxidation potential. It appears that +M donor ligands improve the performance of a dye because the great distribution of atoms to be ionized in the push parts.     

High-performance liquid chromatography determination of nitrated polycyclic aromatic hydrocarbons by indirect fluorescence detection

A high-performance liquid chromatography (HPLC) method for the analysis of nitrated polcyclic aromatic hydrocarbons (NPAHs) is reported. NPAH mixtures were pre-concentrated using solid-phase extraction and well resolved on a C(18) column. They were detected using an indirect method involving the quenching of the emission from the fluorophores 5,6,7,8-tetrahydronaphthol (5,6,7,8-THN-1-OH), 7-amino-4-methyl coumarin (Coumarin 120, COU-120) and 3-hydroxy-4-(2-hydroxy-4-sulfo-1-naphthylazo)2-naphthalene carboxylic acid (Calcon carboxylic acid, CCA). Linear calibration curves were obtained in the range 1.1 x 10(-9) to 1.1 x 10(-8) mol/L. Using COU 120 as the fluorophore, the detection limit was 2.9 x 10(-10) mol/L for 1-nitronaphthalene and 2.1 x 10(-11) mol/L for 2-nitrofluorene. Recoveries of NPAHs from spiked tap water samples were between 88 and 100%.     

On dominance-based multiobjective local search: design, implementation and experimental analysis on scheduling and traveling salesman problems

This paper discusses simple local search approaches for approximating the efficient set of multiobjective combinatorial optimization problems. We focus on algorithms defined by a neighborhood structure and a dominance relation that iteratively improve an archive of nondominated solutions. Such methods are referred to as dominance-based multiobjective local search. We first provide a concise overview of existing algorithms, and we propose a model trying to unify them through a fine-grained decomposition. The main problem-independent search components of dominance relation, solution selection, neighborhood exploration and archiving are largely discussed. Then, a number of state-of-the-art and original strategies are experimented on solving a permutation flowshop scheduling problem and a traveling salesman problem, both on a two- and a three-objective formulation. Experimental results and a statistical comparison are reported in the paper, and some directions for future research are highlighted.     

Thermal and hydrodynamic performance of a microchannel heat sink with carbon nanotube nanofluids

Journal of Thermal Analysis and Calorimetry - The method of evaluating the magnetocaloric effect (MCE) and heat capacity of various magnetic samples from calorimetric experiments are presented....