The multicomponent discrete equation hierarchy with variable spectral parameters and a new integrable coupling system

This Letter reports on a study of the multicomponent discrete integrable equation hierarchy with variable spectral parameters. An instance of new multicomponent lattice equation is obtained. Correspondingly, a feasible way to construct the integrable couplings is presented. It indicates that the study of integrable couplings using the block matrix-form of Lie algebra is an important and effective method.     

Analysis of the pure-rotational spectrum in the ν28 = 1 excited torsional state and torsional couplings of trans-ethyl methyl ether

The trans-ethyl methyl ether molecule has three low-lying torsional modes, that is, two inequivalent methyl internal rotations and an asymmetric skeletal torsion. The internal rotations of the CCH₃ and OCH₃ methyl rotors and the skeletal torsion correspond to the vibrational modes, ν₂₈, ν₂₉ and ν₃₀ respectively. In this study, the microwave absorption spectrum in the ν₂₈ = 1 CCH₃ torsional state was analyzed for the first time. Nine hundred fifty seven lines up to J = 48 and K = 4 were assigned, and the rotational, centrifugal distortion and internal rotational tunneling parameters were determined with the use of a tunneling matrix formalism. By combining the present results on the ν₂₈ = 1 torsional state with those for the ν₃₀ = 1 skeletal torsional state and the ν₂₉ = 1 OCH₃ torsional state, torsional couplings are estimated in order to understand quantitatively the inverted A/E sequence patterns observed for those three excited torsional states.     

Demixing of severely overlapped H NMR resonances and interpretation of anomalous intensity pattern of dipolar coupled A3 spins in a weakly aligning medium

The increasing scientific and industrial interest towards metabonomics takes advantage from the high qualitative and quantitative information level of nuclear magnetic resonance (NMR) spectroscopy. However, several chemical and physical factors can affect the absolute and the relative position of an NMR signal and it is not always possible or desirable to eliminate these effects a priori. To remove misalignment of NMR signals a posteriori, several algorithms have been proposed in the literature. The icoshift program presented here is an open source and highly efficient program designed for solving signal alignment problems in metabonomic NMR data analysis. The icoshift algorithm is based on correlation shifting of spectral intervals and employs an FFT engine that aligns all spectra simultaneously. The algorithm is demonstrated to be faster than similar methods found in the literature making full-resolution alignment of large datasets feasible and thus avoiding down-sampling steps such as binning. The algorithm uses missing values as a filling alternative in order to avoid spectral artifacts at the segment boundaries. The algorithm is made open source and the Matlab code including documentation can be downloaded from www.models.life.ku.dk.     

Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures

We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra. Then its super Hamiltonian structure is furnished by super trace identity. As its reduction, we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.     

Non-linear couplings,from the early to the late time universe

Deciphering the mechanisms at play in the formation and evolution of the large-scale structure of the universe is part of the scientific goals of many projects of observational cosmology. In particular, large-scale structure observations can be used to infer mode-coupling effects, whether they come from the physics of the early universe or from its late time evolution. Specificities of such couplings are presented, noting that in principle they can be directly detected through bispectra of the cosmic microwave background temperature anisotropies or density in the local universe. The existence of such couplings have however more far-reaching consequences for the growth of the structure. Those are sketched as well as their possible observational impacts.     

Integrable Rosochatius Deformations for an Integrable Couplings of CKdV Equation Hierarchy

We propose a method to construct the integrable Rosochatius deformations for an integrable couplings equations hierarchy. As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy with self-consistent sources and its Lax representation are presented.     

Utilization of photocatalysts in decarboxylative coupling of carboxylic N-hydroxyphthalimide (NHPI) esters

Recently, the visible-light photoredox decarboxylative couplings of N-(acyloxy)phthalimides (NHPI esters) and its derivatives have become an efficient chemical transformation. Under visible light, the NHPI esters undergo a single-electron transfer (SET) process to afford the corresponding carbon or nitrogen radicals that participate in many chemical transformations. The photoredox decarboxylative couplings have been applied to achieve construction of an array of carbon–carbon and carbon–heteroatom bonds as well as the synthesis of carbocycles and heterocycles. This review categorises photocatalysts, discusses the application and catalysis mechanisms of NHPI esters, and details recent progress in this field.     

Metal‐Catalyzed Reductive Coupling Reactions of Organic Halides with Carbonyl‐Type Compounds

Metal‐catalyzed reductive coupling reactions of aryl halides and (pseudo)halides with carbonyl‐type compounds have undergone an impressive development within the last years. These methodologies have shown to be a powerful alternate strategy, practicality aside, to the use of stoichiometric, well‐defined, and, in some cases, air‐sensitive organometallic species. In this Minireview, the recent findings in this field are summarized, with particular emphasis on the mechanistic interpretation of the results and future aspects of this area of expertise.     

b→ssd decay in Randall-Sundrum models

The extremely small branching ratio of the b → ssd decay in the Standard Model makes it a suitable channel to explore new-physics signals.We study this ?S = 2 process in Randall-Sundrum models,including the custodially protected and the bulk-Higgs Randall-Sundrum models.Exploring the experimentally favored parameter spaces of these models suggests a possible enhancement of the decay rate,compared to the Standard Model result,by at most two orders of magnitude.