Tensor Gauge Fields in Arbitrary Representations of GL(D, ℝ). Duality and Poincaré Lemma

Using a mathematical framework which provides a generalization of the de Rham complex (well-designed for p-form gauge fields), we have studied the gauge structure and duality properties of theories for free gauge fields transforming in arbitrary irreducible representations of GL(D, ). We have proven a generalization of the Poincaré lemma which enables us to solve the above-mentioned problems in a systematic and unified way.     

Evaluation of standard and advanced preprocessing methods for the univariate analysis of blood serum 1H-NMR spectra

Proton nuclear magnetic resonance (¹H-NMR)-based metabolomics enables the high-resolution and high-throughput assessment of a broad spectrum of metabolites in biofluids. Despite the straightforward character of the experimental methodology, the analysis of spectral profiles is rather complex, particularly due to the requirement of numerous data preprocessing steps. Here, we evaluate how several of the most common preprocessing procedures affect the subsequent univariate analyses of blood serum spectra, with a particular focus on how the standard methods perform compared to more advanced examples. Carr–Purcell–Meiboom–Gill 1D ¹H spectra were obtained for 240 serum samples from healthy subjects of the Asklepios study. We studied the impact of different preprocessing steps—integral (standard method) and probabilistic quotient normalization; no, equidistant (standard), and adaptive-intelligent binning; mean (standard) and maximum bin intensity data summation—on the resonance intensities of three different types of metabolites: triglycerides, glucose, and creatinine. The effects were evaluated by correlating the differently preprocessed NMR data with the independently measured metabolite concentrations. The analyses revealed that the standard methods performed inferiorly and that a combination of probabilistic quotient normalization after adaptive-intelligent binning and maximum intensity variable definition yielded the best overall results (triglycerides, R = 0.98; glucose, R = 0.76; creatinine, R = 0.70). Therefore, at least in the case of serum metabolomics, these or equivalent methods should be preferred above the standard preprocessing methods, particularly for univariate analyses. Additional optimization of the normalization procedure might further improve the analyses.     

Symmetries and dynamics in constrained systems

We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total Hamiltonian systems. In particular, in analogy to total Hamiltonians, we introduce the notion of total Noether charges. Grassmannian degrees of freedom are also addressed in detail.     

Tris­[(R)‐lact­amide‐κ2O,O′]­zinc(II) tetra­bromo­zincate

The title compound, tris­[(R)‐2‐hydroxy­propan­amide‐κ²O,O′]­zinc(II) tetra­bromo­zincate, [Zn(C₃H₇NO₂)₃][ZnBr₄], contains one monomeric six‐coordinate zinc complex cation and one tetrahedral [ZnBr₄]²⁻ anion. Both Zn^II atoms lie on threefold axes. Coordination in the cation occurs via the amide and hydroxy O atoms [Zn—O = 2.074 (5) and 2.073 (6) Å] and has a distorted octahedral geometry, with cis‐O—Zn—O angles in the range 76.2 (2)–109.2 (2)°. In the crystal structure, the cations and anions are linked by N—H⋯Br and O—H⋯O hydrogen bonds, generating a three‐dimensional network.     

Deformations of duality-symmetric theories

We prove that a sum of free non-covariant duality-symmetric actions does not allow consistent, continuous and local self-interactions that deform the gauge transformations. For instance, non-abelian deformations are not allowed, even in 4 dimensions where Yang–Mills type interactions of 1-forms are allowed in the non-manifestly duality-symmetric formulation. This suggests that non-abelian duality should require to leave the standard formalism of perturbative local field theories. The analyticity of self-interactions for a single duality-symmetric gauge field in four dimensions is also analyzed.     

Tensor Gauge Fields in Arbitrary Representations of GL( D, $${\mathbb{R})}$$ : II. Quadratic Actions

Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in D-dimensional Minkowski space are explicitly written in a compact form by making use of Levi–Civita tensors. The field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non-Lagrangian local field equations proposed previously. Moreover, these actions allow a frame-like reformulation à la MacDowell–Mansouri, without any trace constraint in the tangent indices. Chargé de Recherches FNRS, Belgium     

Représentation à l'échelle microscopique d'un mécanisme de rupture dans un milieu a joints

. A representation of a class of failure mechanisms defined on a homogenized jointed medium by a velocity jump along a planar surface, is analyzed at the scale of the joints. The approach consists in representing a velocity jump at the macroscopic level by the kinematics of a finite band in the heterogeneous medium characterized by a piecewise rigid body motion of elementary blocs. The equivalence (in the sense of the yield design theory) between the macroscopic and macroscopic representations of such failure mechanisms is ensured by the equality of the corresponding maximum resisting rates of work. To cite this article: S. Maghous et al., C. R. Mecanique 333 (2005).     

WEFTA interlaboratory comparison on total lipid determination in fishery products using the Smedes method

Lipid determination by the Smedes method was tested in an interlaboratory trial performed by nine laboratories from seven countries belonging to the West European Fish Technologists Association Analytical Methods Working Group. Five samples of fish and fishery products with different lipid contents, including two blind duplicates, were distributed among the participants. All laboratories applied a slightly modified Smedes method, which included extraction of lipids by cyclohexane and isopropanol, transfer of lipids to the cyclohexane phase by addition of water, phase separation by centrifugation, and gravimetric lipid determination. The results indicate that the RSD for reproducibility (RSD(R)) was between 4.11 and 6.31% for samples with moderate (7%) and high (14%) lipid content, depending on the sample. Larger SDs among the laboratories were obtained for a cod sample with low lipid content of 0.5%. The method is judged to be suitable as a routine method for lipid determination in fish and fishery products.     

Higher-order singletons,partially massless fields,and their boundary values in the ambient approach

Using ambient space we develop a fully gauge and o(d,2)$\mathfrak{o}(d,2)$-covariant approach to boundary values of _AdSd+1${\mathit{AdS}}_{d+1}$ gauge fields. It is applied to the study of (partially) massless fields in the bulk and (higher-order) conformal scalars, i.e. singletons, as well as (higher-depth) conformal gauge fields on the boundary. In particular, we identify the corresponding generalized Fradkin–Tseytlin equations as obstructions to the extension of the off-shell boundary value to the bulk, generalizing the usual considerations for the holographic anomalies to the partially massless fields. We also relate the background fields for the higher-order singleton to the boundary values of partially massless fields and prove the appropriate generalization of the Flato–Fronsdal theorem, which is in agreement with the known structure of symmetries for the higher-order wave operator. All these facts support the following generalization of the higher-spin holographic duality: the O(N)$O(N)$ model at a multicritical isotropic Lifshitz point should be dual to the theory of partially massless symmetric tensor fields described by the Vasiliev equations based on the higher-order singleton symmetry algebra.     

N-Methylpyrrolidin-2-one hydrotribromide (MPHT) a mild reagent for selective bromination of carbonyl compounds: synthesis of substituted 2-bromo-1-naphtols

The reaction of the N-methylpyrrolidin-2-one hydrotribromide complex (MPHT) with substituted-1-tetralones has been investigated. This safety reagent proved to be successful for selective α,α-dibromination of tetralones. Moreover, under base-free conditions, several 2-bromo-1-naphtols were obtained from tetralones in a ‘one pot’ sequence in good to excellent yields.