Infinite Infrared Regularization and a State Space for the Heisenberg Algebra

We present a method for the construction of a Krein space completion for spaces of test functions, equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order. This generalizes a regularization method for infrared singularities in quantum field theory, introduced by G. Morchio and F. Strocchi, to the case of singularites of infinite order. We give conditions for the possibility of this procedure in terms of local differential operators and the Gelfand- Shilov test function spaces, as well as an abstract sufficient condition. As a model case we construct a maximally positive definite state space for the Heisenberg algebra in the presence of an infinite infrared singularity.Comment: 18 pages, typos corrected, journal-ref added, reference adde

2-Aminoterephthalic acid dimethyl ester

Single crystals of the title compound, C10H11NO4, an inter­mediate in the industrial synthesis of yellow azo pigments, were obtained from the industrial production. The mol­ecules crystallize as centrosymmetic dimers connected by two symmetry-related N—H⋯O=C hydrogen bonds. Each mol­ecule also contains an intra­molecular N—H⋯O=C hydrogen bond. The dimers form stacks along the a-axis direction. Neighbouring stacks are arranged into a herringbone structure

On the theory of cavities with point-like perturbations. Part I: General theory

The theoretical interpretation of measurements of "wavefunctions" and spectra in electromagnetic cavities excited by antennas is considered. Assuming that the characteristic wavelength of the field inside the cavity is much larger than the radius of the antenna, we describe antennas as "point-like perturbations". This approach strongly simplifies the problem reducing the whole information on the antenna to four effective constants. In the framework of this approach we overcame the divergency of series of the phenomenological scattering theory and justify assumptions lying at the heart of "wavefunction measurements". This selfconsistent approach allowed us to go beyond the one-pole approximation, in particular, to treat the experiments with degenerated states. The central idea of the approach is to introduce ``renormalized'' Green function, which contains the information on boundary reflections and has no singularity inside the cavity.Comment: 23 pages, 6 figure

On the Nodal Count Statistics for Separable Systems in any Dimension

We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and analyse some of its universal properties. Our results are illustrated by detailed discussion of simple examples and numerical nodal count distributions.Comment: 21 pages, 4 figure

Analysis of Optical Layouts for the Phase 1 upgrade of the CERN Large Hadron Collider Insertion Regions

In the framework of the studies for the upgrade of the insertions of the CERN Large Hadron Collider, four optical layouts were proposed with the aim of reducing the beta-function at the collision point down to 25 cm. The different candidate layouts are presented. Results from the studies performed on mechanical and dynamic aperture are summarized, together with the evaluation of beam-beam effects. Particular emphasis is given to the comparison of the optics performance, which led to retain the most promising layouts for further development

Counting nodal domains on surfaces of revolution

We consider eigenfunctions of the Laplace-Beltrami operator on special surfaces of revolution. For this separable system, the nodal domains of the (real) eigenfunctions form a checker-board pattern, and their number $\nu_n$ is proportional to the product of the angular and the "surface" quantum numbers. Arranging the wave functions by increasing values of the Laplace-Beltrami spectrum, we obtain the nodal sequence, whose statistical properties we study. In particular we investigate the distribution of the normalized counts $\frac{\nu_n}{n}$ for sequences of eigenfunctions with $K \le n\le K + \Delta K$ where $K,\Delta K \in \mathbb{N}$. We show that the distribution approaches a limit as $K,\Delta K\to\infty$ (the classical limit), and study the leading corrections in the semi-classical limit. With this information, we derive the central result of this work: the nodal sequence of a mirror-symmetric surface is sufficient to uniquely determine its shape (modulo scaling).Comment: 36 pages, 8 figure

Identification and validation of small molecule analytes in mouse plasma by liquid chromatography–tandem mass spectrometry: A case study of misidentification of a short-chain fatty acid with a ketone body

Recently, there has been growing interest in short-chain fatty acids (SCFA) and ketone bodies (KB) due to their potential use as biomarkers of health and disease. For instance, these diet-related metabolites can be used to monitor and reduce the risk of immune response, diabetes, or cardiovascular diseases. Given the interest in these metabolites, different targeted metabolomic methods based on UPLC-MS/MS have been developed in recent years to detect and quantify SCFA and KB. In this case study, we discovered that applying an existing validated, targeted UPLC-MS/MS method to mouse plasma, resulted in a fragment ion (194 m/z) being originally misidentified as acetic acid (a SCFA), when its original source was 3-hydroxybutyric acid (a KB). Therefore, we report a modified, optimized LC method that can separate both signals. In addition, the metabolite coverage was expanded in this method to detect up to eight SCFA: acetic, propanoic, butyric, isobutyric, 2-methylbutyric, valeric, isovaleric, and hexanoic acids, two KB: 3-hydroxybutyric, and acetoacetic acids, and one related metabolite: 3-hydroxy-3-methylbutyric acid. The optimization of this method increased the selectivity of the UPLC-MS/MS method towards the misidentified compound. These findings encourage the scientific community to increase efforts in validating the original precursor of small molecule fragments in targeted methods

Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count

The nodal domains of eigenvectors of the discrete Schrodinger operator on simple, finite and connected graphs are considered. Courant's well known nodal domain theorem applies in the present case, and sets an upper bound to the number of nodal domains of eigenvectors: Arranging the spectrum as a non decreasing sequence, and denoting by $\nu_n$ the number of nodal domains of the $n$'th eigenvector, Courant's theorem guarantees that the nodal deficiency $n-\nu_n$ is non negative. (The above applies for generic eigenvectors. Special care should be exercised for eigenvectors with vanishing components.) The main result of the present work is that the nodal deficiency for generic eigenvectors equals to a Morse index of an energy functional whose value at its relevant critical points coincides with the eigenvalue. The association of the nodal deficiency to the stability of an energy functional at its critical points was recently discussed in the context of quantum graphs [arXiv:1103.1423] and Dirichlet Laplacian in bounded domains in $R^d$ [arXiv:1107.3489]. The present work adapts this result to the discrete case. The definition of the energy functional in the discrete case requires a special setting, substantially different from the one used in [arXiv:1103.1423,arXiv:1107.3489] and it is presented here in detail.Comment: 15 pages, 1 figur