Curve reconstruction: Connecting dots with good reason

Curve reconstruction algorithms are supposed to reconstruct curves from point samples. Recent papers present algorithms that come with a guarantee: Given a sufficiently dense sample of a closed smooth curve, the algorithms construct the correct polygonal reconstruction. Nothing is claimed about the output of the algorithms, if the input is not a dense sample of a closed smooth curve, e.g., a sample of a curve with endpoints. We present an algorithm that comes with a guarantee for any set P of input points. The algorithm constructs a polygonal reconstruction G and a smooth curve Γ that justifies G as the reconstruction from P.     

Design of peptides with α,β-de­hydro residues: a dipeptide with a branched β-carbon de­hydro residue at the (i+1) position,methyl N-(benzyloxycarbonyl)-α,β-dide­hydro­valyl-l-tryptophanate

The structure of the title peptide, C₂₅H₂₇N₃O₅, has been determined and its conformation analysed. Values of the standard peptide torsion angles are ϕ₁ = −44.2 (3)°, ψ₁ = 135.9 (2)°, ϕ₂ = −141.6 (2)° and ψ₂^T = 168.0 (2)°. The crystal structure is stabilized by an intermolecular hydrogen bond, with an N⃛O distance of 2.919 (3) Å, which is formed between screw-axis-related NH and CO groups of de­hydro­valine residues.     

Spectroscopic quadrupole moment of holmium from pionic X-ray measurement

From the observed quadrupole splitting of the 5g-4f X-ray transition in π-¹⁶⁵Ho we determine the spectroscopic quadrupole moment of ¹⁶⁵Ho to be Q = 3.47±0.11 b. The strong interaction shift and the width of the 4f level are found to be ?₀ = 0.35±0.08 keV and Γ₀ = 0.21±0.04 keV, respectively.     

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition.     

(e, 2e) spectroscopy of N2—valence momentum distributions and configuration interaction

The noncoplanar symmetric (e, 2e) reaction has been applied to N₂ at 1200, 600 and 400 eV. Separation energy spectra are obtained in the valence region, the observed structure extending to above 60 eV. Electron momentum profiles are measured at a number of separation energies. They agree very well with the momentum distributions for valence orbitals given by SCF calculations. Considerable configuration interaction structure is observed, being primarily due to configuration interaction in the 2σ_g hole state. At 1200 eV the spectroscopic sum rule is satisfied within experimental error, confirming the validity of the analysis.     

Charged particle emission following the absorption of stopped π− in 12C, 59Co and 197Au

Energy spectra of charged particles (p, d, t, ³He, α) emitted following the absorption of stopped π^? in ¹²C, ⁵⁹Co and ¹⁹⁷Au have been measured. The results are compared with results from neutron spectroscopy and discussed in the context of the quasi-deuteron model of π^? absorption.     

Endothermic quasicrystalline-to-crystalline phase transition in Al6CuMg4

Electron microscopic and differential scanning calorimetric (DSC) studies have been performed to investigate the phase transitions in the rapidly solidified Al₆CuMg₄ alloy system. We present evidence, for the first time, that anendothermic quasicrystalline to crystalline transition occurs in this system around 340°C. This is an unexpected feature—for conventional wisdom would lead one to expect exothermic behaviour as was seen in Al₈₆Mn₁₄—and points to the fact that stability of certain quasicrystalline phases may be much larger than hitherto expected. Some comments on the recently reported large quasicrystal for the Al₆CuLi₃ system are also made in the light of our observation.     

A new technique to compute polygonal schema for 2-manifolds with application to null-homotopy detection

We provide a new technique for deriving optimal-sized polygonal schema for triangulated compact 2-manifolds without boundary inO(n) time, wheren is the size of the given triangulationT. We first derive a polygonal schemaP embedded inT using Seifert-Van Kampen's theorem. A reduced polygonal schemaQ of optimal size is computed fromP, where a surjective map from the vertices ofP is retained to the vertices ofQ. This helps detecting null-homotopic (contractible to a point) cycles. Given a cycle of lengthk, we determine if it is null-homotopic inO(n+k logg) time and in θ(n+k) space, whereg is the genus of the given 2-manifold. The actual contraction for a null-homotopic cycle can be computed in θ(nk) time and space. This is a considerable improvement over the previous best-known algorithm for this problem.     

Perturbed iterative solution of nonlinear equations with applications to fluid dynamics

In this work a technique has been developed to solve a set of nonlinear equations with the assumption that a solution exists. The algorithm involves nonlinear Gauss-Seidel iteractions and at each iteration the value of the iterate is added to a predetermined perturbation parameter which is computed in terms of quantities already known. This perturbation parameter has two properties: (i) it determines the mode of convergence, that means it shows how many more computations are required so that convergence may be achieved, and (ii) it accelerates the rate of convergence. The algorithm is computationally simple. Several nonlinear equations have been studied. The results seem to be encouraging.     

OH radical reactions with ethanolamines: formation of reducing as well as oxidizing radicals

OH radical reactions with ethanolamine, diethanolamine and triethanolamine were studied at pH values below and above the pK_a values of these compounds. The rate constants were found to be lower for the protonated amines than those for their neutral forms. The OH radical reaction led to the formation of both oxidizing, as well as reducing species, as observed by their reactions with methyl viologen and ascorbic acid. The oxidizing species formed by OH radical reaction at the amine site was not found to react with the parent molecules and thereby no secondary yield of reducing species was obtained, as in the case of glycine (except in the case of triethanolamine at pH 9.2).