QUADRATURE METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.     

Reconstructing Binary Signals from Local Histograms

In this paper, we considered the representation power of local overlapping histograms for discrete binary signals. We give an algorithm that is linear in signal size and factorial in window size for producing the set of signals, which share a sequence of densely overlapping histograms, and we state the values for the sizes of the number of unique signals for a given set of histograms, as well as give bounds on the number of metameric classes, where a metameric class is a set of signals larger than one, which has the same set of densely overlapping histograms.     

A 1:1 cocrystal of baicalein with nicotinamide

Cocrystallization of baicalein with nicotinamide yields a 1:1 cocrystal [systematic name: pyridine‐3‐carboxamide–5,6,7‐trihydroxy‐2‐phenyl‐4H‐chromen‐4‐one (1/1)], C₆H₆N₂O·C₁₅H₁₀O₅. The asymmetric unit contains one baicalein and one nicotinamide molecule, both in neutral forms. Molecules in the cocrystal form column motifs stabilized by an array of intermolecular hydrogen bonds.     

A Flawed Argument Against Actual Infinity in Physics

In “Nonconservation of Energy and loss of Determinism II. Colliding with an Open Set” (2010) Atkinson and Johnson argue in favour of the idea that an actual infinity should be excluded from physics, at least in the sense that physical systems involving an actual infinity of component elements should not be admitted. In this paper I show that the argument Atkinson and Johnson use is erroneous and that an analysis of the situation considered by them is possible without requiring any type of rejection of the idea of infinity.     

A metal‐mediated dimerization of the ligand bis(N,N‐diethyl­amino)­carbeniumdi­thio­carboxyl­ate

The title compound, methylene bis[bis(N,N‐diethyl­amino)­carbeniumdi­thio­carboxyl­ate] penta­chloro­oxo­rhenium, (C₂₁H₄₂N₄S₄)[ReCl₅O], is the result of an unusual dimerization of the ligand bis(N,N‐diethyl­amino)­carbeniumdi­thio­carboxyl­ate [(Et₂N)₂C₂S₂] upon reaction with [ReOCl₃(PPh₃)₂] in chloro­form under reflux conditions. The compound was obtained as a dicationic moiety, with the molecular [ReOCl₅]²⁻ anion providing the charge compensation. The planes of the carbenium and thio­carboxyl­ate moieties are nearly perpendicular to one another and the backbone C—C bond length in the N₂CCS₂ group is the same as a normal C—C single‐bond length.     

The Liouville-Bratu-Gelfand Problem for Radial Operators

We determine precise existence and multiplicity results for radial solutions of the Liouville-Bratu-Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.     

The Synthesis of L-aminosugar and the studies of L-pyranoses on the ring III of pyranmycins

The synthesis of a novel class of aminoglycoside, pyranmycin, and a convenient method for the preparation of 6-amino-L-idopyranosides were reported. One of the members in the reported pyranmycin families, TC010, has prominent activity against Escherichia coli, Staphylococcus aureus, and Bacillus megaterium. We also discovered that the (4)C(1) chair conformation on ring III of pyranmycin is essential for the antibacterial activity. [reaction: see text]     

Optical trapping of nanoparticles and microparticles by a Gaussian standing wave

The optical trapping of nanoparticles and microparticles by a Gaussian standing wave is experimentally demonstrated for the first time to the authors' knowledge. The standing wave is obtained under a microscope objective as a result of the interference of an incoming laser beam and a beam reflected on a microscope slide that has been coated with a system of reflective dielectric layers. Experimental results show that three-dimensional trapping of nanoparticles (100-nm polystyrene spheres) and one or more vertically aligned micro-objects (5-mum polystyrene spheres, yeast cells) can easily be achieved by use of even highly aberrated beams or objectives with low numerical apertures.     

STOPPING RULES AND THE CONTROL OF STOCK POLLUTANTS

A stock pollutant is defined as a residual waste that might accumulate over time. This paper examines some of the important distinctions between degradable and nondegradable stock pollutants and between nondegradable stock pollutants with known versus uncertain environmental cost. The latter case is examined using the more recent literature on stochastic control with Brownian motion. The presence of irreversibility and uncertainty is known to lead to more conservative investment rules and places a value on the preservation of options. In the case of a nondegradable stock pollutant with Brownian environmental cost, options are preserved by stopping accumulation at a lower level than in the corresponding certainty-equivalent problem. The model presented in this paper permits the derivation of closed-form stopping rules. For a simple numerical problem, the optimal nondegradable stock with Brownian environmental cost was 20 to 45 percent lower than the optimal level with known environmental cost. The empirical study of an actual nondegradable stock pollutant will require time series data on private and social cost in order to estimate drift and variance parameters which will influence the actual extent to which the optimal stock is less than the certainty-equivalent stock.     

EOM/Propagator ionization potentials: Extension of the excitation operator manifold

The excitation operator manifold required for the calculation of vertical IPs in the EOM/propagator formalism is extended to include products of five spin orbital field operators (refered to as the h₅ basis). Spin symmetry adaptation is used for all the operators of this manifold. Using a direct diagonalization technique introduced previously the effect of inclusion of the h₅ basis on calculated IPs is illustrated for various levels of approximation to the electron density by numerical applications to ethylene and water. The fourth-order terms thus introduced are shown to have greater magnitude than previously included third-order terms, in agreement with earlier work.