Radiolysis of 1-naphthol in aqueous solutions

The effects of absorbed doses, initial pH and 1-naphthol concentration onto its radiolysis in aqueous sulphuric and hydrochloric acids by gamma rays from ⁶⁰Co were investigated. Under the experimental conditions, 1-naphthol degradation yields increased with increasing the absorbed doses (0.3–3.0 kGy) and with decreasing the initial 1-naphthol concentration (20–1 ppm). It was found out that the hydrated electrons did not play any significant roles in 1-naphthol radiolysis, as the degradation yields were higher at pH₀ ~ 0.46 compared to those at pH₀ ~ 2.0–5.0. The corresponding radiolytic yields G(−1-naphthol) were (6.13 ± 1.00)) × 10⁻² and (5.11 ± 0.22) × 10⁻² μmol/J in sulphuric acids, (15.61 ± 3.85) × 10⁻² and (4.76 ± 0.48) × 10⁻² μmol/J in hydrochloric acids. 1-Naphthol degradation rates could be described by the kinetic equations of pseudo-first-order reactions. An empirical relation between the observed reaction constants k _D and the initial 1-naphthol concentrations was established, enabling to predict the absorbed doses required for a given treatment efficiency. Three products of 1-naphthol degradation were revealed using an HPLC/UV procedure.     

Dimensional variance inequalities of Brascamp–Lieb type and a local approach to dimensional Prékopaʼs theorem

We give a new approach, inspired by Hörmander?s L²$L^2$-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the Brunn–Minkowski inequalities. We also present several applications of these variance inequalities, including reverse Hölder inequalities for convex functions, weighted Brascamp–Lieb inequalities and sharp weighted Poincaré inequalities for generalized Cauchy measures.     

Spectrum created by line defects in periodic structures

We study a Helmholtz‐type spectral problem related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a three‐dimensional periodic medium; the defect is infinitely extended in one direction, but compactly supported in the remaining two. This perturbation introduces guided mode spectrum inside the band gaps of the fully periodic, unperturbed spectral problem. We will show that even small perturbations lead to additional spectrum in the spectral gaps of the unperturbed operator and investigate some properties of the spectrum that is created.     

Advanced form-finding for cable-strut structures

A numerical method is presented for form-finding of cable-strut structures. The topology and the types of members are the only information that is required in this form-finding process. Dummy members are used to transform the cable-strut structure with supports into self-stressed system without supports. The requirement on rank deficiencies of the force density and equilibrium matrices for the purpose of obtaining a non-degenerate d-dimensional self-stressed structure has been explicitly discussed. The spectral decomposition of the force density matrix and the singular value decomposition of the equilibrium matrix are performed iteratively to find the feasible sets of nodal coordinates and force densities which satisfy the minimum required rank deficiencies of the force density and equilibrium matrices, respectively. Based on numerical examples it is found that the proposed method is very efficient, robust and versatile in searching self-equilibrium configurations of cable-strut structures.     

Spectrally Adjustable Picosecond Dye Laser Pulses Generated with Nanosecond Nitrogen Lasers

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On duality bound methods for nonconvex global optimization

A counter-example is given to several recently published results on duality bound methods for nonconvex global optimization.     

Reversing the Stereoselectivity of a Palladium‐Catalyzed O‐Glycosylation through an Inner‐Sphere or Outer‐Sphere Pathway

An efficient and concise method for the construction of various O‐glycosidic bonds by a palladium‐catalyzed reaction with a 3‐O‐picoloyl glucal has been developed. The stereochemistry of the anomeric center derives from either an inner‐sphere or outer‐sphere pathway. Harder nucleophiles, such as aliphatic alcohols and sodium phenoxides give β‐products, and α products result from using softer nucleophiles, such as phenol.     

Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures

In this paper, we extend the basic distance measure in picture fuzzy sets to the new measures called generalized picture distance measures and picture association measures. Some properties of these measures are examined. An application to clustering problem is given to illustrate applicability of the proposed works.