On the convergence of vector random measures

Summary The aim of this paper is to study Banach space-valued symmetric independently scattered random measures with emphasis on their convergence properties. The Vitali-Hahn-Saks Theorem, the Skorokhod theorem about the relations between the convergence a.e. and the convergence in law of random variables, and the central limit theorem for Banach valued random variables due to Hoffmann-Jorgensen, Pisier are extended to such measures.     

Nonlinear coordinate representations of smooth optimization problems

Nonlinear coordinate representations of smooth optimization problems are investigated from the point of view of variable metric algorithms. In other words, nonlinear coordinate systems, in the sense of differential geometry, are studied by taking into consideration the structure of smooth optimization problems and variable metric methods.Both the unconstrained and constrained cases are discussed. The present approach is based on the fact that the nonlinear coordinate transformation of an optimization problem can be replaced by a suitable Riemannian metric belonging to the Euclidean metric class. In the case of equality and inequality constraints, these questions are related closely to the right inverses of full-rank matrices; therefore, their characterization is a starting point of the present analysis. The main results concern a new subclass of nonlinear transformations in connection with the common supply of coordinates to two Riemannian manifolds, one immersed in the other one. This situation corresponds to the differentiable manifold structure of nonlinear optimization problems and improves the insight into the theoretical background of variable metric algorithms. For a wide class of variable metric methods, a convergence theorem in invariant form (not depending on coordinate representations) is proved. Finally, a problem of convexification by nonlinear coordinate transformations and image representations is studied.This research was supported by the Hungarian National Research Foundation, Grant Nos. OTKA-2568 and OTKA-2116, and by the Project Trasporti of the Italian National Research Council (CNR).     

Low-pressure membrane filtration of secondary effluent in water reuse: Pre-treatment for fouling reduction

Fouling in the low-pressure membrane filtration of secondary effluent for water reuse can be severe due to the complex nature of the components in the water. Pre-filtration, coagulation and anion exchange resin were investigated as pre-treatments for reducing fouling of microfiltration (MF) and ultrafiltration (UF) membranes in the treatment of activated sludge-lagoon effluent. The key fouling components were determined using several analytical techniques to detect differences in the organic components between the feed and permeate.Pre-filtration (1.5 μm) enhanced the permeate flux for MF by removing particulates, but had little effect for UF. Marked flux improvement was obtained by coagulation pre-treatment at 5 mg L⁻¹ Al³⁺ with internal membrane fouling being substantially alleviated. Anion exchange resin removed >50% of effluent organic matter but did not improve the flux or reduce irreversible membrane fouling. These results, together with detailed organic compositional analyses, showed that the very high-molecular weight organic materials (40–70 kDa) comprised of hydrophilic components such as soluble microbial products, and protein-like extracellular matter were the major cause of membrane fouling.     

Conjugate duality for vector-maximization problems

In this article we present a conjugate duality for a problem of maximizing a polyhedral concave nondecreasing homogeneous function over a convex feasible set in the nonnegative n-dimensional orthant. Using this duality we obtain a zero-gap duality for a vector-maximization problem.     

Radioactivity in airborne particulate and rainwater samples and deposition to ground in Ho Chi Minh City (Vietnam)

In this study, radioactivity of airborne particulate and rainwater samples were analysed during 2016 at three different sites in Ho Chi Minh City, Vietnam. The activities of gross alpha and gross beta measured in airborne particulate are in the range from (<?MDA-7.50) and (0.73–45.41) mBq m^?3 respectively. In rainwater, theirs are in the range from (1.9–4.1) and (14.9–28.6) mBq l^?1 respectively. Mean values of annual deposition fluxes of gross alpha and gross beta were found in the range from (5.56–10.65) and (50.9–70.5) Bq m^?2 y^?1 respectively. The correlation between radioactivity levels and meteorological factors are presented in this paper.     

Quantum Morphing and the Jones Polynomial

We will explore the experimental observation that on the set of knots with bounded crossing number, algebraically independent Vassiliev invariants become correlated, as noticed first by S. Willerton. We will see this through the value distribution of the Jones polynomial at roots of unit. As the degree of the roots of unit is getting larger, the higher order fluctuation is diminishing and a more organized shape will emerge from a rather random value distribution of the Jones polynomial. We call such a phenomenon “quantum morphing”. Evaluations of the Jones polynomial at roots of unity play a crucial role, for example in the volume conjecture. Received: 15 February 2001 / Accepted: 8 June 2001     

Improving the knowledge and design of end groups in polymers produced by free radical polymerization

Several techniques have been used to probe polymer end groups. The nitroxide radical trapping technique has been used (i) to show that initiator-derived unsaturated end groups in polymethyl methacrylate can be minimized by using t-hexyl peroxypivalate as the initiator (ii) to predict the end and penultimate groups in acrylonitrile/ethyl vinyl ether copolymer produced by t-butoxyl initiation by analogy with the initiation mechanism (iii) to predict probable end groups in polyacrylonitrile and polystyrene produced by cyanoisopropyl initiation in the presence of adventitious oxygen. NMR techniques have been used to show that the end groups of functionalized oligomers, made from styrene and methacrylonitrile by the addition-fragmentation chain transfer technique with allylic sulphides, conform to the expected structures. © 1998 John Wiley & Sons, Ltd.     

Corrigendum to the paper “Hermitian forms over division algebras over real function fields”

In the previous paper [T] we gave a classification of hermitian forms over the real function fieldk=R(t) and its completionsk _v with respect to valuationsv trivial onR. Unfortunately in the local case the arguments given for cases A and D, in general, were not correct. Therefore the resulting local and local-global classifications obtained were incorrect. I would like also to thank Dr. D. Hoffmann for pointing out these mistakes and the referee for useful comments. Here we would like to make necessary corrections to [T]. We keep the same notation used there, except that in the first paragraph,J is not the standard involution of a quaternion division algebraD (with basis {1,i,j,ij}). All hermitian forms will be hermitian forms with respect toJ, with values inD.     

Novel flavanes from Livistona halongensis

A study of the chemical constituents of a methanolic extract of the roots of Livistona halongensis (Arecaceae) led to the isolation of two new flavanes, 2S,3S-3,5,7,3'-tetrahydroxy-5'-methoxyflavane (1) and 3,7,3'-trihydroxy-5'-methoxyflavane 5-O-beta-glucopyranoside (2), together with trans-3,5,3',5'-tetrahydroxy-4-methoxystilbene, saccharose and beta-sitosterol-3-O-beta-glucopyranoside. The structures of these compounds were elucidated on the basis of spectroscopic data.     

Flexible calibration technique for fringe-projection-based three-dimensional imaging

Fringe projection profilometry (FPP) has evolved dramatically, with many highly demanded features for three-dimensional (3D) imaging, such as high accuracy, easy implementation, and capability of measuring multiple objects with complex shapes. A vital component for an FPP-based 3D imaging system is the calibration process. The existing calibration methods lack the ability to be flexibly compatible with various scales of the field of imaging. In this Letter, a technique to cope with this issue is presented; it employs a checkerboard along with practical considerations to ensure reliable and accurate calibration. The validity and practicality of the technique are verified by experiments.