Operation of industrial-scale electron beam wastewater treatment plant

Textile dyeing processes consume large amount of water, steam and discharge filthy and colored wastewater. A pilot scale e-beam plant with an electron accelerator of 1 MeV, 40 kW had constructed at Daegu Dyeing Industrial Complex (DDIC) in 1997 for treating 1,000 m³ per day. Continuous operation of this plant showed the preliminary e-beam treatment reduced bio-treatment time and resulted in more significant decreasing TOC, COD_Cr, and BOD₅. Convinced of the economics and efficiency of the process, a commercial plant with 1 MeV, 400 kW electron accelerator has constructed in 2005. This plant improves the removal efficiency of wastewater with decreasing the retention time in bio-treatment at around 1 kGy. This plant is located on the area of existing wastewater treatment facility in DDIC and the treatment capacity is 10,000 m³ of wastewater per day. The total construction cost for this plant was USD 4 M and the operation cost has been obtained was not more than USD 1 M per year and about USD 0.3 per each m³ of wastewater.     

Effect of ionic liquid treatment on the structures of lignins in solutions: molecular subunits released from lignin

The solution structures of three types of isolated lignin-organosolv (OS), Kraft (K), and low sulfonate (LS)-before and after treatment with 1-ethyl-3-methylimidazolium acetate were studied using small-angle neutron scattering (SANS) and dynamic light scattering (DLS) over a concentration range of 0.3-2.4 wt %. The results indicate that each of these lignins is comprised of aggregates of well-defined basal subunits, the shapes and sizes of which, in D(2)O and DMSO-d(6), are revealed using these techniques. LS lignin contains a substantial amount of nanometer-scale individual subunits. In aqueous solution these subunits have a well-defined elongated shape described well by ellipsoidal and cylindrical models. At low concentration the subunits are highly expanded in alkaline solution, and the effect is screened with increasing concentration. OS lignin dissolved in DMSO was found to consist of a narrow distribution of aggregates with average radius 200 ± 30 nm. K lignin in DMSO consists of aggregates with a very broad size distribution. After ionic liquid (IL) treatment, LS lignin subunits in alkaline solution maintained the elongated shape but were reduced in size. IL treatment of OS and K lignins led to the release of nanometer-scale subunits with well-defined size and shape.     

Parallel Algorithm and Software for Image Inpainting via Sub-Riemannian Minimizers on the Group of Rototranslations

The paper is devoted to an approach for image inpainting developed on the basis of neurogeometry of vision and sub-Riemannian geometry. Inpainting is realized by completing damaged isophotes (level lines of brightness) by optimal curves for the left-invariant sub-Riemannian problem on the group of rototranslations (motions) of a plane SE(2). The approach is considered as anthropomorphic inpainting since these curves satisfy the variational principle discovered by neurogeometry of vision. A parallel algorithm and software to restore monochrome binary or halftone images represented as series of isophotes were developed. The approach and the algorithm for computation of completing arcs are presented in detail.     

Low and high frequency approximations to eigenvibrations of string with double contrasts

We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density inhomogeneity is the same as the order of stiffness inhomogeneity, with heavier part being softer. The limit problem for high frequency approximations depends nonlinearly on the spectral parameter. The quantization of the spectral semiaxis is applied in order to get a close approximations of eigenvalues as well as eigenfunctions for the prime problem under perturbation.     

Constraint aggregation principle in convex optimization

A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single surrogate inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration continues. This general aggregation principle is incorporated into a number of specific algorithms. Convergence of the new methods is proved and speed of convergence analyzed. Next, dual interpretation of the method is provided and application to decomposable problems is discussed. Finally, a numerical illustration is given.     

Algebras of Convolution Type Operators with Piecewise Slowly Oscillating Data. II: Local Spectra and Fredholmness

Let ${\mathcal{B}_{p,w}}$ be the Banach algebra of all bounded linear operators acting on the weighted Lebesgue space ${L^p(\mathbb{R},w)}$ , where ${p\in(1,\infty)}$ and w is a Muckenhoupt weight. We study the Banach subalgebra ${\mathfrak{U}_{p,w}}$ of ${\mathcal{B}_{p,w}}$ generated by all multiplication operators aI ( ${a\in PSO^\diamond}$ ) and all convolution operators W ⁰(b) ( ${b\in PSO_{p,w}^\diamond}$ ), where ${PSO^\diamond\subset L^\infty(\mathbb{R})}$ and ${PSO_{p,w}^\diamond\subset M_{p,w}}$ are algebras of piecewise slowly oscillating functions that admit piecewise slowly oscillating discontinuities at arbitrary points of ${\mathbb{R}\cup\{\infty\}}$ , and M _p,w is the Banach algebra of Fourier multipliers on ${L^p(\mathbb{R},w)}$ . Under some conditions on the Muckenhoupt weight w, using results of the local study of ${\mathfrak{U}_{p,w}}$ obtained in the first part of the paper and applying the theory of Mellin pseudodifferential operators and the two idempotents theorem, we now construct a Fredholm symbol calculus for the Banach algebra ${\mathfrak{U}_{p,w}}$ and establish a Fredholm criterion for the operators ${A\in\mathfrak{U}_{p,w}}$ in terms of their Fredholm symbols. In four partial cases we obtain for ${\mathfrak{U}_{p,w}}$ more effective results.     

A strong invariance principle for nonconventional sums

In Kifer and Varadhan (Nonconventional limit theorems in discrete and continuous time via martingales, 2010) we obtained a functional central limit theorem (known also as a weak invariance principle) for sums of the form ${\sum_{n=1}^{[Nt]} F\big(X(n), X(2n), .\, .\, .\, .\, X(kn), X(q_{k+1}(n)), X(q_{k+2}(n)), .\, .\, .\, , X(q_\ell(n))\big)}$ (normalized by ${1/\sqrt N}$ ) where X(n), n ≥ 0 is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polynomial growth and certain regularity properties and q _i , i > k are positive functions taking on integer values on integers with some growth conditions which are satisfied, for instance, when q _i ’s are polynomials of growing degrees. This paper deals with strong invariance principles (known also as strong approximation theorems) for such sums which provide their uniform in time almost sure approximation by processes built out of Brownian motions with error terms growing slower than ${\sqrt N}$ . This yields, in particular, an invariance principle in the law of iterated algorithm for the above sums. Among motivations for such results are their applications to multiple recurrence for stochastic processes and dynamical systems as well, as to some questions in metric number theory and they can be considered as a natural follow up of a series of papers dealing with nonconventional ergodic averages.     

Integer programming formulations and efficient local search for relaxed correlation clustering

Relaxed correlation clustering (RCC) is a vertex partitioning problem that aims at minimizing the so-called relaxed imbalance in signed graphs. RCC is considered to be an NP-hard unsupervised learning problem with applications in biology, economy, image recognition and social network analysis. In order to solve it, we propose two linear integer programming formulations and a local search-based metaheuristic. The latter relies on auxiliary data structures to efficiently perform move evaluations during the search process. Extensive computational experiments on existing and newly proposed benchmark instances demonstrate the superior performance of the proposed approaches when compared to those available in the literature. While the exact approaches obtained optimal solutions for open problems, the proposed heuristic algorithm was capable of finding high quality solutions within a reasonable CPU time. In addition, we also report improving results for the symmetrical version of the problem. Moreover, we show the benefits of implementing the efficient move evaluation procedure that enables the proposed metaheuristic to be scalable, even for large-size instances.

     

Wave Operators on Quantum Algebras via Noncanonical Quantization

We suggest a method to quantize basic wave operators of Relativistic Quantum Mechanics (Laplace, Maxwell, Dirac ones) without using canonical coordinates. We define two-parameter deformations of the Minkowski space algebra and its 3-dimensional reduction via the so-called Reflection Equation Algebra and its modified version. Wave operators on these algebras are introduced by means of quantized partial derivatives described in two ways. In particular, they are given in so-called pseudospherical form which makes use of a q-deformation of the Lie algebra sl(2) and quantum versions of the Cayley-Hamilton identity.