Free multiflows in bidirected and skew-symmetric graphs

A graph (digraph) G=(V,E) with a set T⊆V of terminals is called inner Eulerian if each nonterminal node v has even degree (resp. the numbers of edges entering and leaving v are equal). Cherkassky and Lovász, independently, showed that the maximum number of pairwise edge-disjoint T-paths in an inner Eulerian graph G is equal to , where λ(s) is the minimum number of edges whose removal disconnects s and T-{s}. A similar relation for inner Eulerian digraphs was established by Lomonosov. Considering undirected and directed networks with “inner Eulerian” edge capacities, Ibaraki, Karzanov, and Nagamochi showed that the problem of finding a maximum integer multiflow (where partial flows connect arbitrary pairs of distinct terminals) is reduced to O(logT) maximum flow computations and to a number of flow decompositions.In this paper we extend the above max-min relation to inner Eulerian bidirected graphs and inner Eulerian skew-symmetric graphs and develop an algorithm of complexity for the corresponding capacitated cases. In particular, this improves the best known bound for digraphs. Our algorithm uses a fast procedure for decomposing a flow with O(1) sources and sinks in a digraph into the sum of one-source-one-sink flows.     

In situ generation of H2Se and hydrothermal synthesis of new polynuclear rhenium carbonyl polyselenides

Two new polyselenide-bridged rhenium carbonyl complexes, [Re₅(CO)₁₈(Se₂)₃]⁻ and [Re₄(CO)₁₄(Se₂)(Se₅)], were obtained by hydrothermal reaction of [Re(CO)₅Cl] with in situ generated H₂Se and have been characterized by X-ray diffraction.     

Hermite‐Padé Approximants for a Pair of Cauchy Transforms with Overlapping Symmetric Supports

Hermite‐Padé approximants of type II are vectors of rational functions with a common denominator that interpolate a given vector of power series at infinity with maximal order. We are interested in the situation when the approximated vector is given by a pair of Cauchy transforms of smooth complex measures supported on the real line. The convergence properties of the approximants are rather well understood when the supports consist of two disjoint intervals (Angelesco systems) or two intervals that coincide under the condition that the ratio of the measures is a restriction of the Cauchy transform of a third measure (Nikishin systems). In this work we consider the case where the supports form two overlapping intervals (in a symmetric way) and the ratio of the measures extends to a holomorphic function in a region that depends on the size of the overlap. We derive Szeg?‐type formulae for the asymptotics of the approximants, identify the convergence and divergence domains (the divergence domains appear for Angelesco systems but are not present for Nikishin systems), and show the presence of overinterpolation (a feature peculiar for Nikishin systems but not for Angelesco systems). Our analysis is based on a Riemann‐Hilbert problem for multiple orthogonal polynomials (the common denominator).© 2016 Wiley Periodicals, Inc.     

Topological Links between Duplex DNA and a Circular DNA Single Strand

DNA nanostructures of building blocks topologically linked at a precise position can be assembled from DNA duplexes and circularized oligonucleotides with the aid of peptide nucleic acids (PNAs). Shown schematically is a linked catenane yielding an earring topological DNA label.     

Topological solitons in branched aliphatic molecules

Polymorphic transitions are typical for molecular crystals of long chain aliphatic compounds. In the present work we studied the possibility of polymorphic transitions via the mechanism of topological solitons. The solitons correspond to stretching/compression of aliphatic chain by a half of the period, accompanied by 180° turn in branched molecules. Triacyglycerides (TAG) were chosen as an object of study; temperature dependencies of the specific heat capacity at constant pressure, complex dielectric permittivity, spectral (IR) and structural (powder XRD) properties of TAGs were characterized performed at ?170 ÷ 70°C. Following model was proposed to explain the experimental results. Thermal transformations of TAGs started from initiation of topological solitons on the methyl groups. The solitons passed along the alkyl chains and reoriented the ester groups, resulted in thermal dipole-relaxation polarization defrost observed as a relaxation process in the range (?80÷0)°C. Reaching the stoichiometric obstruction (branching), the solitons reflect from it. When the temperature increases up to 60°C, melting of TAG polycrystals takes place.     

Effective preconditioning of Uzawa type schemes for a generalized Stokes problem

Summary. The Schur complement of a model problem is considered as a preconditioner for the Uzawa type schemes for the generalized Stokes problem (the Stokes problem with the additional term in the motion equation). The implementation of the preconditioned method requires for each iteration only one extra solution of the Poisson equation with Neumann boundary conditions. For a wide class of 2D and 3D domains a theorem on its convergence is proved. In particular, it is established that the method converges with a rate that is bounded by some constant independent of . Some finite difference and finite element methods are discussed. Numerical results for finite difference MAC scheme are provided. Received May 2, 1997 / Revised version received May 10, 1999 / Published online May 8, 2000