Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].     

Hypergeometric approach to Apéry-like series

By reformulating four hypergeometric series formulae, we derive 36 Apéry-like series expressions for the Riemann zeta function, including a couple of identities conjectured by Sun [New series for some special values of L-functions. Nanjing Univ J Math. 2015;32(2): 189–218].     

Shared Values of Certain Nonlinear Differential Polynomials of Meromorphic Functions

In this paper,by using the idea of truncated counting functions of meromorphic functions,we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one finite nonzero value.     

Some Results on the Growth of Polynomials

In this paper,we have studied the Lacunary type of polynomials and proved a result which generalizes as well as refines some well-known polynomial inequalities regarding the growth of polynomials not vanishing inside a circle.Further the paper corrects the proofs of some already known results.     

LITTLEWOOD-PALEY THEOREM FOR SCHR(O)DINGER OPERATORS

Let H be a Schr(o)dinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.     

Comonotone approximation with interpolation at the ends on an interval

Let a function f ∈ C[-1, 1], changes its monotonisity at the finite collection Y := {y1,… ,ys} of s points yi ∈ (-1, 1). For each n ≥ N(Y), we construct an algebraic polynomial Pn, of degree ≤ n, which is comonotone with f, that is changes its monotonisity at the same points yi as f, and |f(x)-Pn(x)|≤c(s)ω2(f,(√1-x2)/n), x∈[-1,1],where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s and ω2 (f, t) is the second modulus of smoothness of f.     

Subsonic Radiation Gas Dynamics in a Laser Plasma Generator Channel

The radiation gasdynamic processes in the channel of an air laser plasma generator operating at atmospheric pressure are analyzed. In the multigroup approximation a numerical radiation gasdynamic model is formulated on the basis of the equations of motion of a viscous heat-conducting gas and the selective thermal radiation transport equation. Laminar and turbulent subsonic generator operation regimes are considered.For the purpose of approximately describing the turbulent gas and plasma mixing the Navier-Stokes equations averaged after Reynolds and the k-ε turbulence model are used. The problem is solved in the time-dependent two-dimensional axisymmetric formulation.Strong radiation-gasdynamic interaction regimes are investigated. In these regimes the energy losses due to radiation from the high-temperature region of the laser plasma and the absorption of its thermal self-radiation by the surrounding plasma and gas layers (radiation reabsorption) appreciably affect the gasdynamic flow structure. Two methods of integrating the selective thermal radiation transport equation in the generator channel are discussed. In one of these the thermal radiation transport is calculated inside the heated volume and in the other the radiation heat fluxes are calculated on the surfaces bounding the volume. The results of calculating the spectral and integral radiation heat fluxes on the inner surface of the generator are given.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 126–143.Original Russian Text Copyright © 2005 by Surzhikov.