Numerical analysis of vortex cell efficiency in laminar and turbulent flows past a circular cylinder with embedded rotating bodies

The effect of flow intensification in small-sized vortex cells on the flow pattern in the near wake downstream of a cylinder and the cylinder drag in laminar and turbulent flows is analyzed on the basis of a numerical simulation of the two-dimensional steady-state flow past a circular cylinder with rotating cylindrical bodies built into the cylinder contour. St. Petersburg, Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

Spatial harmonics of the field in a quadrupole mass filter with circular electrodes

The amplitudes of the spatial harmonics of the field are calculated for given displacements of the electrodes in a quadrupole mass filter relative to their optimum positions. The cases of radial and angular displacements of the electrodes, asymmetries in voltage supplied to the electrodes, and nonidentical rod diameters are considered. These data are required for calculating the actual shape of the mass peaks and will be useful in designing mass filters. Zh. Tekh. Fiz. 69, 96–101 (October 1999)     

The chromatic numbers of random hypergraphs

For a pair of integers 1≤γ<r, the γ-chromatic number of an r-uniform hypergraph H=(V, E) is the minimal k, for which there exists a partition of V into subsets T₁,…,T_k such that |e∩T_i|≤γ for every e∈E. In this paper we determine the asymptotic behavior of the γ-chromatic number of the random r-uniform hypergraph H_r(n, p) for all possible values of γ and for all values of p down to p=Θ(n^−r+1). © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12: 381–403, 1998     

The Weizsäcker phenomenon and a canonical definition of Gaussian Lebesgue–Rokhlin measures

The notion of “Gaussian Lebesgue–Rokhlin space” is introduced. The definition is canonical, i.e., is given without use of topological and others irrelevant mathematical structures. The object under discussion completes the category of finite-dimensional Gaussian vector spaces. Some nontrivial examples are considered and historical comments are given. Bibliography: 30 titles.     

Large Kr‐free subgraphs in Ks‐free graphs and some other Ramsey‐type problems

In this paper we present three Ramsey‐type results, which we derive from a simple and yet powerful lemma, proved using probabilistic arguments. Let 3 ≤ r < s be fixed integers and let G be a graph on n vertices not containing a complete graph K_s on s vertices. More than 40 years ago Erd?s and Rogers posed the problem of estimating the maximum size of a subset of G without a copy of the complete graph K_r. Our first result provides a new lower bound for this problem, which improves previous results of various researchers. It also allows us to solve some special cases of a closely related question posed by Erd?s. For two graphs G and H, the Ramsey number R(G, H) is the minimum integer N such that any red‐blue coloring of the edges of the complete graph K_N, contains either a red copy of G or a blue copy of H. The book with n pages is the graph B_n consisting of n triangles sharing one edge. Here we study the book‐complete graph Ramsey numbers and show that R(B_n, K_n) ≤ O(n³/log^3/2n), improving the bound of Li and Rousseau. Finally, motivated by a question of Erd?s, Hajnal, Simonovits, Sós, and Szemerédi, we obtain for all 0 < δ < 2/3 an estimate on the number of edges in a K₄‐free graph of order n which has no independent set of size n^1‐δ. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

The Turán Number Of The Fano Plane

  Let PG₂(2) be the Fano plane, i. e., the unique hypergraph with 7 triples on 7 vertices in which every pair of vertices is contained in a unique triple. In this paper we prove that for sufficiently large n, the maximum number of edges in a 3-uniform hypergraph on n vertices not containing a Fano plane is