There is no low maximal d. c. e. degree – Corrigendum

We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

There exists a polyhedron with infinitely many left neighbors

We show that there exists a finite polyhedron homotopy dominating infinitely many finite polyhedra of different homotopy types such that there isn't any homotopy type between and . This answers negatively the question raised by K. Borsuk in 1975: Does every FANR have only finitely many left neighbors?

     

The total coloring of a multigraph with maximal degree 4

In this paper it is proved that every multigraph with maximal degree 4 has a total coloring in six colors.     

On the reduced signless Laplacian spectrum of a degree maximal graph

For a (simple) graph G, the signless Laplacian of G is the matrix A(G)+D(G), where A(G) is the adjacency matrix and D(G) is the diagonal matrix of vertex degrees of G; the reduced signless Laplacian of G is the matrix Δ(G)+B(G), where B(G) is the reduced adjacency matrix of G and Δ(G) is the diagonal matrix whose diagonal entries are the common degrees for vertices belonging to the same neighborhood equivalence class of G. A graph is said to be (degree) maximal if it is connected and its degree sequence is not majorized by the degree sequence of any other connected graph. For a maximal graph, we obtain a formula for the characteristic polynomial of its reduced signless Laplacian and use the formula to derive a localization result for its reduced signless Laplacian eigenvalues, and to compare the signless Laplacian spectral radii of two well-known maximal graphs. We also obtain a necessary condition for a maximal graph to have maximal signless Laplacian spectral radius among all connected graphs with given numbers of vertices and edges.     

There is No Low Maximal D.C.E. Degree

We show that for any computably enumerable (c.e.) set A and any set L, if L is low and , then there is a c.e. splitting such that . In Particular, if L is low and n‐c.e., then is n‐c.e. and hence there is no low maximal n‐c.e. degree.     

Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness

In this paper we consider interpolatory quadrature formulae with multiple nodes that have the maximal trigonometric degree of exactness. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness

In this paper we consider interpolatory quadrature formulae with multiple nodes, which have the maximal trigonometric degree of exactness. Our approach is based on a procedure given by Ghizzeti and Ossicini (Quadrature formulae, Academie-Verlag, Berlin, 1970). We introduce and consider the so-called σ-orthogonal trigonometric polynomials of semi-integer degree and give a numerical method for their construction. Also, some numerical examples are included. The authors were supported in part by the Serbian Ministry of Science and Technological Development (Project: Orthogonal Systems and Applications, grant number #144004) and the Swiss National Science Foundation (SCOPES Joint Research Project No. IB7320-111079 “New Methods for Quadrature”).     

Graphs with degree sets of maximal cardinality: a handshaking problem revisited

We establish new upper and lower bounds for the generalized Euler-constant function γ(z) for z ∈ (0, 1) in terms of logarithm function, dilogarithm function and Lerch transcendental Φ.     

No graph has a maximal 3-ring of bonds

It is shown that no graph contains a maximal 3-ring of bonds.     

The elliptic K3 surfaces with a maximal singular fibre

We give the defining equation of complex elliptic K3 surfaces with a maximal singular fibre. Then we study the reduction modulo p at a particularly interesting prime p. To cite this article: T. Shioda, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

There exist no 2-type surfaces in E 3 which are images under stereographic projection of minimal surfaces in S 3

In this paper we deal with the following particular case of a weaker conjecture by B. Y. Chen: Are there 2-type Willmore surfaces in E ³? In particular we prove that the above question has a negative answer when the surface is the image under stereographic projection of a minimal surface in S ³.     

Averages of coefficients of a class of degree 3 L-functions

The Ramanujan Journal - In this note, we give a detailed proof of an asymptotic for averages of coefficients of a class of degree three L-functions which can be factorized as a product of a degree...     

On list incidentor coloring of a multigraph of degree 3

It is shown that if the number of colors in a list of each arc of a directed multigraph of degree 3 is at least the weight of this arc plus 3 then the incidentors of this multigraph can be colored according to these lists.     

Subgroups of a spinor group containing a maximal split torus. I

This paper studies subgroups of the split spinor group G=Spin (n, k),n 6, over a field K containing a maximal split torus T=T(n,K)assuming that charK2and ||K ||7.The main result of the first pan of the paper is the reduction of the proof that subgroups containing T are standard to the study of subgroups not containing root unipotent elements.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 49–75, 1991.     

On the maximal number of du Val singularities for a K3 surface

A complex K3 surface or an algebraic K3 surface in characteristics distinct from 2 cannot have more than 16 disjoint nodal curves.