We consider the following two classes of simple graphs: open necklaces and closed necklaces, consisting of a finite number of cliques of fixed orders arranged in path-like pattern and cycle-like pattern, respectively. In these two classes we determine those graphs whose index (the largest eigenvalue of the adjacency matrix) is maximal.

We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain 2 ⊕ 2. We also study proper interval orders and thei...

This paper analyzes the limits of applicability of the time domain surface impedance concept. Numerical results obtained by the boundary element formulation employing time domain surface impedance boundary conditions (SIBCs) of different orders of approximation are compared with experimental data and numerical results obtained using the finite element method. An analytical formula for evaluatio...

Abstract Let G be a finite group and let ? ( ) denote the sum of element orders . It is well-known that maximum value on set groups order n , where positive integer, will occur at cyclic C For nilpotent groups, we prove natural generalization this result, obtained by replacing with relative to certain subgroup H

Periodic nanostructuring can enhance the optical nonlinearity of plasmonic metals by several orders of magnitude. By patterning a gold film, the largest sub-100 femtosecond nonlinearity is achieved, which is suitable for terahertz rate all-optical data processing as well as ultrafast optical limiters and saturable absorbers.

Let Q = {qj, qz,..., qn / be a set of n points on the plane. The largest empty circle (LEC) problem consists in finding the largest circle C with center in the convex hull of Q such that no point q(C Q lies in the interior of C. Shamos recently outlined an O(n log n) algorithm for solving this problemJ 9) In this paper it is shown that this algorithm does not always work correctly. A different ...

Given a set of blue points and a set of red points in ddimensional space, we show how to find an axis-aligned hyperrectangle that contains no red points and as many blue points as possible. Our algorithm enumerates the set of relevant hyperrectangles (inclusion maximal axisaligned hyperrectangles that do not contain a red point) and counts the number of blue points in each one. The runtime of o...

We find an explicit bound, in terms of g when it is even, for the largest element of an aliquot cycle of repdigits to base g.

We conjecture a generalization of Dilworth’s theorem to direct products of partial orders. In particular, we conjecture that the largest “semiantichain” and the smallest “unichain covering” have the same size. We consider a special c lass of semiantichains and unichain coverings and determine when equality holds for them. This conjecture implies the existence of k-saturated partitions. A strong...

An iterative algorithm that approximates the polyconvex envelope f pc of a given function f : R → R, i.e. the largest function below f which is convex in all minors, is established. A rigorous error analysis with a focus on reliability and optimal orders of convergence, an efficient strategy that reduces the large number of unknowns, as well as numerical experiments are presented.