New Bounds for the Maximum Size of Ternary Constant Weight Codes

This work was partially supported by the Bulgarian National Science Fund under Grant I–618/96.

Sharp Bounds on the Number of Resonances for Symmertic Systems II. Non-Compactly Supported Perturbations

We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems.

New Upper Bounds for Some Spherical Codes

The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.

Matricial Model for the Study of Lower Bounds

Let V be an array. The range query problem concerns the design of data structures for implementing the following operations. The operation update(j,x) has the effect vj ← vj + x, and the query operation retrieve(i,j) returns the partial sum vi + ... + vj. These tasks are to be performed on-line. We define an algebraic model – based on the use of matrices – for the study of the problem. In this paper we establish as well a lower bound for the sum of the average complexity of both kinds of operations, and demonstrate that this lower bound is near optimal – in terms of asymptotic complexity.

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

Upper and Lower Bounds in Relator Spaces

2000 Mathematics Subject Classification: 06A06, 54E15

Some Bounds for Almost Absorbing Birth and Death Processes with Catastrophes

2000 Mathematics Subject Classification: 60J27.

Upper and Lower Bounds for Ruin Probability

In this note we discuss upper and lower bound for the ruin probability in an insurance model with very heavy-tailed claims and interarrival times.

Lower Bounds on the Directed Sweepwidth of Planar Shapes

We investigate a recently introduced width measure of planar shapes called sweepwidth and prove a lower bound theorem on the sweepwidth.