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.

Upper and Lower Bounds in Relator Spaces

2000 Mathematics Subject Classification: 06A06, 54E15

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.

Remarks on the Nagata Conjecture

2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.

Maximal Number of Successors in a Nginar(1) Process

2000 Mathematics Subject Classification: 60J80, 60J20, 60J10, 60G10, 60G70, 60F99.

Distance Distributions and Energy of Designs in Hamming Spaces

We obtain new combinatorial upper and lower bounds for the potential energy of designs in q-ary Hamming space. Combined with results on reducing the number of all feasible distance distributions of such designs this gives reasonable good bounds. We compute and compare our lower bounds to recently obtained universal lower bounds. Some examples in the binary case are considered.

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.