Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate finite versions of recurrence, and describe connections to combinatorial problems. In particular, we show that sets of Bohr recurrence (meaning sets of recurrenc...

Forward-SBNDM is a recently introduced variation of the BNDM algorithm for exact string matching. Forward-SBNDM reads a text character following an alignment of the pattern. We present a generalization of this lookahead idea and apply it to SBNDMq for q ≥ 3. As a result we get several new variations of SBNDMq. We introduce a greedy skip loop for SBNDM2. In addition, we tune up our algorithms an...

Many people in sub-Saharan Africa have to rely on meager water resources within mudstones for their only water supply. Although mudstones have been extensively researched for their low permeability behavior, little research has been undertaken to examine their ability to provide sustainable water supplies. To investigate the factors controlling the occurrence of usable ground water in mudstone ...

One of the methods of building the fundamentals of Differential Geometry is the shape operator approach and everything you could want to know about a surface’s curvature is locked up in the shape operator. In this work we consider the variation of the shape operator and the normal, the mean and the principals curvatures and, at last, the Willmore energy, under infinitesimal bending of surface g...

The calculus of variations is a branch of mathematical analysis that studies extrema and critical points of functionals (or energies). Here, by functional we mean a mapping from a function space to the real numbers. One of the first questions that may be framed within this theory is Dido’s isoperimetric problem (see Subsection 2.3): to find the shape of a curve of prescribed perimeter that maxi...

We give thirty-two diverse proofs of a small mathematical gem—the fundamental Euler sum identity ζ(2,1) = ζ(3) = 8 ζ(2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.

Are acquired characteristics inherited? We admit that individuals inherit a certain constitution, and that definite variations from this constitution are acquired during life-time, according to well-known laws. The question is: Are these definite acquired variations in any degree transmitted, or are the congenital variations in the constitution of the offspring independent of those which have b...

In one of the first papers about the complexity of puzzles, Robertson and Munro [12] proved that a generalized form of the thenpopular Instant Insanity puzzle is NP-complete. Here we study several variations of this puzzle, exploring how the complexity depends on the piece shapes and the allowable orientations of those shapes. Prepared in honor of Ian Munro’s 66th birthday.

HTTP cache servers reduce network traffic by storing popular files nearer to the client and have been implemented worldwide. Their reported performance on key metrics such as hit rate varies greatly. In order to optimise the design of the cache network this variation needs to be understood. The variation in hit rate across a number of caches is investigated and is shown to be partly stochastic ...

It has been appreciated for some time now that humans react differently to opioids. A specific opioid such as morphine sulfate may have specific analgesic effects for certain patients with postherpetic neuralgia whereas in other patients with postherpetic neuralgia, it may provide quite different analgesic qualities. Also, in any one individual patient a particular opioid may provide better ana...