Abstract When we have a digital image which contains some objects and a ruler, we know the size of objects by rough estimate. Since measuring the object size in the digital image is usually manual, we developed the detection method of scale interval on a ruler. In our method we transfer digital image into frequency space using two-dimensional discreet fourier transformation, a specific frequenc...

This paper relates democracy, public and private international capital flows, and odious debt. Democracy commits a ruler to pass borrowed funds on to the private sector which builds the country’s international collateral, and the consequent rise in the credit ceiling is a Pareto-improvement up to a point because the ruler can appropriate a smaller share of rising loan. However, the ruler may st...

Geometric Algebra is a very general mathematical system providing simultaneously a geometrification of algebra, and also an algebrification of geometry. As an example, we present a specific Geometric Algebra, that we call Compass Ruler Algebra, which is very well suited to compute similar to working with compass and ruler. Geometric objects such as circles and lines as well as geometric operati...

A Golomb ruler with m marks can be defined as a set of m distinct integers such that the differences between them are all distinct. An optimal Golomb ruler minimizes the value of the largest mark. The Golomb ruler problem is highly combinatorial and difficult to solve efficiently even for small sizes. Golomb rulers and related problems play an important role in, e.g., radio communication, VLSI ...

The Golomb ruler problem has been proposed as a challenging constraint satisfaction problem. We consider a large number of di erent models of this problem, both binary and non-binary. The problem can be modelled using quaternary constraints, but in practice using a set of auxiliary variables and ternary constraints gives better results. A binary encoding of the problem gives a smaller search tr...

Since 1968, when the Golomb–Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb–Welch conjecture. Further, new results on Golomb–Welch con...

The Math Factor podcast posed the problem of finding the smallest number of inch marks on a 12 inch ruler so that one could still measure any integer length from 1 to 12. One needs only four additional marks besides 0 and 12; for example 1, 4, 7, 10 works. This entertaining problem lead to others during the next few minutes (you can listen at mathfactor.uark.edu/2005/10) and inspired us to look...

In the early 1950s, Golay studied binary sequence pairs whose autocorrelation properties are ideal for use in the design of multislit spectrometers. He found examples for some small lengths, but, unable to find more, he suggested that perhaps further examples do not exist and turned his attention to an alternative solution to the design problem (involving what are now called Golay complementary...

The Golomb Ruler problem consists in finding n integers such that all possible differences are distinct and such that the largest difference is minimum. We review three lower bounds based on linear programming that have been proposed in the literature for this problem, and propose a new one. We then show that these 4 lower bounds are equal. Finally we discuss some computational experience aimin...