Ricardo E. Monge

Osvaldo Skliar, Ricardo E. Monge, Sherry Gapper et al.

A novel Mathematical Random Number Generator (MRNG) is presented here. In this case, "mathematical" refers to the fact that to construct that generator it is not necessary to resort to a physical phenomenon, such as the thermal noise of an electronic device, but rather to a mathematical procedure. The MRNG generates binary strings - in principle, as long as desired - which may be considered genuinely random in the sense that they pass the statistical tests currently accepted to evaluate the randomness of those strings. From those strings, the MRNG also generates random numbers expressed in base 10. An MRNG has been installed as a facility on the following web page: http://www.appliedmathgroup.org. This generator may be used for applications in tasks in: a) computational simulation of probabilistic-type systems, and b) the random selection of samples of different populations. Users interested in applications in cryptography can build another MRNG, but they would have to withhold information - specified in section 5 - from people who are not authorized to decode messages encrypted using that resource.

Osvaldo Skliar, Ricardo E. Monge, Guillermo Oviedo et al.

The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT is used to analyze a sequence of samples (that is, of measured values) taken from an electroencephalographic recording.

Osvaldo Skliar, Sherry Gapper, Ricardo E. Monge

A characterization is provided for each natural number except one (1) by means of an ordered pair of elements. The first element is a natural number called the type of the natural number characterized, and the second is a natural number called the order of the number characterized within those of its type. A one-to-one correspondence is specified between the set of binary trees such that a) a given node has no child nodes (that is, it is a terminal node), or b) it has exactly two child nodes. Thus, binary trees such that one of their parent nodes has only one child node are excluded from the set considered here.

Osvaldo Skliar, Sherry Gapper, Ricardo E. Monge

A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although it is very simple, and easy to implement, it provides a very high level of security. According to this approach, a sequence of operations applied to a message ($M$) yields the encrypted message ($M_E$). In that series of operations, the one with the most important role is operation 6, which involves a random binary sequence (RBS) generated by using the Hybrid Random Number Generator (HRNG) or the Mathematical Random Number Generator (MRNG). A sequence of anti-operations applied to $M_E$ makes it possible to recover $M$.

Osvaldo Skliar, Ricardo E. Monge, Sherry Gapper

The Square Wave Method (SWM), previously introduced for the analysis of signals and images, is presented here as a mathematical tool suitable for the analysis of time series and signals. To show the potential that the SWM has to analyze many different types of time series, the results of the analysis of a time series composed of a sequence of 10,000 numerical values are presented here. These values were generated by using the Mathematical Random Number Generator (MRNG).

Osvaldo Skliar, Ricardo E. Monge, Sherry Gapper

A brief review is provided of the use of the Square Wave Method (SWM) in the field of signal and image analysis and it is specified how results thus obtained are expressed using the Square Wave Transform (SWT), in the frequency domain. To illustrate the new approach introduced in this field, the results of two cases are analyzed: a) a sequence of samples (that is, measured values) of an electromyographic recording; and b) the classic image of Lenna.