This paper presents a general analysis of all the quartic equations with real coefficients and multiple roots; this analysis revealed some unknown formulae to solve each kind of these equations and some precisions about the relation between these ones and the Resolvent Cubic; for example, it is well-known that any quartic equation has multiple roots whenever its Resolvent Cubic also has multiple roots; however, this analysis reveals that any non-biquadratic quartic equation and its Resolvent Cubic always have the same number of multiple roots; additionally, the four roots of any quartic equation with multiple roots are real whenever some specific forms of its Resolvent Cubic have three non-negative real roots. This analysis also proves that any method to solve third-degree equations is unnecessary to solve quartic equations with multiple roots, despite the existence of the Resolvent Cubic; finally, here is developed a generalized variation of the Ferrari Method and the Descartes Method, which help to avoid complex arithmetic operations during the resolution of any quartic equation with real coefficients, even though this equation has non-real roots; and a new, more simplified form of the discriminant of the quartic equations is also featured here.

In this work, we study the effects of geometric confinement on the point statistics in a quasi-low-dimensional system. Specifically, we focus on the nearest-neighbor statistics. Accordingly, we have performed comprehensive numerical simulations of binomial point process on quasi-one-dimensional rectangle strips for different values of the confinement ratio defined as the ratio of the strip width to the mean nearest-neighbor distance. We found that the nearest-neighbor distance distributions (NNDDs) conform to an extreme value Weibull distribution with the shape parameter depending on the confinement ratio, while the process intensity remains constant. This finding reveals the reduction of effective spatial degrees of freedom in a quasi-low-dimensional system under the geometric confinement. The scale dependence of the number of effective spatial degrees of freedom is found to obey the crossover ansatz. We stress that the functional form of the crossover ansatz is determined by the nature of the studied point process. Accordingly, different physical processes in the quasi-low-dimensional system obey different crossover ansatzes. The relevance of these results for quasi-low-dimensional systems is briefly highlighted.

The purpose of this survey is twofold. First, we survey the studies of percolation on fractal networks. The objective is to assess the current state of the art on this topic, emphasizing the main findings, ideas and gaps in our understanding. Secondly, we try to offer guidelines for future research. In particular, we focus on effects of fractal attributes on the percolation in self-similar networks. Some challenging questions are outlined.

The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension D which exceeds the topological dimension d. In this regard, we point out that the constitutive inequality D>d can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined.

Performing a clinical pre-diagnosis of a cardiac pathology in a public institution in Mexico, takes waiting time, so the proposed system aims to reduce the time of diagnosis, and aims to resolve this deficiency, since having a mathematical algorithm can be programmed and implemented on any platform with an operating system, reducing the cost of the equipment, since only electrodes are required. In addition, it can be implemented in mobile equipment, which would increase its portability.

In spite of the advances in the state of the art in semantic artificial intelligence applications, there is still a long way to go to bring it to a level of mass adoption. Thus, in order to contribute to the advancement of this topic, this study develops a feasible model with a potential scalability for semantic applications’ mass adoption, specifically for news or statement cluster attribute identification, either positive, negative or neutral. This paper proposes a disruptive system based on Blockchain using a Semantic Browser Expert System Bot with artificial intelligence called Blockchain Semantic Browser Expert System (BSBES) to look for and analyze relevant information that significantly represents the cryptocurrencies adoption patterns. The artificial intelligence in this study consists of a deep learning neural network to process the input information to identify the news pattern in a semantic way using deep learning based on two aspects of the news: technical aspect and adoption aspect of the cryptocurrencies. BSBES performance is achieved based on deep learning tools, and scalability is supported by a blockchain system including a stability study.

The dynamics seismic activity occurred in the Cocos Plate-Mexico is analyzed through the evolution of Hurst exponent and 3D fractal dimension, under the mathematical fractal structure based on seismic activity time series, taking into account the magnitude (M ) as the main parameter to be estimated. The seismic activity time series and, annual intervals are considered first for finding the Hurst exponent of each year since 1988 (the year in which the database is consistent) until 2012, and then the following years are accumulated describing the cumulative Hurst exponent. The seismic activity description is based on Cocos Plate data information; during a period conform from 1 January 1988 to 31 December 2012. Analyses were performed following methods, mainly considering that the Hurst exponent analysis provides the ability to find the seismicity behavior time-space, described by parameters obtained under the fractal dimension and complex systems.

La taza es uno de los artefactos más antiguos y que menos cambios ha presentado a través del tiempo, sin embargo, el diseño tradicional presenta dos limitantes: la incapacidad de almacenaje espacial y el desperdicio de área perimetral. En este trabajo se propone el desarrollo de un prototipo de taza basado en la descomposición del plano Euclidiano, específicamente en la utilización del hexágono como figura principal. La disminución del desperdicio perimetral se ha logrado modificando el asa lateral externa de forma tal que quede contenida en una de las caras laterales del hexágono permitiendo la optimización del espacio cúbico en lugares reducidos de almacenamiento; para lograr un estibaje vertical en varios niveles se incorporó una base circular que facilita la interconectividad de las piezas al momento de su estibación. Por otra parte, la forma ergonómica y estética del nuevo diseño facilita su sujeción durante su uso y manipulación. La descripción de las partes que integran el diseño, así como su justificación, se tratan a continuación