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Climate change has brought increased temperatures and decreased rainfall on a global scale; however, population growth requires greater volumes of water and food each year that must be supplied in one way or another. In Mexico, application efficiencies in gravity irrigation are below 50%. Although in recent years the decision has been made to change to pressurized irrigation systems to increase the efficiency of water use, border or furrow irrigation is still the most widely used in agriculture. In this work, we show that with a methodology developed and applied in these systems, application efficiencies greater than 90% were obtained, while the Water Use Efficiency (WUE) increased by 27, 38 and 47% for the three crops where it was applied: sorghum, barley, and corn, respectively. Irrigation times per hectare and applied irrigation depths decreased by more than 30%, representing increased irrigation efficiencies and WUE. Finally, the water savings obtained can mitigate water scarcity in cities.

The present work proposes a new model to capture high heterogeneity of single phase flow in naturally fractured vuggy reservoirs. The model considers a three porous media reservoir, namely, fractured system, vugular system and matrix, the case of an infinite reservoir is considered in a full-penetrating wellbore. Furthermore, the model relaxes classic hypotheses considering that matrix permeability has a significant impact on the pressure deficit from the wellbore, reaching the triple permeability and triple porosity model wich allows the wellbore to be fed by all the porous media and not exclusively by the fractured system, where it is considered a pseudostable interporous flow. In addition, it is considered the anomalous flow phenomenon from the pressure of each independent porous medium and as a whole, through the temporal fractional derivative of Caputo type, the resulting phenomenon is studied for orders in the fractional derivatives in (0, 2), known as superdiffusive and subdiffusive phenomena. Synthetic results highlight the effect of anomalous flows throughout the entire transient behavior considering a significant permeability in the matrix and it is contrasted with the effect of an almost negligible matrix permeability. The model is solved analytically in the Laplace space, incorporating the Tartaglia&ndash, Cardano equations.

Growth models have been widely used to describe behavior in different areas of knowledge, among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases, this model is generalized by including the Caputo-type fractional derivative of order 0&lt, β≤1, resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination R2&gt, 0.999.

Concentrator photovoltaic systems get the highest conversion efficiencies among all solar applications. However, they need to increase their efficiency even more to compete with traditional photovoltaic systems. The hybridization with thermoelectric generators allows recovering part of the waste heat and converting it to electricity, enhancing the global efficiency. The physical model of hybrid thermoelectric-concentrator photovoltaic module involves five non-linear equations. In this paper, two adapted Newton-Raphson methods using fractional derivatives are developed to solve such non-linear system, one using the conformable derivative operator and the other using the Riemann-Liouville fractional derivative. Both methods are mathematically innovative and are applied within the photovoltaic field for the first time. They can be used in energy prediction or in design optimisation. As an example of application, one month of real atmospheric data from Jaen, Southern Spain, were processed with the help of the developed methods. The performance outputs of the hybrid system were analysed giving interesting findings on their real behaviour, which is largely unknown nowadays. Linear functions dependent on direct normal irradiance can approximate the total generated power with 12.8 W/m2 root mean squared error and, the thermoelectric efficiency with 0.08% error.

The principal objective of neural rehabilitation therapies is helping affected people to recover their mobility and reduce their dependency to other people in personal and occupational life. The way neural rehabilitation therapies are applied used to be based on the experience of the therapists and the epidemiological data available. Meanwhile, computer games (serious games), specially, based on virtual reality, are already used to treat exclusively certain types of phobia considering that an effective therapy consists on exposing patients to the source of their pathological fear within a controlled and safe environment. At present, at National Autonomous University of Mexico we are developing a set of applications based on videogames technology, programming them by the Unity SDK. The idea is helping patients to recover their mobility, which was lost by a neurological accident, or to confront their phobia. In this work we present the corresponding advances. In the case of neural rehabilitation, we focus the applications for ocular, head and neck recovery, developing some 3D scenarios for the Oculus Rift device. Respect to phobia treatment we consider attending arachnophobia, acrophobia and aviophobia, developing some 3D scenarios for Card Boards and also the Oculus Rift.

We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM) accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H, the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging) in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean HR/S=0.15), significantly different to Andosol under conventional tillage (HR/S=0.47).

The standardisation in architectural orientation and construction forms, as well as the symmetric and highly proportional spatial distribution of buildings, suggest that the major structures of Teotihuacan were laid out from its inception according to a master plan (or plans) intended to express a specific worldview in material form. Fractal analysis of the Teotihuacan radar image and aerial photographs has confirmed that a master plan does exist in this archaeological area. The Sierpinski carpet, one of the best known deterministic fractal models, is proposed as the model for Teotihuacan in two-dimensional Euclidean space. Its dimension (1·89) is also proposed as the basic unit which joins in space the Mesoamerican calendar and the buildings' geometrical measures. It is hypothesised that inside the master plan of Teotihuacan, the information pertaining to space is expressed across the two-dimensional planes, and that of time through the pyramid verticals. A value of 0·83 m, which corroborates with the Teotihuacan measurement unit (TMU) proposed by different anthropologists, was derived from an analysis of the height of the Sun and Moon Pyramids. These results open new prospects for future comparisons between different settlements and monuments, that were supposedly constructed by the people from Teotihuacan.

Self-similar fractals are useful models for soil solid and pore sets. The scaling properties of these fractals along a line and across an area can be described by the fractal dimensions. One method, for estimating the soil areal fractal dimension from the solid and pore set distributions along the lines, was proposed and tested with real macro- and micromorphological data on three soils of Mexico. The soil areal fractal dimension ( D a ) was compared with the soil mass fractal dimension ( D m ) estimated by two-dimensional binary image analysis, separately for solids and pores. Both methods are based on the box-counting technique and are suitable for determining the soil `box' or `capacity' fractal dimension, that seems to be apt to estimate the alternative filling of an area by a fractal set of solids and pores. This paper examines the relations between the fractal dimensions obtained along a line, across an area and directly from the image. Analysis of D a and D m data seems to suggest that both soil genesis and management practice can contribute to areal fractal dimension dynamics. It was shown that fractal dimensions are useful parameters able to monitor tillage influence on soil properties and to estimate the degree of soil compaction.

A necessary and sufficient condition on a sequence { A n}n ∈ Nof σ-subalgebras that assuresLp-convergence of the conditional expectations is given. This result generalizes theLp-martingales, the Fetter and the Boylan (equiconvergence) theorems.

The purpose of this study was to document the fractal nature of three soils of Mexico with contrasting genesis and marked differences in morphology and to estimate the fractal dimensions of their sets of aggregates and pores. These dimensions were estimated along lines and were called linear fractal dimensions. A single, ‘ideal’ fractal dimensionality was detected in the three soils studied. The soil linear fractal dimensions, calculated from macro and micromorphological data, had larger values than the dimension of the Cantor fractal dust model, but were less than unity. It was shown, that the fractal structure of the soil pore space could not be described by the same dimension as that of the aggregates. The linear fractal dimensions of soils of distinct genesis, were significantly different on all scales compared, but the differences fluctuated between 0.4% and 9.1%.

Currently gravity irrigation remains the most widely used in agricultural areas and 90 percent of plantings, the water is applied to the plots by gravity. One of the main problems with these systems is erosion, which is a by product of the erosive forces of water over the row, which brings soil loss and therefore decreases in crop yield. Erosion is the removal of surface soil material caused by water or wind (Kirkby, 1984). It is caused by several factors, such as steep slopes, climate, inadequate use of soil, vegetation cover and natural disasters; however, human activities can greatly accelerate erosion rates. This phenomenon is considered a severe problem because it is associated with inappropriate agricultural practices, overgrazing, poor utilization of forests, thickets, grasslands, forests, and changes in land use from forest land primarily for agricultural purposes. According to Becerra (2005), the two main types of erosion are geological erosion and accelerated erosion. Geological erosion includes both training and erosive processes, which maintain the soil in a favorable balance, suitable for plant growth. Accelerated erosion and loss of soil degradation is a result of human activities. Geological erosion when the soil is found in its natural environment under the cover of native vegetation. This type of erosion is responsible for the formation of soils and its distribution on the Earth's surface. The long-term effect of this type of erosion has led to larger landscape features such as canyons, meandering rivers, and valleys. In other words, this type of erosion is the result of the action of water, wind, gravity and glaciers. Accelerated erosion, soil loss is usually associated with changes in vegetation and soil conditions and is caused mainly by water and wind. The forces involved in accelerated erosion are: (1) attack forces, which remove and transport the soil particles, (2) resistance forces, which limit the erosion. Soil erosion is the main source responsible for the gradual decrease in fertility and therefore the productive capacity of soils. Erosion caused by hydric erosion, include the action of rain and runoff. In general, water erosion is divided into erosion or splashing raindrops, sheet erosion, rill erosion, gully erosion and irrigation channels. Soil splashing occurs when raindrops fall directly onto the soil particles or very thin areas of water, spraying huge amounts of soil due to the kinetic energy of impact. In plane soils, the

El movimiento y la distribución de fl uidos a través de los medios porosos están determinados por su geometría. La naturaleza autosimilar de la estructura de estos medios ha sido el objeto de numerosos estudios que han documentado las relaciones de potencia (‘power law’) entre las principales medidas de poros y sólidos, y la resolución del método utilizado para su análisis. En la presente investigación se introduce un esquema fractal para clasifi car los yacimientos naturalmente fracturados (YNF) a partir de imágenes de tomografía computarizada de rayos X. Esta clasifi cación tiene como propósito extraer y medir algunos rasgos geométricos de los poros tanto a nivel global (fi rmagrama), como local (líneas de referencia) vía los clasifi cadores fractales. Los clasifi cadores fractales, extraídos de las imágenes digitales, fueron útiles para hacer un diagnóstico simple y rápido del tipo de porosidad de un núcleo a partir de su imagen. La dimensión fractal de masa (Dm), la dimensión espectral o fractón ( #9135;d), el exponente de Hurst (H) y la lagunaridad ( #923;) de los YNF del sureste de México, son estadísticamente diferentes para los tres patrones de porosidad representativos de estos materiales: fracturas, cavidades y porosidad mixta. Para estimar los primeros dos (Dm y #9135;d), es necesario presegmentar la imagen en conjuntos de poros y sólidos, creando una imagen binaria, previo a la cuantifi cación fractal. En los últimos (H y #923;), la extracción de los parámetros se realiza directamente a partir de las imágenes originales evitando el proceso de segmentación, lo que permite proponer a los clasifi cadores H y #923; como estimadores más confi ables de la porosidad de los YNF. Todos los clasifi cadores fractales, y en especial la dimensión fractal de masa y la lagunaridad de los tres patrones de porosidad arriba especifi cados, mostraron una correlación estadísticamente signifi cativa con la porosidad (medida con técnicas tradicionales) de las capas geológicas con distinta capacidad productora de hidrocarburos. Este hecho abre un nuevo panorama para la modelación y pronóstico de la geometría de los YNF.