Dealing with NeutroGeometry in true, false, and uncertain regions is becoming of great interested for researchers. Not too many studies have been done on this topic, for that reason, aim of this work ...is to define a new method to deal with NeutroGeometry in true, false, and neutrogeometry (T,C,I,F). Furthermore, some real-life application examples in 3D computer graphics, Astrophysics, nanostructure, neutrolaw, neutrogender, neutrocitation, neutrohealth-food, neutroenvironment and quantum space are presented.
General scaling rules or constants for metabolic and structural plant allometry as assumed by the theory of Euclidian geometric scaling (2/3-scaling) or metabolic scaling (3/4-scaling) may meet ...human's innate propensity for simplicity and generality of pattern and processes in nature. However, numerous empirical works show that variability of crown structure rather than constancy is essential for a tree's success in coping with crowding. In order to link theory and empiricism, we analyzed the intra-and inter-specific scaling of crown structure for 52 tree species. The basis is data from 84 long-term plots of temperate monospecific forests under survey since 1870 and a set of 126 yield tables of angiosperm and gymnosperm forest tree species across the world. The study draws attention to (1) the intra-specific variation and correlation of the three scaling relationships: tree height versus trunk diameter, crown cross-sectional area versus trunk diameter, and tree volume versus trunk diameter, and their dependence on competition, (2) the inter-specific variation and correlation of the same scaling exponents (α h,d , α csa,d and α v,d ) across 52 tree species, and (3) the relevance of the revealed variable scaling of crown structure for leaf organs and metabolic scaling. Our results arrive at suggesting a more extended metabolic theory of ecology which includes variability and covariation between allometric relationships as prerequisite for the individual plant's competitiveness.
The inter-disciplinary workshop, entitled 'A New World… Out of Nothing' took place at the University of Warwick during November 2016. This critical review will explore the rationale for the event and ...its features, drawing on the organiser's views on inter-disciplinarity and communicating pure mathematics to a wider audience. The workshop was organised by Francesca Iezzi, who has recently finished a PhD in pure Mathematics and is a fellow of the supporting institutions, the Warwick Institute for Advanced Study (IAS) and the Warwick Institute for Advanced Teaching and Learning (IATL).
Computing the area of an arbitrary polygon is a popular problem in pure mathematics. The two methods used are Shoelace Method (SM) and Orthogonal Trapezoids Method (OTM). In OTM, the polygon is ...partitioned into trapezoids by drawing either horizontal or vertical lines through its vertices. The area of each trapezoid is computed and the resultant areas are added up. In SM, a formula which is a generalization of Green’s Theorem for the discrete case is used. The most of the available systems is based on SM. Since an algorithm for OTM is not available in literature, this paper proposes an algorithm for OTM along with efficient implementation. Conversion of a pure mathematical method into an efficient computer program is not straightforward. In order to reduce the run time, minimal computation needs to be achieved. Handling of indeterminate forms and special cases separately can support this. On the other hand, precision error should also be avoided. Salient feature of the proposed algorithm is that it successfully handles these situations achieving minimum run time. Experimental results of the proposed method are compared against that of the existing algorithm. However, the proposed algorithm suggests a way to partition a polygon into orthogonal trapezoids which is not an easy task. Additionally, the proposed algorithm uses only basic mathematical concepts while the Green’s theorem uses complicated mathematical concepts. The proposed algorithm can be used when the simplicity is important than the speed.
Introducción. La geometría fractal caracteriza los objetos irregulares de la naturaleza incluyendo el cuerpo humano. Objetivo. Desarrollar una metodología geométrica que permita diferenciar, en un ...modelo experimental de restenosis de arterias de porcino, las arterias normales de las patológicas, mediante la aplicación simultánea de la geometría fractal y euclidiana. Materiales y métodos. Para el estudio se tomaron siete (7) imágenes de placas histológicas de arterias normales, y siete (7) de arterias restenosadas, calculando simultáneamente tanto la dimensión fractal de las capas arteriales mediante el método de Box-Counting como el número de cuadros ocupados por las superficies de tres islas o capas arteriales. Posteriormente, se calculó la armonía matemática intrínseca y, finalmente, se establecieron las diferencias entre grupos. Resultados. Los valores del número de cuadros ocupados por la superficie de las siete arterias normales oscilaron entre 27 y 74, y para las restenosadas estuvieron entre 83 y 176; el valor de la dimensión fractal varió entre 0.9241 y 1.2578 para las arterias normales, y para las reestenosadas osciló entre 0.7225 y 1.2937. Conclusión. La metodología desarrollada en el presente trabajo logró diferenciar geométricamente y de manera objetiva las arterias normales de las arterias restenosadas a partir de los espacios de ocupación.
Why the mathematics bears this power of ‘dragging along’ in physics theories? It looks that certain mathematical structures are more convenient to physics than other ones, which seems to evidence the ...presence of some dissimulated physical content in certain mathematical theories. In the case of General Relativity, these mathematical concepts seem to be the ones of continuous surface (or curvature, in a general form) – already foreseen by Gauss and Riemann, who searched for an effective space geometry – and, lastly, invariant, which allowed to express general covariance in an non-equivocal way, by means of tensional calculus. The path stepped by physics in the early 20th century allowed finding the answer to the question made by Gauss and Riemann about space structure.
While representing a true watershed in the development of mathematics, in their original formulations the postulates of Euclid for Planar Geometry are not easy to understand. In fact, according to ...present day standards of rigor, they need to be made more precise as well as to be supplemented by additional statements.
This paper arose out of a study of the notes that Joseph Agassi and Czeslaw Lejewski took at Karl Popper's seminar on Logic and Scientific Method (1954–1955).1 It ponders on a basic logical ...distinction Popper had made: between sound inference (valid inference with sound premises) and proof (a collection of inferences that show that a given sentence follows from any premise). The difference between sound inference and proof seems crucial to Popper's epistemology, especially to his emphasis on the distinctness of epistemology and methodology. In this paper, (1) The distinction is explained; (2) The difference is presented as the basis for Popper's view of the history of logic; (3) Some modern hesitations about all this are discussed.
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