Mathematical simulation analysis of optimal testing of shot puter's throwing path

Objective To study the mathematical simulation analysis of shot-putter throwing optimal path. Methods Shot put was simplified as a parabolic motion of a particle, the corresponding mathematical model was established, and the mathematical relationship between the throwing distance and the initial velocity of shot put, the shooting Angle and the shooting height was defined. Results The fitting formula between shooting speed and shooting Angle was obtained by using the fitting method, and the quantitative relationship between them and the ideal shooting Angle was identified. Conclusion The mathematical principle of shot put is revealed through the process of building a model from simple to complex. However, there are still many problems to be solved, among which the height problem is a complex one. At the present level, it is not possible to find a reasonable height, because it involves many factors. However, the development of grey mathematics will provide a beneficial attempt for it to establish a reasonable and scientific model.

Mathematical Principle Analysis of Separation Point Prediction

During the development of fluid mechanics, fluid separation is an important issue. So far, there is no mathematical formula to reveal and describe the essence of fluid separation. At the same time, due to the high cost and limitation of the experimental method, another method is urgently needed to predict the separation position of the fluid. After axiomatizing fluid mechanics and combining the principle of excited state of quantum mechanics, this paper reveals that fluid separation is a special form of fluid in an excited state, and deduces the state conditions of fluid separation. The research results of this paper provide new ideas for solving problems in fluid separation and engineering applications.

PROBABILISTIC APPROACH TO DETERMINING PRODUCTION FUNCTIONS

The article considers a probabilistic method for determining production functions. The method consists in finding the expected value of the function that determines the economic and mathematical principle of production. It is assumed that the factors of production and/or their specific values included in this function are random variables. It is shown that depending on the principle of production such averaging gives different probabilistic classes of production functions. Functions that are elements of the same class differ from each other in the probability distribution of the relations of production factors to their specific values. Two probabilistic classes of produc-tion functions are constructed. The first class is generated by the Leontief production principle, the second – by generalization of this principle for the case of partially or completely fungible factors of production. There are established the laws of probability distribution and the conditions, under which the linear combination of the AK-model and the Cobb-Douglas production function, as well as the CES production function, are elements of the class of Leontief production functions. It is shown that the linear production function belongs to the class of generalized Leontief production functions. The probability density functions of the products number for these two classes of pro-duction functions are found.

Making things up

In Anaxagoras’s ontology, the Opposites are primitively numerically and qualitatively the same, and exist extremely mixed with each other, according to his ‘Everything in Everything Principle’. Their extreme mixture is facilitated by their being gunky, that is, divided into (proper) parts that have (proper parts) ad infinitum. The chapter examines how objects ‘emerge’ out of gunk, in this system, and how they are qualitatively differentiated in their extreme mixture. Anaxagoras’s ontology is built on a mathematical principle—the unlimited division of the Opposites—whereby Anaxagoras implicitly endorses what we might call the normativity of mathematics on the physical world, which we will encounter again in Plato’s theory of Forms. The chapter examines in more detail the constitution of objects as bundles of properties, which Plato will also adopt, and the reification of structure as seeds, a stance from which Plato will depart.

Information Theory: Deep Ideas, Wide Perspectives, and Various Applications

The history of information theory, as a mathematical principle for analyzing data transmission and information communication, was formalized in 1948 with the publication of Claude Shannon’s famous paper “A Mathematical Theory of Communication” [...]

An Analogical Investigation of the Pythagorean Triangle: From a Mathematical Figure to an Ethical Praxis

This paper exposes an alternative and juxtaposed interdisciplinary view of the Pythagorean Triangle, from a mathematical point of view to ethical applicability. Pythagorean Theorem is understood as a mathematical principle (a2+b2=c2), where the sum of the square of the shorter legs, a and b, is equal to the square of the most extended leg, the hypotenuse, c, resulted in the equation of the right triangle (Pythagorean Triangle). As an antediluvian mathematical figure, the Pythagorean Triangle's beauty and intricacy still amazed and provoked present-day thoughts. It is indubitable that the Theorem intrigues humanity's curiosity to provide proofs of the hypothesis, as well as its application. From such a viewpoint, this paper looks into the interdisciplinary applicability of the mathematical figure of the right triangle (Pythagorean Triangle). Utilizing analogical investigation, as the prime method of this research, the paper argues that the concept of the 'right triangle' could be an analogy for 'right living.' The logic behind the Pythagorean Triangle posits inherent beauty and a transcendent possibility beyond mathematics to other disciplines like ethics. The paper offers an analogical investigation of an alternative insight for the ethical problem of 'right living.' By reflecting on the presence of the existing similar feature, the right triangle (Pythagorean Triangle) could be analogically applied to 'right living.' From extant literature, the paper concludes that uprightness and balance are two essential concepts that could propose alternative ethical views by analogy to understanding what it means for 'right living.' Received: 12 October 2020 / Accepted: 12 December 2020 / Published: 17 January 2021

DISTRIBUTION DEPENDENT CORRELATIONS: A MATHEMATICAL PRINCIPLE UTILIZED IN PHYSIOLOGY, OR CORRELATION BIAS?

In many studies, we may raise the question of whether relative amounts of particular variables are positively or negatively associated, but investigations specifically focusing upon this issue seem hard to find. Previously, we reported some general rules for associations between relative amounts of positive scale variables. The main research question of the present work was: How are correlations between percentages of the same sum brought about? One particular feature of such correlations seemed to be that distributions (ranges) of the variables were crucial for obtaining either positive or negative correlations, and for their strength, suggesting the name Distribution Dependent Correlations (DDC). Certainly, such correlations might cause bias. However, previous findings raise the question of whether DDC might have a physiological relevance as well. In the current work, we extend and systematize theoretical considerations, and show results of computer experiments to test the hypotheses. Finally, we briefly mention a couple of examples from physiology. The results seem to support the idea that true, within-person distributions of the variables are crucial for obtaining positive or negative correlations between their relative amounts, raising the question of whether evolution might utilize DDC to regulate metabolism.

A Mathematical Principle of Art and Human Vision

The study of visual illusions is an old subject and an important part of the psychology of human visual perception, but hitherto there has been no single principle able to explain radically different kinds of visual illusions conjointly. Such a principle does exist, as is to be shown, and has the virtue of being rigorous: it is the mathematical theory of Fourier analysis. A great many visual illusions are what happen when the visual objects involved undergo certain frequency filtering, a concept deduced from Fourier analysis. Phenomena thus explained belong in these distinct categories: brightness illusions, colour illusions, geometrical illusions, and motion illusions, all of which have been simulated with computer programmes based on this mathematical principle. Visual illusions obeying this principle have in fact been depicted in Western painting for centuries, and art can in certain ways shed light on the quest for the understanding of human vision.