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Aerospace ◽  
2022 ◽  
Vol 9 (1) ◽  
pp. 24
Author(s):  
Fabio Celani

The purpose of this paper is to compare performances between stabilization algorithms of quaternion plus attitude rate feedback and rotation matrix plus attitude rate feedback for an Earth-pointing spacecraft with magnetorquers as the only torque actuators. From a mathematical point of view, an important difference between the two stabilizing laws is that only quaternion feedback can exhibit an undesired behavior known as the unwinding phenomenon. A numerical case study is considered, and two Monte Carlo campaigns are carried out: one in nominal conditions and one in perturbed conditions. It turns out that quaternion feedback compares more favorably in terms of the speed of convergence in both campaigns, and it requires less energy in perturbed conditions.


Author(s):  
Walter GOMIDE ◽  

In this short article, I try to show alternative maths to real numbers in such a way that these maths (especially Transreal Numbers by James Anderson and Arithmetic of Infinity by Yaroslav Sergeyev) can also be considered as legitimate instruments for presenting the structure of reality. I call this thesis of expanding the possibilities of understanding Nature mathematically the "Galileo Galilei´s thesis extended". As an example of the application of the thesis that the mathematics that is at the base of Nature must be extended to a better assessment of the scope of physical laws, here we present the Heisenberg´s Uncertainty Principle, approached in an alternative way from a mathematical point of view.


Author(s):  
Dalibor Martišek

So called Higuchi’s method of fractal dimension estimation is widely used and the term Higuchi’s fractal dimension even occurs in many publications. This paper deals with this method from mathematical point of view. Terms distance and dimension and its basic properties are explained and Higuchi’s dimension according the original source is defined. Definition of Higuchi’s dimension was comparated with mathematical definition of the distance and dimension. It is showed, that the definition of the Higuchi’s dimension does not satisfy axioms of distance and dimension. So called Higuchi’s method and Higuchi’s dimension are mathematically incorrect. Therefore, all results achieved by this method are scientifically unreliable.


Author(s):  
Tomasz Witczak

In this paper we analyse logic of false belief in the intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula $\varphi$ is not satisfied in a given world, but we still believe in it (or we think that it should be accepted). Another interpretations are also possible: e.g. that we do not accept $\varphi$ but it is imposed on us by a kind of council or advisory board. From the mathematical point of view, the idea is expressed by an adequate form of modal operator $\mathsf{W}$ which is interpreted in relational frames with neighborhoods. We discuss monotonicity of forcing, soundness, completeness and several other issues. We present also some simple systems in which confirmation of previously accepted formula is modelled.


Radiotekhnika ◽  
2021 ◽  
pp. 79-84
Author(s):  
D.V. Harmash

This work presents the analysis of the essence and possibilities of protection of the Rainbow post-quantum cryptographic algorithm. The main properties of the Rainbow algorithm and the general essence of cryptographic encryption and electronic signature algorithms based on multivariate quadratic transformations are determined. The main provisions regarding the protocols are given. Analyses are given regarding the ability to protect the algorithm against various attacks. The vulnerability of the algorithm to attack by third-party channels is investigated. The general provisions of the algorithm are considered. The algorithm is presented and considered from a mathematical point of view, as well as the mathematical essence of cryptographic algorithms for encryption and electronic signature based on multivariate quadratic transformations. The application of various methods of cryptanalysis against cryptographic algorithm based on multivariate quadratic Rainbow transformations is studied. The method of decreasing rank against the Rainbow algorithm is analyzed. The method of cryptanalysis by attacking the Oil-Vinegar scheme and the method of cryptanalysis "minranku method" are investigated. The attack is studied using a multilayer structure.


Author(s):  
Mario Spagnuolo ◽  
Antonio M. Cazzani

AbstractIn this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact with each other in at least three different ways: indirectly, through microstructural connections that could allow a relative sliding between the two families of fibers; directly, as the fibers of a family can touch each other and can scroll introducing dissipation. From a mathematical point of view, these effects are modeled first by introducing two placement fields for the two fiber families and adding a coupling term to the strain energy and secondly by adding two other terms that take into account the interdistance between the parallel fibers and the Rayleigh dissipation potential (to account for friction).


Author(s):  
Bruce Nevin

Summary Toward the end of his life, Zellig Harris (1909–1992) wrote a brief account of the origins and development of his work to establish the foundations of a science of language on mathematical principles. A French translation was published in 1990, and in the same publication appeared a parallel appraisal from a mathematical point of view by André Lentin (1913–2015). Early the following year, having reread Lentin’s essay several times, Harris wrote him the letter which is presented here. More than a gesture of thanks and appreciation, this letter further illuminates the comprehensive overview afforded by the two essays, both of which appeared in English in 2002.


2021 ◽  
Author(s):  
◽  
Victor Rolando Jara González

In this thesis he addressed the controlled Lagrangian control technique in two magnetic levitation systems, these being the fundamental object of study. An analysis of the natural dynamics of three mechanical systems was made; a simple pendulum, two pendulums attached to a xed beam and an inverted pendulum on a cart, which served to understand from a physical-mathematical point of view the presentation of the Lagrangian formalism. This analysis in mechanical systems was the basis in the study of the natural dynamics of the magnetic levitation systems treated. A geometrical stability analysis was also carried out, both for the mechanical systems and for the magnetic levitation systems; this constitutes the rst novelty as a result of the work. The presentation of the controlled Lagrangian control technique was explained in detail, taking as an example the inverted pendulum system on the cart, to later be implemented in magnetic levitation systems. The results obtained were satisfactory, demonstrating with them that this control technique makes sense in magnetic levitation systems, until now simple. From the mathematical point of view, the establishment of a control law in these magnetic levitation systems guarantees their stability in the understanding that the controlled dynamics will be equal to the desired one.


2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Poshan He

Non-conservative phenomena are very common and very important in physics. They have the characteristic of work divergence (if an object moves under non-conservative force, the work it does is related to the path) and this phenomenon does not satisfy the time reversal invariance. Therefore, they can cause many situations. From a mathematical point of view, they are similar to divergence in infinite series. Therefore, the infinite series can analyze non-conservative phenomena. This paper takes non-conservative force as an example to prove the relationship between non-conservative force and infinite series.


Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 314
Author(s):  
José A. Tenreiro Machado ◽  
Alexandra Galhano ◽  
Daniel Cao Labora

This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive arguments of why is it hard from the mathematical point of view. The second part is dedicated to the visualization of behaviors of the Collatz iteration function and the analysis of the results.


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