scholarly journals A teaching proposal for the study of Eigenvectors and Eigenvalues

2017 ◽  
Vol 7 (1) ◽  
pp. 100 ◽  
Author(s):  
María José Beltrán Meneu ◽  
Marina Murillo Arcila ◽  
Enrique Jordá Mora

In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students’ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

2012 ◽  
Vol 490-495 ◽  
pp. 2156-2159
Author(s):  
Wu Gang Li

In order to find the principal axes of inertia and calculate their moment of inertia to any plane homogeneous rigid body for calculating easily the moment of inertia to any axis of this rigid body, the principal axes could be found and their moment of inertia could be calculated automatically by using the reading-image of MATLAB to read the image messages about the flat surface of the rigid body and by the procedures which ware made according to the logic relation about the principal axis and the moment of inertia of the rigid body. Applying this method in a homogeneous cube, a result was acquired, error of which is small compared with the theoretical value. So this method is reliable, convenient and practical


2012 ◽  
Vol 2 (1) ◽  
pp. 28
Author(s):  
Luigi T. Bercades ◽  
Willy Pieter

<p class="MsoNormal" style="text-align: justify; margin: 0cm 0cm 6pt;"><span style="mso-ansi-language: EN-US;" lang="EN-US"><span style="font-size: small;"><span style="font-family: Calibri;">This study is a theoretical analysis of the kinematic and kinetic aspects of the modified taekwondo axe kick. The traditional or classical axe kick has the whole kicking leg (the thigh and the shank) considered as a rigid body on both the upswing and downswing phases of the kick, which is speculated to have sufficient angular momentum to increase the risk of some forms of injuries in competition. The present study seeks to present an alternate version that will decrease the moment of inertia on the downswing, reduce the subsequent angular momentum<em style="mso-bidi-font-style: normal;">, </em>and finally decrease the resultant impulse to the target. Theoretically, this will reduce the chances of certain types of injury caused by the kick.</span></span></span></p>


2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Huaju Liang ◽  
Hongyang Bai ◽  
Ning Liu ◽  
Xiubao Sui

Unpolarized sunlight becomes polarized by atmospheric scattering and produces a skylight polarization pattern in the sky, which is detected for navigation by several species of insects. Inspired by these insects, a growing number of research studies have been conducted on how to effectively determine a heading angle from polarization patterns of skylight. However, few research studies have considered that the pixels of a pixelated polarization camera can be easily disturbed by noise and numerical values among adjacent pixels are discontinuous caused by crosstalk. So, this paper proposes a skylight compass method based upon the moment of inertia (MOI). Inspired by rigid body dynamics, the MOI of a rigid body with uniform mass distribution reaches the extreme values when the rigid body rotates on its symmetry axes. So, a whole polarization image is regarded as a rigid body. Then, orientation determination is transformed into solving the extreme value of MOI. This method makes full use of the polarization information of a whole polarization image and accordingly reduces the influence of the numerical discontinuity among adjacent pixels and measurement noise. In addition, this has been verified by numerical simulation and experiment. And the compass error of the MOI method is less than 0.44° for an actual polarization image.


1982 ◽  
Author(s):  
Carol Zahner ◽  
M. Stephen Kaminaka

Chelovek RU ◽  
2020 ◽  
pp. 18-53
Author(s):  
Sergei Avanesov ◽  

Abstract. The article analyzes the autobiography of the famous Russian philosopher, theologian and scientist Pavel Florensky, as well as those of his texts that retain traces of memories. According to Florensky, the personal biography is based on family history and continues in children. He addresses his own biography to his children. Memories based on diary entries are designed as a memory diary, that is, as material for future memories. The past becomes actual in autobiography, turns into a kind of present. The past, from the point of view of its realization in the present, gains meaning and significance. The au-thor is active in relation to his own past, transforming it from a collection of disparate facts into a se-quence of events. A person can only see the true meaning of such events from a great distance. Therefore, the philosopher remembers not so much the circumstances of his life as the inner impressions of the en-counter with reality. The most powerful personality-forming experiences are associated with childhood. Even the moment of birth can decisively affect the character of a person and the range of his interests. The foundations of a person's worldview are laid precisely in childhood. Florensky not only writes mem-oirs about himself, but also tries to analyze the problems of time and memory. A person is immersed in time, but he is able to move into the past through memory and into the future through faith. An autobi-ography can never be written to the end because its author lives on. However, reaching the depths of life, he is able to build his path in such a way that at the end of this path he will unite with the fullness of time, with eternity.


Author(s):  
R. R. Palmer

In 1792, the French Revolution became a thing in itself, an uncontrollable force that might eventually spend itself but which no one could direct or guide. The governments set up in Paris in the following years all faced the problem of holding together against forces more revolutionary than themselves. This chapter distinguishes two such forces for analytical purposes. There was a popular upheaval, an upsurge from below, sans-culottisme, which occurred only in France. Second, there was the “international” revolutionary agitation, which was not international in any strict sense, but only concurrent within the boundaries of various states as then organized. From the French point of view these were the “foreign” revolutionaries or sympathizers. The most radical of the “foreign” revolutionaries were seldom more than advanced political democrats. Repeatedly, however, from 1792 to 1799, these two forces tended to converge into one force in opposition to the French government of the moment.


Upravlenie ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 116-122
Author(s):  
Sadeghi Elham Mir Mohammad ◽  
Ahmad Vakhshitekh

The article considers and analyses the basic principles and directions of Russian foreign policy activities during the presidency of V.V. Putin from the moment of his assumption of the post of head of state to the current presidential term. The authors determine the basic principles of Russia's foreign policy in the specified period and make the assessment to them. The study uses materials from publications of both Russian and foreign authors, experts in the field of political science, history and international relations, as well as documents regulating the foreign policy activities of the highest state authorities. The paper considers the process of forming the priorities of Russia's foreign policy both from the point of view of accumulated historical experience and continuity of the internal order, and in parallel with the processes of transformation of the entire system of international relations and the world order. The article notes the multi-vector nature of Russia's foreign policy strategy aimed at developing multilateral interstate relations, achieving peace and security in the interstate arena, actively countering modern challenges and threats to interstate security, as well as the formation of a multipolar world. The authors conclude that at present, Russia's foreign policy activity is aimed at strengthening Russia's prestige, supporting economic growth and competitiveness, ensuring security and implementing national interests. Internal political reforms contribute to strengthening the political power of the President of the Russian Federation and increasing the efficiency of foreign policy decision-making.


2012 ◽  
pp. 66-80
Author(s):  
Michał Mrozowicki

Michel Butor, born in 1926, one of the leaders of the French New Novel movement, has written only four novels between 1954 and 1960. The most famous of them is La Modification (Second thoughts), published in 1957. The author of the paper analyzes two other Butor’s novels: L’Emploi du temps (Passing time) – 1956, and Degrés (Degrees) – 1960. The theme of absence is crucial in both of them. In the former, the novel, presented as the diary of Jacques Revel, a young Frenchman spending a year in Bleston (a fictitious English city vaguely similar to Manchester), describes the narrator’s struggle to survive in a double – spatial and temporal – labyrinth. The first of them, formed by Bleston’s streets, squares and parks, is symbolized by the City plan. During his one year sojourn in the city, using its plan, Revel learns patiently how to move in its different districts, and in its strange labyrinth – strange because devoid any centre – that at the end stops annoying him. The other, the temporal one, symbolized by the diary itself, the labyrinth of the human memory, discovered by the narrator rather lately, somewhere in the middle of the year passed in Bleston, becomes, by contrast, more and more dense and complex, which is reflected by an increasinly complex narration used to describe the past. However, at the moment Revel is leaving the city, he is still unable to recall and to describe the events of the 29th of February 1952. This gap, this absence, symbolizes his defeat as the narrator, and, in the same time, the human memory’s limits. In Degrees temporal and spatial structures are also very important. This time round, however, the problems of the narration itself, become predominant. Considered from this point of view, the novel announces Gerard Genette’s work Narrative Discourse and his theoretical discussion of two narratological categories: narrative voice and narrative mode. Having transgressed his narrative competences, Pierre Vernier, the narrator of the first and the second parts of the novel, who, taking as a starting point, a complete account of one hour at school, tries to describe the whole world and various aspects of the human civilization for the benefit of his nephew, Pierre Eller, must fail and disappear, as the narrator, from the third part, which is narrated by another narrator, less audacious and more credible.


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