scholarly journals The Three Reflections Theorem Revisited

KoG ◽  
2018 ◽  
pp. 41-48
Author(s):  
Gunter Weiss

It is well-known that, in a Euclidean plane, the product of three reflections is again a reflection, iff their axes pass through a common point. For this ``Three reflections Theorem'' (3RT) also non-Euclidean versions exist, see e.g. [4]. This article presents affine versions of it, considering a triplet of skew reflections with axes through a common point. It turns out that the essence of all those cases of 3RT is that the three pairs (axis, reflection direction) of the given (skew) reflections can be observed as an involutoric projectivity. For the Euclidean case and its non-Euclidean counterparts this property is automatically fulfilled. From the projective geometry point of view a (skew) reflection is nothing but a harmonic homology. In the affine situation a reflection is an indirect involutoric transformation, while ``direct'' or ``indirect'' makes no sense in projective planes. A harmonic homology allows an interpretation both, as an axial reflection and as a point reflection. Nevertheless, one might study products of three harmonic homologies, which result in a harmonic homology again. Some special mutual positions of axes and centres of the given homologies lead to elations or even to the identity, too. A consequence of the presented results are further generalisations of the 3RT, e.g. in planes with Minkowski metric, affine or projective 3-space, or in circle geometries.

Author(s):  
R. A. Orekhov ◽  

There is a common point of view in Egyptology that Memphis was a state capital since the earliest times and that its protecting gods were Ptah and his spouse Sekhmet. Arguing this concept, the author tries to find the reason why a pyramid city of Pepi I — Mennefer — became a core of the future capital. The main conclusion is following: Constructing his pyramid complex, Pepi I probably included into it a cult center of Habes where Bastet and Imhotep, a high priest of Ra, were worshiped. Imhotep, a companion of the king Djoser, was known as a priest and charmer who tamed the fiery forces of Sirius associated with Bastet, after which the great drought was over. To commemorate this, New Year celebration and the first sun calendar were established. Imhotep’s tomb became an important cult place, where ceremonies important for surviving of the Egyptian state were conducted. In the second half of the Old Kingdom period the Nile started to flood much less, which led to the decline of agriculture. Thus, the role of the cult center of Habes and Imhotep grew greatly. By including Habes, Pepi protected the dominion of his pyramid city from negative influence of Bastet and decreased flooding. The fact that Mennefer was a successor of the aforementioned cult center determined its capital functions in future.


Author(s):  
Ирина Викторовна Евстафьева

В статье исследуются вопросы попечительства в отношении несовершеннолетних, отбывающих наказание в виде лишения свободы. Проблема, поднимаемая автором настоящей статьи, многогранна, касается различных аспектов отбывания наказания несовершеннолетними в воспитательных колониях и требует комплексного исследования, способного ответить на определенно значимый вопрос: является ли колония законным представителем находящихся в ней несовершеннолетних со всеми вытекающими из статуса законных представителей последствиями. При этом необходимо обращать внимание на специфику правового статуса лиц, отбывающих наказание в воспитательных колониях, которые, во-первых, являются несовершеннолетними, то есть не обладают дееспособностью в полном объеме и нуждаются в особой заботе, защите и представительстве, а во-вторых, осуждены за совершение тяжкого или особо тяжкого преступления, влекущего изоляцию от общества и определенные ограничения и лишения. Отечественное законодательство достаточно детально регламентирует особенности режима отбывания наказания в виде лишения свободы несовершеннолетними, не определяя при этом статуса воспитательных колоний, кем они являются: воспитателями, попечителями или исключительно учреждениями исполнения наказаний. Между тем правильное понимание значения и роли воспитательной колонии в жизни находящихся в ней несовершеннолетних преступников, по мнению автора, поможет избежать ряда проблем, объективно складывающихся в учреждениях подобного рода. С этой точки зрения предлагаемая тема представляет интерес не только для ученых-теоретиков, но и для практиков - сотрудников соответствующих учреждений. Особо следует подчеркнуть, что исследований по данной тематике в специальной литературе нет. Отдельные исследования, встречающиеся в современной литературе, касаются исключительно общего гражданско-правового статуса несовершеннолетних осужденных. Однако это обстоятельство может свидетельствовать только о новизне данной темы, но никак не об отсутствии самой проблемы. The article analyzes the issues of the status of educational colonies as guardians of minors serving a sentence of imprisonment. In fact, the problem raised by the author of this article is multifaceted, concerns various aspects of the serving of punishment by minors in educational colonies and requires a comprehensive study that can answer, it seems, a definitely significant question: whether the colony is the legal representative of the minors in it with all the consequences arising from the status of legal representatives in the form of duties and responsibilities. At the same time, it seems, it is necessary to pay attention to the specifics of the legal status of citizens serving sentences in educational colonies, who, firstly, are minors, i.e. do not have full legal capacity and need special care, protection and representation, and, secondly, are convicted of committing a serious or particularly serious crime, entailing isolation from society and certain restrictions and deprivation. Domestic legislation regulates in sufficient detail the peculiarities of the regime of serving sentences in the form of deprivation of liberty by minors, without determining the status of educational colonies. Who are they: educators, Trustees or only institutions of execution of punishments. Meanwhile, the correct understanding of the importance and role of the educational colony in the life of juvenile offenders in it, according to the author, will help to avoid a number of problems that objectively develop in institutions of this kind. From this point of view, the proposed topic is of interest not only for theoretical scientists, but for practitioners-employees of relevant institutions. It should be emphasized that there are no studies on this subject in the special literature. However, this circumstance can testify only about novelty of the given subject, but in any way about absence of the problem. It seems that the relevance and importance of a problem is not always measured by the number of studies devoted to it. Sometimes these its traits are manifest only under particularly careful consideration.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ryuya Namba

AbstractModerate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.


Author(s):  
J. H. Orton ◽  
D. Bartley Stevenson

The spatfall in 1924, as in 1923, was very slight and from the point of view of the oyster-producer was a failure, and was little better in 1922.The growth of oysters in the summer of 1924 was unusually great; this has had the effect of bringing a large proportion of small oysters to a legally takeable size.The dredging results have, therefore, been much better than they were expected to be in the season of 1924–25, but the effect has been to deplete the beds still more of reserve stocks of small.Practically all the present stocks of small oysters are of a size between 2 and 2½ inches.With only average growth in 1925 and 1926 a large majority of these small oysters will have attained a size which will not pass through a 2½-inch ring; hence the beds are in a dangerous state.If, therefore, dredging continues under the present conditions, almost the whole of the present stock of small will have grown to large oysters and be cleared off the beds in the season of 1926–27.It is shown that although oysters may grow to a size of 2½ inches at Falmouth in small numbers in three summers, yet four summers are required before a fair proportion of spat can be expected to attain a size of 2½ inches.


Nuncius ◽  
1989 ◽  
Vol 4 (1) ◽  
pp. 3-42 ◽  
Author(s):  
MARIA LOSITO

Abstract<title> SUMMARY </title>Book IX of Vitruvius's DE ARCHITECTURA is devoted to the Gnomonica, which is the art of making solar clocks, or the second part of architecture, and to the basic construction of the Analemma, an orthographic projection of different circles of the sky - blue sphere.The present paper explains the changes to this Book between the 1556 edition and the 1567 editions of Daniele Barbaro's Commentationes.Indeed, while in 1556 Barbaro reconstructs the Vitruvian Analemma, that he had studied in the De horologiis describendis libellus, in 1567 he will more clearly define the Vitruvian Analemma by considering the Ptolemaic Analemma, after the 1562 study in Federico Commandino's Claudii Ptolemaei liber de Analemmate. Barbaro will also apply this Analemma in detail to the construction of the sun-dial, which was done neither by Vitruvius nor by Ptolemy, but in Commandino's Liber de Horologiorum descriptione.The relevance of the Analemma to the theory of planar projections of meridians is pointed out here. Indeed, even if the work of Barbaro seems traditional from the point of view of an astronomer, its implications for projective geometry are of great importance.


Author(s):  
Mariana Abakarova

The article analyzes Lak proverbs with the religious cultural code. The research was based on the descriptive method, syntactical analysis, morphological analysis and cognitive analysis. The proverbs collected from 3 books of Lak proverbs were analyzed from the point of view of semantics, axiological connotations, syntax and morphology. Semantic analysis revealed 6 groups of lexemes: (1) denominations of people; (2) words related to religious pillars and rituals; (3) words related to holy scriptures, religious attributes and terms; (4) words denoting death and afterlife; (5) words denoting commendable religious acts and notions; (6) words denoting sin and punishment. In the course of the axiological analysis there have been defined proverbs with positive evaluation of a person and proverbs with negative characteristics of a person. Positive traits include honesty, piety, decency, erudition and diligence, while negative ones include insulation, indecency, hypocrisy and negligence in the religious worship. Syntactical analysis of the Lak proverbs has revealed the presence of adverbs of asyndetic structure within which there have been established adversative, concessive and comparative relations, as well as of proverbs with copulative and disjunctive conjunctions. Some of the proverbs are based on the principle of alogism. Morphological analysis of the proverbs has revealed the most frequent grammatical tense, the Present Affirmative Tense, which is formed by means of adding the affix -r to the present participle. The Present Affirmative Tense in the Lak language denotes an action as an attribute of the subject which explains the fact of usage of this tense in proverbs that summarize the social experience of the native speakers. Lak proverbs with the given code have not been researched earlier that makes this study relevant.


2018 ◽  
Vol 13 (3) ◽  
pp. 72-76
Author(s):  
Гумар Булгариев ◽  
Gumar Bulgariev ◽  
Геннадий Пикмуллин ◽  
Gennadiy Pikmullin ◽  
Ильгиз Галиев ◽  
...  

At the present stage of development of the country’s agro-industrial complex, the technological process of surface tillage by combined soil-cultivating machines, simultaneously combining a number of operations in one pass through the field, causes the presence in their designs of the necessary set of various promising working organs. In view of the foregoing, a rotary soil ripper with a spiral-plate working member equipped with radially directed teeth and connected by means of rods with end flanges has been developed. Also, the researched ripper has the limits of penetration of the working element in the form of flat discs equipped with flanges and the radial stop have the ability to rotate around their axes independently of the ripper shaft. An analytical study of the working units of this ripper was carried out from the point of view of the influence of their size and teeth on the process of interaction with the soil, on the basis of which some of their parameters were determined. In conclusion, it was concluded that the analytical equations obtained allow us to justify the choice of the most important design parameters of the proposed new design and design a toothed rotary working device that reduces to constructive implementation after calculating their basic dimensions.


2019 ◽  
Vol 8 (2) ◽  
pp. 126 ◽  
Author(s):  
Itsaso Nabaskues ◽  
Oidui Usabiaga ◽  
Daniel Martos-García

Ability is a social construction that influences the access to recognition of people in the field of physical activity and sports (PASS) and in PE in particular. However, the notion of ability is defined in a simplistic and traditional manner and, consequently, experiences of symbolic violence are visible for those with specific body and tastes that do not match the dominant normative and hegemonic discourses embedded in the field. This study focuses on the narration of my own experiences of symbolic violence and “capital-dependence” as an “able” woman in the field of PASS. Through the analysis of critical moments from a retrospective point of view, I try to explain the evolution of my way of understanding the notion of ability and the circumstances that have contributed to the transformation of my discourse based on the socio-cultural perspective. I conclude that it is necessary to promote reflective practice in preservice teacher education programs as a way to increase awareness of embodied discourses’ influence in and from the different fields of PASS towards the construction of more inclusive movement contexts.


2019 ◽  
Vol 5 (3) ◽  
pp. 36-44
Author(s):  
Viktor A. Bogachev ◽  
Yuri A. Terentyev ◽  
Viktor V. Koledov ◽  
Taras V. Bogachev

Background: Research is ongoing relating to the analysis of a set of issues that arise in connection with the creation of the operating on the basis of vacuum magnetic technologies a transcontinental high-speed land transport corridor, connecting the eastern regions of China with Russia. As part of the variation calculus task, the geopolitical, economic, social, logistic, geographic, geomorphological, seismological, topographic components of the project are considered, in which it is assumed that the high speed overland route will pass through the north-western part of the historical region of Dzungaria. Aim: Find the most optimal from the point of view of the above components the location of the most important section of high speed overland route passing through Central Asia. Methods: Variational methods for solving an optimization problem with the use of a computer math system. Results: After creating a fairly informative and versatile picture of the region in question, the foundations of the corresponding mathematical models are built. Conclusion: The New Dzungarian Gates is a key element in choosing the location of a high-speed overland route based on VMLT.


2019 ◽  
Vol 7 (1-2) ◽  
pp. 115-120
Author(s):  
Brigitta Zsótér ◽  
Ágnes Milojev

In our research work we aimed at carrying out an economical assessment of an investment and development of substantial volume. The examined project was completed at a pig-farm during which a new farrowing place and pig rearing building were built, as well as the renovation of the existing pig-farm. All of them were financed partly from the firm’s own source, partly from a non-repayable aid granted by the state, and finally from a credit granted by a commercial bank. The term of the credit is 10 years and the return of the investment expected by the investors is 8%, so we carried out our calculations according to these data. We examined the three possible ways of financing the investment from the economical point of view, as a result we proposed three hypotheses. Our hypotheses are: Hypothesis 1 (Case „A”): The investment will be financially recovered within the examined period of 10 years if it is financed from the firm’s own source, the state grant and the bank credit. Hypothesis 2 (Case „B”): The investment can be economically completed within the given period of time if the project meets the costs from the firm’s own source and the credit. Hypothesis 3 (Case „C”): The investment will be economically accomplished within the examined 10 years provided the firm finances the project from their own source and the state grant. In our calculations we used the net present value (NPV), the internal rate of return (IRR), the payback time (PB), the discounted payback time (DPB) and the profitability index (PI) as economy indicators. We carried out our calculations regarding 10 years to be able to compare the results since the term of the granted credit is 10 years, too.  


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