Pub Date : 2021-12-27DOI: 10.51337/jasb20211227004
Zdeněk Pezlar
In this text we provide an introduction to algebraic number theory and show its applications in solving certain difficult diophantine equations. We begin with a quick summary of the theory of quadratic residues, before diving into a select few areas of algebraic number theory. Our article is accompanied by a couple of worked problems and exercises for the reader to tackle on their own.
{"title":"Solving Diophantine Equations by Factoring in Number Fields","authors":"Zdeněk Pezlar","doi":"10.51337/jasb20211227004","DOIUrl":"https://doi.org/10.51337/jasb20211227004","url":null,"abstract":"In this text we provide an introduction to algebraic number theory and show its applications in solving certain difficult diophantine equations. We begin with a quick summary of the theory of quadratic residues, before diving into a select few areas of algebraic number theory. Our article is accompanied by a couple of worked problems and exercises for the reader to tackle on their own.","PeriodicalId":161839,"journal":{"name":"Journal of the ASB Society","volume":"899 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123260617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-27DOI: 10.51337/jasb20211227003
Šimon Sukup, O. Heczko
This study deals with pseudoplastic deformation of Ni50Mn28Ga22 alloy exhibiting mechanically and magnetically induced crystal reorientation. The new approach was introduced, taking into account crystals with single initial variant as well as nucleation of different orientation. Initially, observations from optical microscope and AFM (atomic force microscope) were correlated with the mechanical measurements from stress-strain machine to characterize boundaries between crystal variants. These observations were subsequently used to clarify the results of the mechanical deformation tests. By magnetizing samples in VSM (vibrating-sample magnetometer), analogous magnetic measurements to mechanical tests were conducted. The two types of measurements were then compared with respect to energy. The discrepancy found between the model and measurements is in agreement with previous studies. Some experimental factors and possible errors that may affect measurement have been discussed. Nevertheless, the observed differences remain an unresolved issue suggesting a need for a modification of the model.
{"title":"Magneto-mechanical deformation of ch{Ni50Mn28Ga22} shape memory alloy","authors":"Šimon Sukup, O. Heczko","doi":"10.51337/jasb20211227003","DOIUrl":"https://doi.org/10.51337/jasb20211227003","url":null,"abstract":"This study deals with pseudoplastic deformation of Ni50Mn28Ga22 alloy exhibiting mechanically and magnetically induced crystal reorientation. The new approach was introduced, taking into account crystals with single initial variant as well as nucleation of different orientation. Initially, observations from optical microscope and AFM (atomic force microscope) were correlated with the mechanical measurements from stress-strain machine to characterize boundaries between crystal variants. These observations were subsequently used to clarify the results of the mechanical deformation tests. By magnetizing samples in VSM (vibrating-sample magnetometer), analogous magnetic measurements to mechanical tests were conducted. The two types of measurements were then compared with respect to energy. The discrepancy found between the model and measurements is in agreement with previous studies. Some experimental factors and possible errors that may affect measurement have been discussed. Nevertheless, the observed differences remain an unresolved issue suggesting a need for a modification of the model.","PeriodicalId":161839,"journal":{"name":"Journal of the ASB Society","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122477938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-27DOI: 10.51337/jasb20211227005
V. Zvonícek
The aim of this paper is to generate and examine a pseudorandom sequence over a finite field using the Möbius function. In the main part of the paper, after generating a number of sequences using the Möbius function, we examine the sequences’ pseudorandomness using autocorrelation and prove that the second half of any sequence in $mathbb{F}_{3^n}$ is the same as the first, but for the sign of the terms. I reach the conclusion, that it is preferable to generate sequences in fields of the form $mathbb{F}_{3^n}$, thereby obtaining a sequence of the numbers $-1$,$0$,$1$, each of which appear in the same amounts. There is a variety of applications of the discussed pseudorandom generator and other generators such as cryptography or randomized algorithms.
{"title":"A Pseudorandom Sequence Generated over a Finite Field Using The Möbius Function","authors":"V. Zvonícek","doi":"10.51337/jasb20211227005","DOIUrl":"https://doi.org/10.51337/jasb20211227005","url":null,"abstract":"The aim of this paper is to generate and examine a pseudorandom sequence over a finite field using the Möbius function. In the main part of the paper, after generating a number of sequences using the Möbius function, we examine the sequences’ pseudorandomness using autocorrelation and prove that the second half of any sequence in $mathbb{F}_{3^n}$ is the same as the first, but for the sign of the terms. I reach the conclusion, that it is preferable to generate sequences in fields of the form $mathbb{F}_{3^n}$, thereby obtaining a sequence of the numbers $-1$,$0$,$1$, each of which appear in the same amounts. There is a variety of applications of the discussed pseudorandom generator and other generators such as cryptography or randomized algorithms.","PeriodicalId":161839,"journal":{"name":"Journal of the ASB Society","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130348805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-27DOI: 10.51337/jasb20211227001
T. Wagner, Jana Netušilová
The year 2021 is the year of the 85th anniversary of the birth of Professor Miloslav Frumar the enthusiastic chemist who dedicated his whole professional life to the study of amorphous and glassy chalcogenides which are used in numerous applications like copying machines, laser printers, DVDs or memories.
{"title":"Miloslav Frumar: In the footsteps of the chalcogenide semiconductors","authors":"T. Wagner, Jana Netušilová","doi":"10.51337/jasb20211227001","DOIUrl":"https://doi.org/10.51337/jasb20211227001","url":null,"abstract":"The year 2021 is the year of the 85th anniversary of the birth of Professor Miloslav Frumar the enthusiastic chemist who dedicated his whole professional life to the study of amorphous and glassy chalcogenides which are used in numerous applications like copying machines, laser printers, DVDs or memories.","PeriodicalId":161839,"journal":{"name":"Journal of the ASB Society","volume":"254 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131851488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-28DOI: 10.51337/jasb20201228003
J. Juřica
This work focuses on creating maps of the geomagnetic field and areas of increased cosmic radiation surrounding the Earth. Data were measured by Proba-V satellite at Low-Earth orbit 820 kilometres above the Earth during 2015. The actual measured data were compared with the calculated magnetic values. The created maps serve to a better understanding of the shape of the geomagnetic field and show magnetic equator, north magnetic pole and more. The map confirms that the area of the South Atlantic Anomaly corresponds with the weakest area of the geomagnetic field. Maps of different time periods of 2015 show small changes in the shape of the geomagnetic field during a year. Increased attention was paid to June 2015, when solar flares were passing near the Earth. The observation confirms that solar flares have a significant effect on the shape of the geomagnetic field.
{"title":"Geomagnetic field mapping","authors":"J. Juřica","doi":"10.51337/jasb20201228003","DOIUrl":"https://doi.org/10.51337/jasb20201228003","url":null,"abstract":"This work focuses on creating maps of the geomagnetic field and areas of increased cosmic radiation surrounding the Earth. Data were measured by Proba-V satellite at Low-Earth orbit 820 kilometres above the Earth during 2015. The actual measured data were compared with the calculated magnetic values. The created maps serve to a better understanding of the shape of the geomagnetic field and show magnetic equator, north magnetic pole and more. The map confirms that the area of the South Atlantic Anomaly corresponds with the weakest area of the geomagnetic field. Maps of different time periods of 2015 show small changes in the shape of the geomagnetic field during a year. Increased attention was paid to June 2015, when solar flares were passing near the Earth. The observation confirms that solar flares have a significant effect on the shape of the geomagnetic field.","PeriodicalId":161839,"journal":{"name":"Journal of the ASB Society","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115153759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-28DOI: 10.51337/jasb20201228005
Veronika Babyradova, Jitka Hrežová
The main aim of this work was to create a complex educational kit for learning about poisonous plants growing in the Czech Republic. This set is intended especially for juniors at grammar schools, where it may be utilized in biology seminars. The kit aims to showcase interdisciplinary connections between biology and other natural as well as social sciences, which is a way of positively impacting students’ interests in the sciences through topics that are not strictly related to biology. Using the RWCT (Reading and Writing for Critical Thinking) method allows the students to connect what they already know with new knowledge, develop a complex opinion thanks to that connection and understand issues that overlap to different fields, which may not be necessarily related. The main contribution of this work lies in the educational set consisting of four parts: the teaching brochure, a board game, a matching game, and several worksheets. The whole set is designed to make the students actively think about the subject, its overlaps, and connections to other fields of study, and then to lead them towards creating a complex opinion on the given topic. Another important feature of the set is that it leads the students to make use of their textbook, rather than any digital sources of information (e.g. slides from a teacher, to which they are accustomed nowadays in classes). The teaching set was tested in a sample biology seminar classes attended by 18 students. Following the lesson, the usefulness of the set was evaluated through semi-structured interviews with three respondents, who had taken part in the class. However, more testing lessons and more similar interviews with attending students would be needed to conclusively prove the effectiveness of this teaching set.
{"title":"Ready for the future? Then, teach and think critically","authors":"Veronika Babyradova, Jitka Hrežová","doi":"10.51337/jasb20201228005","DOIUrl":"https://doi.org/10.51337/jasb20201228005","url":null,"abstract":"The main aim of this work was to create a complex educational kit for learning about poisonous plants growing in the Czech Republic. This set is intended especially for juniors at grammar schools, where it may be utilized in biology seminars. The kit aims to showcase interdisciplinary connections between biology and other natural as well as social sciences, which is a way of positively impacting students’ interests in the sciences through topics that are not strictly related to biology. Using the RWCT (Reading and Writing for Critical Thinking) method allows the students to connect what they already know with new knowledge, develop a complex opinion thanks to that connection and understand issues that overlap to different fields, which may not be necessarily related. The main contribution of this work lies in the educational set consisting of four parts: the teaching brochure, a board game, a matching game, and several worksheets. The whole set is designed to make the students actively think about the subject, its overlaps, and connections to other fields of study, and then to lead them towards creating a complex opinion on the given topic. Another important feature of the set is that it leads the students to make use of their textbook, rather than any digital sources of information (e.g. slides from a teacher, to which they are accustomed nowadays in classes). The teaching set was tested in a sample biology seminar classes attended by 18 students. Following the lesson, the usefulness of the set was evaluated through semi-structured interviews with three respondents, who had taken part in the class. However, more testing lessons and more similar interviews with attending students would be needed to conclusively prove the effectiveness of this teaching set.","PeriodicalId":161839,"journal":{"name":"Journal of the ASB Society","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128966702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-28DOI: 10.51337/jasb20201228001
K. Stejskalová, M. Heyrovský
''Professor Heyrovský. You are the originator of one of the most important methods of contemporary chemical analysis. Your instrument is extremely simple - just falling droplets of mercury - but you and your collaborators have shown that it can be used for the most diverse purposes ... May I ask you to advance and receive the Nobel Prize for Chemistry for this year from the hands of our King'', said professor Arne Ölander, member of the Nobel Committee for Chemistry, in Czech language to the laureate Jaroslav Heyrovský at the award ceremony in the Stockholm Concert Hall on 10th December 1959. The year of 2020 is the year of 130th anniversary of the birth of prof. Jaroslav Heyrovský, the first Czech recipient of the Nobel Prize in Chemistry and 61 years since he received his prize in Stockholm (Sweden).
{"title":"Jaroslav Heyrovský: The story of a mercury drop","authors":"K. Stejskalová, M. Heyrovský","doi":"10.51337/jasb20201228001","DOIUrl":"https://doi.org/10.51337/jasb20201228001","url":null,"abstract":"''Professor Heyrovský. You are the originator of one of the most important methods of contemporary chemical analysis. Your instrument is extremely simple - just falling droplets of mercury - but you and your collaborators have shown that it can be used for the most diverse purposes ... May I ask you to advance and receive the Nobel Prize for Chemistry for this year from the hands of our King'', said professor Arne Ölander, member of the Nobel Committee for Chemistry, in Czech language to the laureate Jaroslav Heyrovský at the award ceremony in the Stockholm Concert Hall on 10th December 1959. The year of 2020 is the year of 130th anniversary of the birth of prof. Jaroslav Heyrovský, the first Czech recipient of the Nobel Prize in Chemistry and 61 years since he received his prize in Stockholm (Sweden).","PeriodicalId":161839,"journal":{"name":"Journal of the ASB Society","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133272076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-28DOI: 10.51337/jasb20201228004
Vojtech Kloud, D. Bednařík
This article focuses on the problem of finding a shortest path in plane with obstacles. Problems of such nature occur for instance in robotics or transport and are of great importance. The problem is analyzed using the methods of mathematical analysis and calculus of variations. Definitions of basic concepts of the problem are given. From these definitions, useful properties, such as convexity of the length functional, are proven. These properties are used to show the existence of a solution in one of the considered cases of the problem. Other case of the problem was considered, where it is established under which conditions does a shortest path attain its general form and what this form looks like.
{"title":"Optimizing length of planar curves","authors":"Vojtech Kloud, D. Bednařík","doi":"10.51337/jasb20201228004","DOIUrl":"https://doi.org/10.51337/jasb20201228004","url":null,"abstract":"This article focuses on the problem of finding a shortest path in plane with obstacles. Problems of such nature occur for instance in robotics or transport and are of great importance. The problem is analyzed using the methods of mathematical analysis and calculus of variations. Definitions of basic concepts of the problem are given. From these definitions, useful properties, such as convexity of the length functional, are proven. These properties are used to show the existence of a solution in one of the considered cases of the problem. Other case of the problem was considered, where it is established under which conditions does a shortest path attain its general form and what this form looks like.","PeriodicalId":161839,"journal":{"name":"Journal of the ASB Society","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114670781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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