Elementárna teória čísel 1. časť

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Jozef Strečka

The present textbook deals with exactly solved models and their diverse applications in several branches of physics such as mathematical physics, statistical physics, condensed matter physics and so on. Exactly soluble models are currently considered as an inspiring research field in its own right, which regrettably requires a considerable knowledge of sophisticated mathematics. Accordingly, my primary ambition was to provide an intro- ductory course for undergraduate students that would cover the simplest exactly solved models, whose rigorous solutions are available even after modest calculation. The present textbook should be therefore regarded as an auxiliary graduate-level textbook, which should serve as the student’s guide on this beautiful but surely intricate subject.

Even although I attempted to write largely self-contained textbook for undergraduate students, it is worthy of notice that the course on Exactly Solvable Models in Statistical Physics demands essential knowledges from the quantum mechanics, statistical physics, phase transitions and critical phenomena, which are its indispensable prerequisities. The most crucial fundamentals of these theories are briefly recalled in introductory remarks just for remembering and not for substituting those comprehensive courses. The rest of this textbook is entirely devoted to exactly solved lattice-statistical models with the main emphasis laid on their possible applications in the condensed matter physics. It is the author’s hope that the presented exact solutions are detailed enough in order to be easily followed by undergraduate students even without a support of tedious proofs, cumbersome theorems, longer argumentations, or obvious facts. This rather necessary compromise has of course a certain unadvisable impact on ’exactness’ of the presented solutions.

Finally, it is worthwhile to remark that the present textbook makes just a slight introduction into the simplest exactly solvable models and thus, the interested reader is referred for the follow-up study to several excellent books on exactly solved models quoted in the bibliography list on the next page. Note that the listed books were the major knowledge sources used by creating this textbook and they might be regarded as more advanced literature on this exciting research field.

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Adela Kravčáková • Stanislav Vokál • Janka Vrláková 

The presented “General Physics IV, Part 1: Atomic Physics” is intended as a basic study material for lectures from General Physics IV in the second year of bachelor-level study of physics and interdisciplinary study in combination with physics at the Faculty of Science, P. J. Šafárik University in Košice. The content covers the first part of the given course of physics, devoted to atomic physics. The aim of the course is to obtain basic information about the structure of the atom and the electron shell of the atom.

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Peter Fedoročko (eds.)

From June 14 to June 17, 2022, the 8th annual Spring School for Doctoral Students at Pavol Jozef Šafárik University in Košice will take place in Liptovský Ján. The scientific program of the spring school will comprise 3 plenary lectures by leading scientific experts and 1 workshop. Doctoral students will present their research papers in two sections: 22 doctoral students of Faculty of Public Administration, Faculty of Law and Faculty of Arts, and 26 doctoral students of Faculty of Medicine and Faculty of Science. The scientific programme of the spring school will also include a panel discussion with the management of Pavol Jozef Šafárik University in Košice.

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Jozef Strečka- Katarína Karl’ová (eds.)

Zborník obsahuje program a abstrakty workshopu s názvom: 1st Workshop on Perspective Electron Spin Systems for Future Quantum Technologies, ktorý sa bude konať 28.-29. júna 2022 v Košiciach. Workshop je organizovaný Prírodovedeckou fakultou Pavla Jozefa Šafárika v Košiciach a Ústavom experimentálnej fyziky Slovenskej akadémie vied v Košiciach s finančnou podporou Agentúry na podporu výskumu a vývoja. Ústrednými témami konferencie budú súčasné problémy kvantovej fyziky - kvantovej teórie magnetizmu spinových a elektrónových štruktúr, exotických kvantových spinových stavov, kvantového previazania, kvantových fázových prechodov, topologického kvantového počítania a kvantového spracovania informácie. Účastníci workshopu budú prezentovať originálne pôvodné výsledky svojho výskumu, ktoré môžu zásadným spôsobom ovplyvniť vývoj budúcich kvantových technológií.   

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Rastislav Varga

Posun doménových stien vo feromagnetických materiáloch sa využíva v rôznych magnetických zariadeniach na uchovávanie, spracovanie alebo prenos signálov a informácií. Ide hlavne o jadrá transformátorov, rôzne senzory, pamäťové zariadenia (napr. HDD v PC) ako aj moderné spintronické zariadenia ako sú Racetrack pamäte, elektronika na báze pohybu doménových stien a pod. Táto kniha má slúži ako učebnica pre pokročilejšie kurzy v oblasti magnetických materiálov. Je určená hlavne študentom, ktorí javia záujem o štúdium magnetických materiálov, ako aj odborníkom z rôznych oblastí, ktorí by chceli pochopiť základy doménovej štruktúry a jej zmeny. Je členená do deviatich kapitol. V prvej kapitole sa zaoberá stručnou históriou štúdia doménovej štruktúry v magnetických materiáloch. Druhá kapitola poskytuje úvod do príčin a prejavov magnetických anizotropií. Tretia a štvrtá kapitola sú venované príčinám vzniku doménovej štruktúry a doménovej steny. V piatej kapitole je rozobratá štruktúra doménovej steny, jej potenciál a kritické pole potrebné na pohyb doménovej steny. Šiesta kapitola je venovaná premagnetizačným procesom, z ktorých jeden - pohyb doménovej steny je podrobne preberaný v kapitole 7. Ôsma kapitola obsahuje teoretické riešenie pohybu doménovej steny. Posledná deviata kapitola predstavuje moderný spôsob pohybu doménovej steny, ktorý je indukovaný elektrickým prúdom. Predkladaná práca predpokladá u čitateľa aspoň základné znalosti z oblasti magnetizmu. V opačnom prípade ho autor odkazuje na základnú literatúru (napr. [2.1 -2.6]).

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Ján Guniš • Ľubomír Šnajder

Prílohy

College scripts Programming in Python 1 are intended for future teachers of computer science. The content of the course is related to the teaching of programming in Scratch and is an introduction to text-based programming in Python. Programming is introduced as a means of developing problem-solving skills. The first chapter is devoted to problem solving. The next 12 chapters sequentially introduce basic language constructions, data structures, and selected types of algorithms. Each of these chapters begins with an introduction to the problem. This section is primarily intended for self-study, to prepare students for the exercises. The following subchapter summarizes and completes the knowledge, and additional insights and approaches related to the chapter topic are presented. The chapters include a collection of exercises designed to practice and deepen knowledge and skills on the topic. The final part of the chapter presents the solved problems. This section serves as a guide to solving the problems in the collection.

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Slávka Hamuľaková

The textbook "Structure and reactivity - solved examples and tasks, part 1" is the basis for teaching the subject "Structure and reactivity" for students of the 1st year of master's studies at the Faculty of Science, UPJŠ, department of Organic Chemistry. The textbook is divided into individual chapters, each chapter offering students examples of chemical reactions, where their course is explained on the basis of appropriate reaction mechanisms. A substantial part of the textbook consists of unresolved tasks, the main goal of which is the development of students' knowledge and skills. Due to the fact that the textbook is focused on only one semester of study, it cannot cover all reactions, rather it is only representative examples of different types of reactions, such as: addition reactions, elimination reactions, aromatic substitution, addition-elimination reactions, radical reactions and pericyclic reactions.

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Adriana Zeleňáková - Jozef Bednarčík

Recenzovaný zborník príspevkov z vedeckej konferencie NANOVIR

Hlavným cieľom vedeckej konferencie NANOVIR bola prezentácia vedeckých výsledkov, získaných počas riešenia projektu NANOVIR – Nanočastice pre riešenie diagnosticko- terapeutických problémov s COVID-19, spolufinancovaného z Európskeho Fondu Regionálneho Rozvoja v Operačnom Programe Integrovaná Infraštruktúra 2014 – 2020, ITMS: 313011AUW7. Projekt bol riešený v období 1.1.2021 – 30.6.2023 a bol podporený sumou 1 916 004,79 EUR. Spolupodieľali sa na ňom tri spoluriešiteľské organizácie: Univerzita Pavla Jozefa Šafárika v Košiciach ako hlavný riešiteľ, Univerzita veterinárskeho lekárstva a farmácie v Košiciach ako partner č. 1 a Ústav experimentálnej fyziky Slovenskej akadémie vied ako partner č. 2.

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Ivana Sotáková-Martin Vavra-Mária Ganajová

This textbook has been designed for the master students of chemistry teaching (combined) at the Faculty of Science, Pavol Jozef Šafárik University in Košice as a source of model school experiments in general and inorganic chemistry. It will be used for teaching the Special Practice of School Experiments I compulsory course. It consists of instructions for experiments related to the selected topics in general and inorganic chemistry as well as the didactic and technical aspects of their performance. Each experiment includes an explanation of the principle, specification of the tools and chemicals needed, working procedure, and the respective apparatus assembly scheme. At the end of each experiment, the observation and explanation necessary for the correct interpretation of the results of the chemical experiment performed are provided. To follow the requirements for the digital transformation of education, selected computer-aided experiments and visualiser projections have been included as well. The next part is focused on the work with the monitoring suitcase, which can be used for making simple field experiments related to environmental topics. The final part is dedicated to attractive experiments that complement the topics in inorganic chemistry and can be used to motivate students. All experiment instructions are in line with the requirements specified by the state educational programmes for primary and grammar schools. This book allows teachers to select appropriate demonstrative experiments or experiments for laboratory classes performed by students themselves. The videos of selected experiments are also available as part of the interactive periodical table of elements operated by the Institute of Chemistry, Faculty of Science, Pavol Jozef Šafárik University in Košice.

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Jozef Strečka

Over the past fifteen years, the course on ’Exactly Solvable Models in Statistical Physics’ has become an indispensable ground of the study programme ’Theoretical Physics’ at Faculty of Science of Pavol Jozef ˇSaf´arik University in Koˇsice. At first, the course based on the first edition of this textbook was intended for undergraduate students only, however, I have later prepared follow-up course taught at a postgraduate level on demand of several ambitious students who wished to continue in studying this exciting research field. It is already more than decade when our students enrolled in the study programme ’Theoretical Physics’ graduate from ’Introduction to Exactly Solvable Models in Statistical Physics’ at a master level and ’Exactly Solvable Models in Statistical Physics’ at a postgraduate level. Of course, it was necessary somehow to rearrange topics for the courses of undergraduate and postgraduate students. More specifically, a few more challenging topics concerned with exact solutions of 2D Ising model (chapter 3) were moved to a more advanced course intended for the postgraduate students, while an introductory course intended for the undergraduate students was contrarily supplemented with a few new topics requiring the second edition of this textbook. The second edition of this textbook thus contains a completely new chapter 4 devoted to the exact solution of the Ising model on the Bethe lattice using the method of exact recursion relations, while the chapter 5 was supplemented by exact results for ground state of a few frustrated Heisenberg spin models using the variational method. It is my hope that the next edition of this textbook will come soon and it will involve all topics specifically taught within the postgraduate course as well. 

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Mária Reháková 

Vysokoškolský učebný text určený pre poslucháčov vyšších ročníkov z bioanorganickej chémie. Štúdium bioanorganickej chémie si vyžaduje vedomosti z predchádzajúcich chemický disciplín nižších ročníkov - všeobecnej, anorganickej, organickej, fyzikálnej chémie a biochémie.

Autorka

Daniel Jancura • Erik Sedlák

The textbook "Bioenergetics" should serve as an introduction to the study of bioenergetics. This field of science is currently highly actual, as the results of the bioenergetics research in recent years clearly show that bioenergetics processes in living systems can "serve" not only to transformation of energy, but also affect the course of processes such as apoptosis, aging, origin and development of many diseases (especially neurodegenerative). These facts clearly indicate the need for the existence of quality teaching texts that would allow students to acquire the necessary information and knowledge in this scientific discipline in an acceptable way. For the above mentioned reasons, we decided to create these textbooks, which are in the form of ten chapters, which naturally and logically follow each other. One chapter basically presents one lecture within the course of Bioenergetics, which is realized at the Faculty of Science of the Pavel Jozef Šafárik University in Košice at the master's and doctoral degree of the study program "Biophysics". At the same time, these texts can also be used for teaching in the study subject Biochemistry, which is taught in the bachelor's and master's degree programs of the study programs "Biochemistry" resp. “Biophysics”. We would like to express our conviction that this textbook could in some way also help researchers working in the field of the energy transformation in biological organisms and the phenomena associated with this transformation. This textbook presents knowledge about the basic concepts of bioenergetics, the mechanisms of processes such as glycolysis and the Krebs cycle (in addition to a detailed and comprehensive description of these processes, there is also a general view of the interconnectedness of these processes and their incorporation into a compact view of the overall energy transformation in biological organisms), the structure and functionality of biological membranes (this area is necessary for a better understanding of the knowledge presented in the following chapters). In the following chapters, the textbook deals with the description of the structure and function of mitochondria, with great emphasis on the properties and mechanisms of functioning of the four complexes of the respiratory chain and ATP-synthase. These complexes create the basis for the existence of the "most important" process in bioenergetics, oxidative phosphorylation. In the final two chapters, the mechanisms of the processes that produce photosynthesis, its light and dark phases, are presented. There is presented relevant information about this "second" most important bioenergetics process taking place in many biological organisms and providing the possibility of transforming the energy of electromagnetic radiation into energy "hidden" in the chemical bonds of certain chemical molecules. We want to express our conviction that the textbooks "Bioenergetics" will be a good "helper and inspirer" for many students who want to learn as much as possible about the fascinating structures and mechanisms for energy transformation in living systems, without which it would not be possible existence of life as we know it.

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E-book

Danica Sabolová

Tento vysokoškolský učebný text je určený pre poslucháčov Prírodovedeckej fakulty UPJŠ v Košiciach, ktorí si zapísali praktické cvičenia z Biotechnológie, ale aj všetkým ostatným študentom, ktorí majú záujem zoznámiť sa s praktickými aplikáciami biotechnológií. Cieľom praktického kurzu je zoznámiť študentov so základnými biotechnologickými metódami a ich aplikáciami. Poslucháči si v praxi overia teoretické poznatky získané na prednáškach z Biotechnológie ako je priebeh fermentačných procesov, výroba vína, príprava kyslomliečnych výrobkov a syrov, príprava kultivačných médií, očkovanie a kultivácia mikroorganizmov atď. Súčasťou praktických cvičení je aj využívanie analytických a spektrálnych metód, ktoré sú neoddeliteľnou súčasťou biochémie. Skriptá sú vydávané iba v elektronickej podobe a sú sprístupnené na webovej stránke univerzity: http://kosice.upjs.sk/~kbch/sk, z dôvodu, že stále sa bude dať aktualizovať a modernizovať obsah laboratórnych úloh.

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Ondrej Hutník (ed.)

Book of abstract

Uncertainty Modeling 2024 (UM 2024) is organized by Pavol Jozef ˇSaf´arik University in Koˇsice. It is a continuation of the series of colloquia held in Rzesz´ow under the name International Symposium on Fuzzy Sets (ISFS) and in Bratislava under the name Uncertainty Modeling.

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Božena Mihalíková - Ján Ohriska

Tento učebný text je určený poslucháčom prvého ročníka študijného odboru 76–12–8 „Učiteľstvo všeobecnovzdelávacích predmetov“ v kombináciách s matematikou. Je vyhotovený na základe prednášok autorov a ich viac ako desaťročných skúseností z výučby tohoto predmetu na PF UPJŠ. Pri jeho písaní sa autori snažili zohľadniť špecifickosť učiteľského štúdia matematiky. Predkladaný učebný text nebol písaný pre nedostatok učebníc matematickej analýzy. Dôvodom pre jeho napísanie boli zistenia autorov, že poslucháči nemajú zo strednej školy dostatočné skúsenosti v práci s odbornou literatúrou, ťažkosti mnohým spôsobuje (najmä v prvých semestroch) čo i len trochu odlišný výklad, nie zriedka aj zmena v označovaní, čím im uniká podstata študovanej problematiky. Autori textu si nekládli za ciel byt originálni. Ich snahou bolo urobiť taký výber tém, aký je nutný pre budúceho učiteľa matematiky a zvoliť takú metódu výkladu, ktorá je podla ich názoru vhodná pre poslucháčov prvého ročníka. Dobré zvládnutie učiva (rozšírenie matematického aparátu a s tým súvisiace možnosti uplatnenia iných dokazovacích metód ako aj získanie potrebných početných schopností) predpokladá použitie aj ďalších literárnych prameňov (učebníc, zbierok úloh) podla odporúčania vyučujúceho.

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Adriana Zeleňáková

One of the fundamental characteristics of the magnetic state of ferromagnetic materials is the existence of a domain structure. The university textbook "MAGNETIC DOMAINS: SPECIAL PHYSICAL PRACTICE 1" is intended primarily for students of the Master's programme in Physics of Condensed Matter FKLm and for the PhD programme in Progressive Materials PMd within the profile subject Special Practice 1 at the Institute of Physical Sciences of the Faculty of Sciences of the Pavol Jozef Šafárik University in Košice.  The textbook is divided into seven chapters. The first chapter is devoted to the basics of domain theory, including the history of domain observation and the specification of different types of energies in ferromagnetic body. The second chapter presents the relationship between domain structure and magnetisation processes in ferromagnetic materials The third chapter describes the different types of domain-wall interactions with the defect. The fourth chapter illustrates examples of domain structure in selected ferromagnetic body such as grain oriented and non-grain oriented electrical steels, amorphous and nanocrystalline ribbons. The fifth chapter summarises an overview of the different experimental methods used to visualise the domain structure and their advantages or disadvantages with respect to the structure of ferromagnetic materials. The last two chapters, the sixth and the seventh, are devoted to specific experimental tasks for observing the domain structure of a selected polycrystalline sample using the optical microscope Bitter powder method and the MFM (magnetic force microscopy) method. During the preparation of this undergraduate text, its individual parts were developed using the foreign language literature listed in the recommended references.

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