Elementárna teória čísel 1. časť

E-book

Božena Mihalíková - Ondrej Hutník - Jozef Kiseľák

The textbook is devoted to the mathematical analysis of infinite series of numbers and functions. It is intended for students of mathematics, physics and computer science, as well as interdisciplinary study of combination with mathematics. It contains a theoretical background for investigating the convergence of infinite series, expanding functions into power and Taylor series, as well as the use of these results in various problems of mathematics, physics, and computer science. Using the historical background the textbook clarifies the motivations and the need to introduce some key concepts and their further development. Basic concepts and statements are demonstrated on a large number of solved exercises, but it contains a number of exercises for independent practice. Several results are supplemented by dynamic animations executable in the electronic version of the textbook.

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Peter Fedoročko a kol. 

Vysokoškolský učebný text Prírodovedeckej fakulty UPJŠ.

E-book

Michal Jaščur

This monograph is devoted to the discussion of effective field theory based on the differential operator method, originally introduced by Honmura and Kaneyoshi in 1979, which remains actively used for theoretical studies of localized spin models of magnetism—particularly variants of the Ising model. To date, this methodology has been applied by numerous authors to investigate a wide range of systems, including crystalline systems, diluted magnetic systems, systems with random exchange interactions, amorphous magnetic materials, systems under random magnetic and crystalline fields, thin magnetic layers, magnetic systems with free surfaces, binary and ternary magnetic alloys, among others.

During my scientific career, I have collaborated with several leading experts in this field—including Prof. Kaneyoshi, with whom I completed two long-term research stays—to advance the development of the differential operator method (and consequently effective field theory). Within this research area, I have published over 40 scientific papers in prominent international physics journals. These works include both methodological advancements and significant applications that predict intriguing physical phenomena, such as multicompensation phenomena in ferrimagnets.

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Karel Saksl

Solving crystal structures is the royal discipline of X-ray crystallography. Its primary task, with the exception of defects, is to describe the atomic structure of the motif that, by its repetition, fills the volume of the entire crystal or crystalline phase. This task is nowadays more or less routine for single-crystal X-ray diffraction, which can locate hundreds to thousands of non-hydrogen atoms in large unit cells. However, in real practice, we often have material available only in powder form instead of single crystals. Solving the atomic structure from its X-ray diffraction data is non-trivial, mainly because the three-dimensional diffraction space of a single crystal is reduced to one dimension by measuring a large number of randomly oriented microcrystals (crystallites). Therefore, the solution itself requires, in addition to proper measurement methodology, the selection of suitable tools, procedures, and strategies that, through optimization, will lead to the solution and refinement of the given crystalline phase. The current limit of this method is approximately 100 non-hydrogen atoms in the asymmetric part of the unit cell, which, however, is sufficient for most inorganic materials.

The goal of these educational texts is to provide students in the second and third levels of university studies with specific guidance on solving crystal structures from powder X-ray diffraction data. These scripts build upon my first monograph and require practical knowledge of its content. Similar to my previous monograph, I offer solved examples without a deep theoretical introduction, demonstrating procedures and strategies leading to the correct solution of crystalline phases using the freely available GSAS-II program. The examples are arranged from simpler to more complex, and the reader will find many useful pieces of information in the literature references as well as in the comments below the line. Part of these scripts are data intended for your individual practice of the described procedures. 

Karel Sakls

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E-book

Ondrej Krídlo - Gabriel Semanišin

For computer scientists, the constant challenge is to seek efficient algorithms and various technical and implementation possibilities to improve the computational complexity of currently known algorithms. Partial solutions are offered by approaches such as grid-based methods and parallelization of computation. Quantum computers represent a significant but still unfulfilled promise. From a theoretical perspective, probabilistic and approximation approaches provide very effective solutions, and these are the methods we aim to explore in detail.

These electronic university textbooks serve as supplementary materials for the course Approximation and Probabilistic Algorithms. They were developed from the authors' materials and contributions by Prof. RNDr. Viliam Geffert, DrSc., whom the authors thank for providing the manuscript. Acknowledgments also extend to RNDr. Ján Katrenič, PhD., who prepared the first set of exercises for the course, and Žaneta Semanišinová, who reviewed large portions of the text and contributed suggestions for its improvement.

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Martin Bačkor - Miriam Bačkorová

The proposed text focuses on the history of studying biology, medicine, and pharmacy as scientific disciplines from prehistoric times through antiquity, the Middle Ages, and the modern era. The text chronologically organizes the most significant figures in the history of biological scientific disciplines, outlines key characteristics of major historical discoveries, and reevaluates their significance from the perspective of 21st-century science.

The educational text is chronologically divided into the most significant periods of civilization development. The last two completed centuries—the 19th and 20th—are subdivided into major life science fields due to the unprecedented growth of biological disciplines and the resulting volume of acquired information.

Since it can sometimes be challenging in science to define what constitutes the past versus the present of a particular discipline, we have excluded significant biological discoveries from the early 21st century, which are typically regarded as the “present” of biology.

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E-publication

Denisa Maceková-Monika Václavková-Marek Kvet-Ivana Sotáková

The publication Digiform: A Supporting Application to Digilib – User Guide, Part B presents the Digiform web application as a tool that extends the functionality of the Digilib digital library of formative assessment tools. The application enables the creation and editing of formative assessment tool templates, which can be adapted to the specificities of individual subjects and levels of education and subsequently imported into the Digilib environment for use in the teaching process. The guide provides a detailed description of how to work with the Digiform application, from creating new templates, editing and personalising them, through to their export and implementation in the main Digilib application. Attention is also given to the interconnection with the Digilib Images application, which enables the integration of visual elements into the assessment tools, thereby enhancing their didactic effectiveness and visual appeal. The guide is intended for teachers at all levels of education, student teachers, school administrators, and digital coordinators who are interested in the systematic use of the Digilib digital library to support the implementation of formative assessment, enhance the quality of the educational process, and foster the development of students’ self-assessment and reflective competences.

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E-book

Tomáš Samuely

Today, scanning probe microscopes are standard tools in materials science, physics, chemistry, biology, and engineering. Thousands of these microscopes are in operation worldwide and are at least as common and popular as scanning electron microscopes.

Despite the vast number of newer scanning probe microscopy techniques, classical STM remains a significant and irreplaceable method, widely used, for example, in solid-state research. In this text, we will focus on both traditional and innovative STM techniques that are available and utilized in the laboratories of the Center for Low Temperature Physics in Košice.

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Michal Jaščur -Michal Hnatič

In the textbook, the processes belonging to an area of  nonequilibrium physics, which make the basis for the study and analysis of compex phenomena  of statistical mechanics, are described. The Boltzmann equation for distribution function is derived and on this basis the hydrodynamic equations are constructed.  Stochastic processes are described separately and Fokker-Planck equation for density probability  is derived. Textbook is intended for the students of second year of master study at Faculty of Science of P. J. Šafarik University.   

Autors

E-book

Mária Kožurková (ed.)

Book of Abstracts

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Tatiana Kimáková

Táto vedecká monografia je komplexnou vedeckou prácou zameranou na prítomnosť a pôsobenie ortuti v životnom prostredí, ale aj na rizikové faktory zdravia, ktoré sú s ňou spojené. Monografia predstavuje charakteristiku ortuti v multidisciplinárnom zábere, prezentuje využitie v priemysle a v zdravotníctve, popisuje negatívne vplyvy ortuti v životnom prostredí, na zdravotný stav obyvateľstva. Zároveň prináša návrhy a odporúčania pre rizikové skupiny ľudí. Súčasťou monografie je komplexný výskum koncentrácie ortuti vo vzorkách komodít domácej i zahraničnej produkcie a vo vzorkách rastlín pomocou atómového absorpčného spektrometra AMA 254. Vedecká monografia je vhodná pre vedeckú komunitu, študentov medicínskych, veterinárnych, prírodovedných a poľnohospodárskych odborov ako aj pre študentov verejného zdravotníctva všetkých troch stupňov vysokoškolského štúdia. Monografia je učená aj pre všetkých záujemcov z radov informovanej verejnosti.

Autorka

E-book

Jana Špaková Raschmanová - Zuzana Kudličková - Kvetoslava Stanková

Organic chemistry plays a key role in our lives, from the pharmaceutical industry to the production of plastics and food additives. Additionally, it is essential in biochemistry, as it deals with the basic building blocks of living organisms, such as carbohydrates, lipids, proteins, and nucleic acids. One of the best ways to teach organic chemistry and increase students' interest in the subject is through conducting school experiments. This study material presents a collection of visually striking practical experiments in organic chemistry that will help students better understand the chemical processes and techniques used in the field. This electronic study material is supplemented with visual material, allowing students to verify the results of experiments and better understand the individual procedures. At the end of each section, there are questions to help assess the acquired knowledge and encourage deeper understanding of the experiments conducted.

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Jozef Strečka - Hana Čenčariková - Andrej Gendiar (eds.)

The proceeding involves programme and abstracts of Workshop on Quantum Magnetism: Theoretical Challenges and Future Perspectives, which was held on June 7th – June 8th, 2019, in Košice, Slovakia.

The workshop is organized by Faculty of Science of Pavol Jozef Šafárik University in Košice and Institute of Experimental Physics of Slovak Academy of Sciences in Košice under the financial support of Slovak Research and Development Agency.

The main conference topics are devoted to state-of-the-art problems of Quantum Theory of Magnetism inncluding molecular magnetism, highly frustrated magnetism, magnetic phase transitions, quantum spin liquids, strongly correlated systems, exotic quantum states, flat-band systems and quantum entanglement.

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Ivan Potočňák a kol.

The textbook represents a study literature on the subject of General chemistry, which is a compulsory subject of bachelor courses in Chemistry and Chemistry -  interdisciplinary study, the first year. This textbook contains 15 + 2 chapters in the whole range of 170 pages that follow the content of lectures and by means of examples and theoretical tasks consolidate and extend knowledge gained from lectures.

E-book

Peter Fedoročko (ed.)

Proceedings of the 7th Annual Doctoral Spring School 2020

From November 10 to November 11, 2020, the 7th annual Spring School for Doctoral Students at Pavol Jozef Šafárik University in Košice will take place in Košice in a modified mode in the on-line space. The scientific program of the spring school will comprise 2 plenary lectures by leading scientific experts of Pavol Jozef Šafárik University in Košice. Doctoral students will present their research papers in two sections: 24 doctoral students of Faculty of Public Administration, Faculty of Law and Faculty of Arts, and 22 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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Ľubomír Kováč

Učebný text „Zoogeografia“ objasňuje základné princípy a historický vývoj rozšírenia živočíchov na Zemi, a ďalej analyzuje faktory, ktoré ho ovplyvňujú. Vďaka moderným vedeckým metódam a technikám výskumu je zoogeografia veľmi dynamicky sa rozvíjajúcou disciplínou. Z geologických etáp je podrobnejšie spracovaná problematika paleoklimatických cyklov kvartéru, holocénu a vývoja postglaciálnej klímy, ktoré zohrali významnú úlohu pri dynamike vývoja živočíšnych areálov. Areálová analýza charakterizuje a triedi areály živočíchov a ich dynamiku v nadväznosti na speciáciu. Podrobne je spracovaná problematika zoogeografických oblastí s dôrazom na palearktickú oblasť. Časť zameraná na dynamickú zoogeografiu rieši najmä problematiku refúgií a reliktov v súvislosti s vývojom pleistocénnej paleoklímy. Text stručnou formou sumarizuje základné antropogénne faktory, ktoré v recentnej dobe drastickým spôsobom limitujú rozšírenie živočíchov v rýchlo ubúdajúcom prírodnom prostredí na Zemi. Text ďalej prehľadným spôsobom charakterizuje biogeografiu Karpát a faunu územia Slovenska. Záverečná časť prezentuje fylogeografiu ako modernú vednú disciplínu zameranú na rekonštrukciu migračných ciest v postglaciáli, ktorá je podložená analýzou molekulárnych markerov populácií živočíchov v širšom geografickom kontexte. 

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