Zbierka úloh z matematiky pre nematematické odbory

E-book

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

Download the e-book for free  (pdf)

Ondrej Hutník a kol. 

Zbierka úloh z matematickej analýzy III. je pokračovaním predchádzajúcich dvoch vydaných zbierok autorov Kulcsár a Kulcsárová. Táto časť obsahuje príklady na zopakovanie a precvičenie učiva stredných škôl, ako aj časti prvého semestra kurzu matematická analýza určeného pre študentov matematiky, fyziky, informatiky a učiteľského štúdia v kombinácii s matematikou. Zbierka môže tiež pomôcť všetkým učiteľom, ktorí chcú použiť rôzne úlohy vo svojom vyučovaní. Zbierka zahŕňa oblasť postupností reálnych čísel: aritmetické a geometrické postupnosti, všeobecne a rekurentne zadané postupnosti, nachádzajú sa tu úlohy na vyšetrovanie vlastností postupností (monotónnosť, ohraničenosť, konvergencia) a výpočet rôznych typov limít. Všetky zadané úlohy sú vyriešené na konci každej kapitoly s podrobným komentárom.

Autori

E-book

Erik Čižmár

Textbook Automation of Laboratory Experiments in LabVIEW environment is devoted to the basics of graphical programming and shows the way how to communicate with measuring equipment and Arduino development boards in LabVIEW. The basic concepts of creating a virtual instrument and its interactive user environment are introduced. Three physical tasks are presented, the practical implementation of which takes place with the use appropriate instrumentation and LabVIEW. Practical tasks are dedicated to measuring the transmission characteristics of a low-pass RC filter, measuring the natural resonant frequency of a quartz tuning fork using the heterodyne pulse method, and mapping the magnetic field of a permanent magnet using Arduino.

Download the e-book for free (pdf)

E-book

Rastislav Varga

The movement of domain walls in ferromagnetic materials is utilized in various magnetic devices for storing, processing, or transmitting signals and information. This mainly includes transformer cores, various sensors, memory devices (e.g., HDDs in PCs), as well as modern spintronic devices such as Racetrack memories, domain wall motion-based electronics, and so on.

This book is intended to serve as a textbook for advanced courses in the field of magnetic materials. It is primarily aimed at students interested in studying magnetic materials, as well as professionals from various fields who wish to understand the basics of domain structure and its changes. It is divided into nine chapters. The first chapter deals with a brief history of the study of domain structure in magnetic materials. The second chapter provides an introduction to the causes and manifestations of magnetic anisotropies. The third and fourth chapters are devoted to the causes of domain structure formation and domain walls. The fifth chapter discusses the structure of domain walls, their potential, and the critical field required for domain wall movement. The sixth chapter is dedicated to magnetization processes, one of which - domain wall movement - is discussed in detail in chapter 7. The eighth chapter contains a theoretical solution for domain wall movement. The final ninth chapter presents a modern method of domain wall movement induced by electric current.

The presented work assumes that the reader has at least basic knowledge in the field of magnetism. Otherwise, the author refers the reader to basic literature (e.g., [2.1 - 2.6]).

Download the e-book for free (pdf)

E-book

Michal Jaščur

This is a supporting text for the undergraduate students interested in quan- tum theory of magnetism. The text represents an introduction to various theoretical approaches used in this eld. It is an open material, in the sense that it will be supported by appropriate problems to be solved by student at seminars and also as a homework.

The text consists of four chapters that form closed themes of the in- troductory quantum theory of magnetism. In the rst part we explain the quantum origin of the magnetism illustrating the appearance of the ex- change interaction for the case of hydrogen molecule. The second chapter is devoted to the application of the Bogolyubov inequality to the Heisenberg model and it represents the part which is usually missing in the textbooks of magnetism. The third chapter deals with the standard spin wave-theory including the Bloch and Holstein-Primakoff a approach. Finally, we discuss the application of the Jordan-Wigner transformation to one-dimensional spin-1/2 XY model.

The primary ambition of this supportive text is to explain diverse math- ematical methods and their applications in the quantum theory of mag- netism. The text is written in the form which should be sufficient to de- velop the skills of the students up to the very high level. In fact, it is expected that students following this course will able to make their own original applications of the methods presented in this book.

Download the e-book for free (pdf)

E-book

Erik Sedlák - Rastislav Varhač -  Patrik Danko - Helena Paulíková - Dušan Podhradský

The presented scripts were created in an effort to update and especially clarify the tasks that are solved in the basic practical exercises in biochemistry students of the 2nd and 3rd year of the bachelor's degree in chemistry, biology and their combinations with other disciplines. Most of the tasks come from the original scripts "Podhradský, Mihalovová: Praktické cvičenia z biochémie, Košice 1989".

Some of them have been modified to a greater or lesser extent and adapted to current conditions in the laboratory. New tasks were also added, such as those dedicated to nucleic acids. The scripts are thematically divided into six separate units, each of which consists of several tasks. The names of the units correspond to the nature of the biomacromolecules, which form their central theme. Theoretical introductions at the beginning of the unit are newly constructed and their main goal is to provide a brief overview of the basic biochemical methods used in the study of biomacromolecules.

These scripts are intentionally only available in electronic form. The reason is the effort to continuously update and modernize individual tasks according to the changing possibilities of our laboratory. We hope that the scripts will fulfill their role and that students will have sufficient theoretical knowledge and practical skills in the field of basic biochemical methods after completing these laboratory exercises.

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E-book

Vladimír Sedlák

The university textbooks entitled Global Navigation Satellite Systems: GPS, GLONAS, Galileo, Compass present four navigation systems of the GNSS (Global Navigation Satellite Systems): American NAVSTAR GPS, Russian GLONASS, European Galileo and Chinese Compass. The Satellite-Based Augmentation Systems (SBAS) are also briefly explained. They provide regional service in augmenting the reach and support of signals from satellites of the GNSS (GPS, GLONASS, Galileo, Compass). Each satellite navigation system in the frame of GNSS is elucidated in terms of its principles of operation, structure, specificities, applications, and future perspectives.

The university textbook aims to improve the reader’s understanding of the principles and activities of the presented GNSS. The book emphasizes the possibilities of GNSS applications in geodesy and geography. The university textbook constitutes the basic study literature for the class Global Navigation Satellite Systems within the study program Geography and Geoinformatics at the Faculty of Science of the Pavol Jozef Šafárik University in Košice. For a deeper study of the GNSS issue, it is necessary to extend the study materials to include other educational scientific literature dealing with navigation satellite systems and their applications.

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E-book

Jana Shepa (ed.)

The book of abstracts from 6th International Conference on Nanomaterials: Fundamentals and Applications, NFA 2022 is composed of contributions from the participants of this international conference. The conference consisted of 4 invited lecture and 52 abstracts of participants. The conference is focused on nanotechnology and its application in various research areas. All contributions are professionally processed and inspiring.

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E-book

Kveta Markušová - Daniela Kladeková

Electrochemistry is the science that studies ionic systems and the processes or phenomena that occur at the interface between ionic systems and metals or semiconductors. At the current stage of development, electrochemistry can be divided into two main areas based on its focus. The first one - ionics - deals with the properties of ionic systems (solutions, melts, solid electrolytes). The second area - electrodeics - focuses on phenomena at the electrode/ionic system interface.

Both ionics and electrodeics investigate equilibrium and non-equilibrium phenomena and processes. Research into the properties of ionic systems under equilibrium conditions provides information and insights into the structure and composition of electrolyte solutions, melts, and solid electrolytes, while measurements under non-equilibrium conditions provide data on the electrical conductivity of ionic systems. In the field of electrodeics, the study of equilibria at the electrode/solution (or melt) interface is the domain of electrochemical thermodynamics. Measuring the rates of processes occurring at this phase interface and explaining the principles governing these processes fall under the scope of electrode process kinetics or electrochemical kinetics.

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E-book

Juraj Ševc - Anna Alexovič Matiašová

Among students of single-discipline and interdisciplinary biology studies at faculties with a natural science focus, there often arises a problem in defining the scope of the curriculum when studying the subject of Human Anatomy. The presented study material aims to help students of non-medical scientific fields navigate the extensive anatomical terminology and to limit the amount of required anatomical terms to an optimum, so that alongside mastering Latin nomenclature, students still have sufficient capacity to memorize additional knowledge in the areas of systemic, comparative, developmental, and functional anatomy.

Emphasis on organizing individual anatomical terms into logical units simultaneously supports a hierarchical view of the architecture of the human body. Despite its seemingly self-serving nature, anatomical terminology thus becomes the framework upon which students build knowledge from more or less related scientific disciplines studying the human body and the processes occurring within it throughout their further studies. At the same time, alongside this ambition that goes beyond the scope of the anatomy discipline, the Anatomical Terms follow a long tradition of anatomical handbooks while respecting the valid Latin and Slovak anatomical nomenclature.

This script represents a practical supplement to university textbooks of Anatomy or Neuroanatomy and especially to anatomical atlases, but it certainly does not aim to replace them. Here you will find all the necessary terms gathered in one place, which you can always have at hand on your phone, e-reader, or laptop. The emphasis on organizing individual anatomical terms into logical units supports a hierarchical view of the architecture of the human body, and the inclusion of a brief introduction to each system is intended to encourage you to seek further, more detailed information about the structure and function of the given organ system.

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E-book

Jozef Strečka,Katarína Karľová

The 48th Conference of the Middle European Cooperation in Statistical Physics (MECO48) will be held on May 22nd-26th, 2023, in Stará Lesná, High Tatras, Slovakia. The MECO48 conference continues a long tradition of regular international meetings in the domain of statistical physics established in the early 1970s with the aim of bridging the gap between the communities of scientists from the Eastern and Western parts of Europe separated by the iron curtain.

In the modern era the MECO conferences attract attention of the community of scientists who are active in the field of statistical physics including various interdisciplinary applications to biology, medicine, geography, finance, quantum information theory, and machine learning.

The MECO48 conference is organized jointly by Faculty of Science of Pavol Jozef Šafárik University in Košice, Institute of Experimental Physics of Slovak Academy of Sciences in Košice, Institute of Physics, Slovak Academy of Sciences in Bratislava and Faculty of Humanities and Natural Sciences, University of Prešov under the financial support of Slovak Research and Development Agency (grant No. APVV-20-0150) and other sponsors.

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Jana Šandrejová - Andrea Gajdošová (eds.)

The scientific book of abstracts from the conference „Novel Trends in Chemistry, Research and Education 2024“ is a summary of the contributions of conference participants, which contain the original results of their scientific and research activities. The contributions published in this volume are divided according to content into the fields of analytical, inorganic, organic, physical chemistry, biochemistry and didactics of chemistry.

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E-book

Jozef Bednarčík

Crystallography deals with discerning the arrangement and bonding of atoms in crystalline solids. Almost immediately after their discovery, X-rays began to be used to study the internal structure of substances.

The first chapter of this textbook deals with the basic concepts of crystallography. At the beginning, crystalline solids are characterized. In the next section, the basic types of bonds and their characteristics are briefly presented. The main subject of this chapter is the interpretation of basic concepts such as symmetry operations, translational periodicity, grid, elementary cell. Spatial lattices and crystal systems are presented. At the end of this chapter, attention is paid to the description of individual types of defects in crystal structures. In the second chapter, the Bohr model of the hydrogen atom is presented. Individual quantum numbers and their meaning are given.

Next, energy levels and allowed transitions within an atom with multiple electrons are described. The second chapter concludes with the characterization of the basic absorption and emission processes. The third chapter is devoted to the production of X-ray radiation and its properties. Sources of X-ray radiation and a description of their operation are presented.

Interaction of X-ray radiation with matter, absorption and detection of X-ray radiation are the subject of the last part of this chapter.

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E-book

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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E-book

Soňa Király (ed.)

The book of abstracts from International Meeting on Advanced Materials, IMAM 2025, is composed of contributions from participants of this conference. The conference consisted of 16 lectures by mentioned conference participants. The conference is focused on advanced materials and its application in various research areas. All contributions are professionally processed and inspiring.

Download the e-book for free (pdf)

E-book

Miroslav Repčák - Martin Bačkor - Peter Paľove-Balang - Silvia Gajdošová

The establishment of the Plant Physiology Laboratory at the Department of Botany, Faculty of Arts, Pavol Jozef Šafárik University in Košice in 1969 was associated with the name of Ing. Štefan Kocúrik, CSc. (1923–2006), who also prepared the first "Instructions for Exercises in Plant Physiology" (Košice 1972, 1976).

Since 1980, the manual by Associate Professor RNDr. Karol Erdelský, CSc., and Ing. Fridrich Frič, DrSc., titled "Practicum and Analytical Methods in Plant Physiology" (Bratislava 1980) has been used. With the increase in the number of students, it became relevant in 1991 to publish the "Instructions for Exercises in Plant Physiology" again to improve preparation and the efficient organization of practical work. Associate Professor RNDr. A. Košturiak, CSc., contributed significantly to the expansion of the introductory part of the instructions with his valuable advice, for which the authors are grateful. For the fourth edition, some tasks were updated and modernized, taking into account the possibilities of the renovated laboratory. The selection of tasks was adapted to the current scope of exercises for individual plant physiology subjects within the bachelor's and master's study programs in biology and ecology. These subjects include: Plant Physiology, Plant Metabolism, Mineral Nutrition of Plants, Plant Growth and Development, and Plant Ecology. Some tasks are also suitable for high school experiments.

The choice of topics was influenced by the research focus of our workplace on secondary metabolism, ecophysiology, and medicinal plants. The instructions generally adhere to the SI unit system, occasionally including other commonly used units.

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E-book

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

Download the e-book for free  (pdf)

Ondrej Hutník a kol. 

Zbierka úloh z matematickej analýzy III. je pokračovaním predchádzajúcich dvoch vydaných zbierok autorov Kulcsár a Kulcsárová. Táto časť obsahuje príklady na zopakovanie a precvičenie učiva stredných škôl, ako aj časti prvého semestra kurzu matematická analýza určeného pre študentov matematiky, fyziky, informatiky a učiteľského štúdia v kombinácii s matematikou. Zbierka môže tiež pomôcť všetkým učiteľom, ktorí chcú použiť rôzne úlohy vo svojom vyučovaní. Zbierka zahŕňa oblasť postupností reálnych čísel: aritmetické a geometrické postupnosti, všeobecne a rekurentne zadané postupnosti, nachádzajú sa tu úlohy na vyšetrovanie vlastností postupností (monotónnosť, ohraničenosť, konvergencia) a výpočet rôznych typov limít. Všetky zadané úlohy sú vyriešené na konci každej kapitoly s podrobným komentárom.

Autori

E-book

Erik Čižmár

Textbook Automation of Laboratory Experiments in LabVIEW environment is devoted to the basics of graphical programming and shows the way how to communicate with measuring equipment and Arduino development boards in LabVIEW. The basic concepts of creating a virtual instrument and its interactive user environment are introduced. Three physical tasks are presented, the practical implementation of which takes place with the use appropriate instrumentation and LabVIEW. Practical tasks are dedicated to measuring the transmission characteristics of a low-pass RC filter, measuring the natural resonant frequency of a quartz tuning fork using the heterodyne pulse method, and mapping the magnetic field of a permanent magnet using Arduino.

Download the e-book for free (pdf)

E-book

Rastislav Varga

The movement of domain walls in ferromagnetic materials is utilized in various magnetic devices for storing, processing, or transmitting signals and information. This mainly includes transformer cores, various sensors, memory devices (e.g., HDDs in PCs), as well as modern spintronic devices such as Racetrack memories, domain wall motion-based electronics, and so on.

This book is intended to serve as a textbook for advanced courses in the field of magnetic materials. It is primarily aimed at students interested in studying magnetic materials, as well as professionals from various fields who wish to understand the basics of domain structure and its changes. It is divided into nine chapters. The first chapter deals with a brief history of the study of domain structure in magnetic materials. The second chapter provides an introduction to the causes and manifestations of magnetic anisotropies. The third and fourth chapters are devoted to the causes of domain structure formation and domain walls. The fifth chapter discusses the structure of domain walls, their potential, and the critical field required for domain wall movement. The sixth chapter is dedicated to magnetization processes, one of which - domain wall movement - is discussed in detail in chapter 7. The eighth chapter contains a theoretical solution for domain wall movement. The final ninth chapter presents a modern method of domain wall movement induced by electric current.

The presented work assumes that the reader has at least basic knowledge in the field of magnetism. Otherwise, the author refers the reader to basic literature (e.g., [2.1 - 2.6]).

Download the e-book for free (pdf)

E-book

Michal Jaščur

This is a supporting text for the undergraduate students interested in quan- tum theory of magnetism. The text represents an introduction to various theoretical approaches used in this eld. It is an open material, in the sense that it will be supported by appropriate problems to be solved by student at seminars and also as a homework.

The text consists of four chapters that form closed themes of the in- troductory quantum theory of magnetism. In the rst part we explain the quantum origin of the magnetism illustrating the appearance of the ex- change interaction for the case of hydrogen molecule. The second chapter is devoted to the application of the Bogolyubov inequality to the Heisenberg model and it represents the part which is usually missing in the textbooks of magnetism. The third chapter deals with the standard spin wave-theory including the Bloch and Holstein-Primakoff a approach. Finally, we discuss the application of the Jordan-Wigner transformation to one-dimensional spin-1/2 XY model.

The primary ambition of this supportive text is to explain diverse math- ematical methods and their applications in the quantum theory of mag- netism. The text is written in the form which should be sufficient to de- velop the skills of the students up to the very high level. In fact, it is expected that students following this course will able to make their own original applications of the methods presented in this book.

Download the e-book for free (pdf)