Základy znalostných systémov

E-book

Valéria Skřivánková - Martina Hančová

The publication is focused on discrete random processes, primarily on Markov chains, which have wide application in the field of economics and finance.

The textbook is divided into five chapters, the first of which serves as an introduction to random processes and provides definition, properties and classification of random processes in general. The second chapter discusses Markov chains with discrete time, including valuation of transitions between states and their optimal management. The third chapter focuses on special Markov chains with continuous time and emphasizes construction and solution to the system of Kolmogorov differential equations, which describe the dynamics of the process development. The last two chapters illustrate applications of Markov chains using examples of queuing system modeling and renewal theory.

Besides the explanation of basic terms, definitions and theorems with proofs, this textbook also provides number of solved examples to illustrate the discussed theory. Problem assignments are placed at the end of each chapter, so that readers can test their understanding of the content as they progress through the book. Solutions to all the problems and the list of references are provided at the end of the publication.

This textbook is primarily intented for students majoring in Economics and Financial Mathematics at the Faculty of Science of Pavol Jozef Šafárik University in Košice, and it covers content of the course “Random Proceses 1“ thought there. It might however serve also students from other schools in similar progams or professionals interested in this topic.

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E-book

Marek Bombara

The collection of exercises summarises and supplements the exercises realised at the Pavol Jozef Šafárik in Košice within the lecture course Elementary Particle Physics. The collection is intended for the master students of the Nuclear and Subnuclear Physics subject, but it could be beneficial also for other physics subjects or even for interdisciplinary study. 

The division of chapters roughly copies the order of lectures. At the beginning, students will briefly familiarize themselves with the basics of special relativity and its practical use in particle physics.

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E-publication

Beáta Valkay ed.
Ivana Slepáková-Lenka Maliničová a kol.

The publication EFFUSE – Educational Materials for the Public was developed within the EFFUSE project and focuses on current environmental issues of river landscapes. It emphasizes the importance of water as an irreplaceable resource and the need to protect it. Special attention is given to bioindicators – organisms whose presence or absence reflects the state of the environment. Monitoring bioindicators makes it possible to detect ecosystem changes before serious damage occurs. The publication highlights that biodiversity is essential for ecosystem stability and health. As such, it serves as a valuable educational resource for the public, raising environmental awareness and encouraging active involvement in nature conservation.

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E-book

Katarína Cechlárová

Linear programming belongs to parts of mathematics with the greatest number of real applications. This Slovak-English problem collection provides an overview of basic knowledge in the area, application problems as well as problems to acquire routine in calculations. It is complemented by questions motivating the student to look for further theoretical principles, construct conterexamples  and formulate arguments to explain the studied phenomena.

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E-book

Vladislav Kolarčik

Flow cytometry is a diagnostic and research technique that enables rapid analysis of cells, nuclei and organelles of plants and other organisms. In plant biology, it is most often used for DNA content analysis in a wide range of applications. It is the method of first choice and its importance is even increasing compared to competing technologies. It is unrivaled in speed, accuracy, repeatability and low cost. Flow cytometry has become a standard tool in laboratories focused on biological-ecological plant research.

This textbook provides information on the historical development of flow cytometry and its establishment in the analysis of the plant genome. It describes the procedure of sample analysis to determine the nuclear DNA content and presents the basic applications, such as determination of genome size, ploidy level and reproduction modes of plants and determination of endopolyploidy level in plant tissues. These college textbooks are intended for students, teachers and anyone interested in the use of flow cytometry in scientific work with plant cells.

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E-book

Michal Hnatič - Tomáš Lučivjanský

This textbook is primarily intended for first-year master's degree students at Pavol Jozef Šafárik University in Košice, especially those in the nuclear physics, subnuclear physics, and theoretical physics programs. For many years, these lectures were taught by one of the authors at this university, and naturally, over time, there arose an effort to provide these lectures to students in printed form.

In this textbook, we will focus mainly on classical field theory, its quantization based on the operator approach, and the introduction of interactions. Descriptions based on functional integration, Feynman diagram techniques, and more advanced parts will be covered in a subsequent volume of the textbook. In this context, we want to emphasize that in many modern quantum field theory textbooks, the operator approach is used to a lesser extent and is replaced by the approach using (functional) path integrals.

This is probably due to time considerations, as the functional approach leads much faster to practical calculations. On the other hand, we believe that the operator approach is better from a pedagogical point of view. It is much closer to the traditional quantum mechanics course, which is often based on the Schrödinger or Heisenberg formalism. Therefore, students can much more easily follow the flow of ideas that led to the construction of quantum field theory and its fundamental concepts.

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E-book

Marián Kireš  (ed.)

Proceedings of Abstracts from the Student Scientific Conference of the Faculty of Science, Pavol Jozef Šafárik University in Košice

The Student Scientific Conference (SSC) represents the culmination of long-term and intensive work on a selected topic, collaboration with a supervisor, or a broader team at the workplace. In practice, however, it often marks the beginning of scientific research, focusing on a chosen subject, field, or close cooperation with a future supervisor of a bachelor's, master's, or doctoral thesis.

This year, the Student Scientific Conference took place on April 19, 2023, featuring 14 sections, a programming competition, and the IHRA contest. Bachelor’s and master’s students presented 101 contributions. Additionally, 8 high school students participated non-competitively, presenting their SOČ projects; 14 students took part in the programming competition, and 3 students competed in the IHRA contest.

We believe that the proceedings of abstracts and related documents serve not only as an archive but also as a dignified presentation of scientific activities at our faculty for the wider public.

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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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E-book

Janka Vrláková - Adela Kravčáková - Stanislav Vokál

The presented "Collection of Problems in Atomic and Nuclear Physics" is intended as a basic study material for lectures in General Physics IV in the second year of the bachelor's single-subject physics program and interdisciplinary studies combined with physics at the Faculty of Science of P. J. Šafárik University in Košice.

Its aim is to support independent student work and to deepen the acquired knowledge from the given physics course by solving selected problems. It is divided into three main parts: Atomic Physics, Nuclear Physics, and Experimental Methods of Nuclear Physics.

Each thematic chapter contains an overview of basic concepts, relations, and formulas necessary for better understanding of sample problems and for solving the attached set of unsolved problems.

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E-book

Vladimír Zeleňák (ed.)

The proceedings contain contributions from participants of the Student Scientific Conference of the Faculty of Science at UPJŠ in Košice, which took place on April 24, 2014.

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E-book

Ondrej Hutník

The concept of the integral is one of the most significant concepts in mathematics as a whole. In its most primitive form, it was already used by the ancient Greeks in the creation of Euclidean geometry. However, it was only after Descartes' work on analytical geometry in 1637 that mathematicians could begin to consider the integral as a subject of analysis. Descartes' work laid the groundwork for the discovery of infinitesimal calculus by Leibniz and Newton around 1665. At that time, a great dispute arose over the priority of this discovery, dividing scholars of Germany and England into two opposing camps, each favoring their own champion. Today, we know that Newton's work on fluxions and fluents was somewhat earlier, but Leibniz's notation and approach have gained more acceptance in the mathematical world, and the symbols ∫ ∫ and d d are still used today. A brief overview of the history of the integral will be presented in Chapter 1.

Today, there is a plethora of scripts, textbooks, and books dedicated to explaining the concept of the integral. Therefore, every potential author faces the initial question of whether to write another text on this topic. Our affirmative answer to this question was driven by the students' request to find the subject matter of a part of the winter semester of the second year presented in a coherent form. The second motivation is a slightly different approach to the topic. If we consider the methods typically used in solving problems and gaining routine with a certain integral, it mainly involves the Newton-Leibniz formula, and often there is little time left to compute the definite (Riemann) integral using its definition. Therefore, we included a discussion of the Newton integral in Chapter 2, which reflects this fact and is directly related to the indefinite integral, whose various calculation methods receive relatively much attention in the previous semester. Only after that, in Chapter 3, do we build the theory of the Riemann integral, present criteria for its existence, classes of integrable functions, basic properties, and finally its relationship with the Newton integral. Questions primarily concerning geometric applications are addressed in Chapter 4, and in the final chapter, we focus on extending the Riemann integral to unbounded functions and unbounded intervals.

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Marcel Uhrin - Petr Benda -  Peter Kaňuch

Bats represent a unique group of mammals, characterised by different life strategies. They are the only mammals capable of active flight, which, combined with their almost exclusively nocturnal activity, has led to the evolution of specific adaptations. One of the most striking is echolocation, which enables them to orientate themselves perfectly in their surroundings in the dark. Bats are mainly native to the tropics, but have also colonised areas outside the tropics, which, has led to a complex phenological cycle with active phases and interruptions during hibernation, especially in temperate zones. In this diverse and species-rich group (almost 1,500 known species), there is a wide range of social organisation as well as feeding and roosting strategies. The textbook "Fundamentals of Chiropterology" brings the current state of knowledge about these extraordinary animals in eleven chapters and two appendices for the first time in the Slovak language.

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

Monika Tvrdoňová - Miroslava Martinková

The scientific book of abstracts from conference „Novel Trends in Chemistry, Research and Education 2022“ 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 can be divided according to content into the field of analytical, inorganic, organic, physical chemistry, biochemistry, didactics of chemistry and NMR spectroscopy.

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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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Valéria Skřivánková 

Predložený učebný text sa pokúša ilustrovať možné aplikácie Teórie pravdepodobnosti na príkladoch z oblastí (vo fyzike, chémii,  biológii, ekonomike, finančníctve, atď.), ktoré sú spestrené o úlohy na hľadanie optimálnej stratégie.

Text je určený predovšetkým poslucháčom Prírodovedeckej fakulty UPJŠ, budúcim učiteľom matematiky, študentom odboru matematika a informatika prípadne iným záujemcom, ktorí budú aplikovať pravdepodobnostné metódy pri riešení reálnych problémov. Obsahom pokrýva prvú časť predmetu "Pravdepodobnosť a štatistika".

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