FIHS 2025

One of the most widely used models of handheld radios is the Baofeng UV-5R. We'll look at the basics of its operation and talk about common findings on the available radio frequencies. Not to be missed are the basics of etiquette for ham radio operators and neccessary precautions.

The author will present the most important results that he came to during the preparation of his master's thesis and will elaborate on the ones that can help the audience the most to orient themselves in the given area of pedagogical research. The lecture will develop the epistemological background of the audience and can facilitate their navigation among scientific theories in any field. It will also summarize selected social research concepts that aid in the modernization of the science curriculum, necessary for the education of the new generation of scientists. The author will be happy to share what he learned from the journey.

As every year, we will open with a lecture containing a selection of recent discoveries in various fields of natural science. In addition, listeners will be encouraged to share insights from recent conferences they have attended.

Perturbation theory provides a systematic framework for deriving approximate solutions to problems involving a small parameter, particularly in ordinary differential equations (ODEs). In this talk, we will establish the foundational concepts and key methodologies of this field. We will begin by examining the Poincaré-Lindstedt method for periodic oscillators, using Duffing's equation to illustrate how secular terms are eliminated to yield uniformly valid approximations for oscillatory behavior. We will then explore the two-scale method for analyzing damped oscillators, with examples such as Cole's and the van der Pol's oscillator, focusing on systems with multiple time scales. Finally, a core focus will be placed on boundary layer problems, where we will introduce the method of matched asymptotic expansions. Using Friedrichs' equation, we will detail the construction of inner and outer solutions and their matching to form a composite solution. This presentation aims to provide a clear understanding of these powerful perturbation techniques and their wide applicability in applied mathematics and engineering.

Stochastic Differential Equations (SDEs) are a powerful mathematical framework for modeling systems evolving under random influences. In this talk, we will establish the foundational concepts of SDEs, beginning with Martingale, Wiener, and Itô processes, and introduce Itô's Lemma. We will then examine the Fokker-Planck equation and its derivation, which describes the evolution of probability density functions for stochastic processes. A core focus will be placed on the precise computation of hitting probabilities and expected stopping times, exploring general solutions and specific cases like decaying processes. Finally, we will apply these concepts to "Limit Laws for Critical Dispersion on Complete Graphs." This section will illustrate how the Central Limit Theorem can be utilized to analyze the dispersion of particles on a complete graph, framing the system as a Harris chain (a continuous Markov chain), and conclude with a discussion on the mean time to reach a specific state and boundary layer behavior.

Active look at phenomena distinguishing its properties especially ones which somehow are emerging from the perception and close observation. This activity could lead to new point of views and new question could come. We will look at different phenomena and try this process, we will try to be integral in our description and try not to loose connection between the human and the phenomenon. The practical philosophy will be helping us.

Reichenbach's Common Cause Principle (RCCP) posits that correlations arise either from direct causal links or common causes. We investigate its mathematical structure under four foundational axioms. Focusing first on countably additive states, we show that RCCP is meaningful only for positively correlated events and compare the classical Boolean and quantum settings, highlighting key differences in maximal correlation. A counterexample is constructed using a free orthomodular lattice, resolving an open question. We then relate RCCP to the Darboux property and prove that atomless countable complete quantum logics are common-cause complete. Additionally, we demonstrate that certain incomplete quantum logics can be embedded into complete ones. Finally, we explore RCCP under finitely additive states, constructing countable Boolean and quantum logics with states that are common-cause complete, thus uncovering novel examples within this broader framework.

The author will present basics of light and biological tissue interactions and their applications in medical field. Theoretical basics will be followed by presentation of authors' experiments and their results aimed at harvesting the information to build diagnostical optical medical tools on.