The Cantor Trilogy

The Cantor trilogy is a mathematical dystopia featuring JHM as an important part of that world... at least to humans

A novel approach to Hurst analysis of motor vibration data in aging processes

Determining age in motors and rotating machinery in general is a serious question. Using the vibration signals collected during motor aging is challenging due to nonlinear and non-stationary nature of these signals. This paper presents a study on applicability of Hurst analysis in motor vibration data collected in an artificial aging process, which at first seems to suggest inapplicability of Hurst Exponents in motor age determinations. Conclusions drawn from the straightforward application of Hurst exponent calculation are used to propose a novel method for Hurst analysis of such signals, named Higuchi-Hurst-Hilbert Vibration Decomposition (H³VD), using Higuchi’s algorithm for Hurst exponent calculation and Feldman’s Hilbert Vibration Decomposition overcoming the shortcomings of the original approach and delivering results that were expected based on previous research on frequency domain features of motor vibration in artificial aging processes. Features of this approach have been presented on both Fractional Gaussian noise model and the real vibration data. Non-accelerated bearing aging vibration data was used to demonstrate practical applicability of this new method

Landauova igra

U ovom radu dan je pregled pravila Landauove igre s automobilskim tablicama, kao i postojećih općih rješenja. Predstavljeno je jedno moguće novo rješenje, kao i računalna verzija ove igre. Također je upozoreno na vezu Landauove igre s jednim zadatkom s natjecanja. Natjecatelji su se možda već susreli sa sljedećim problemom: Zadatak 1 (USAMO 1995/2, [1]) Na pokvarenom džepnom kalkulatoru funkcioniraju samo tipke koje odgovaraju sinusu, kosinusu, tangensu i njima inverznim operacijama. Na zaslonu kalkulatora u početnom se trenutku nalazi 0. Pokazati da se pritiskom na tipke kalkulatora konačan broj puta može dobiti bilo koji pozitivan racionalan broj (Argumenti funkcija su u radijanima, pretpostavka je da kalkulator računa s beskonačnom preciznošću)

Afine transformacije ravnine

U ovom tekstu pokušat ćemo sistematično izložiti teoriju afinih transformacija u ravnini, prilagođenu srednjoškolskom nivou, te kroz niz ilustrativnih primjera pokazati njihovu primjenu pri rješavanju različitih geometrijskih problema. Afine transformacije nalaze se negdje između sintetičkih i nesintetičkih metoda: ne pretvaraju geometrijski problem u algebarski (kao što to čine analitičke metode), ali su neodvojivo povezane s vektorima, vektorskim prostorima i koordinatnim sustavima. Primjeri i zadaci su izabrani tako da pokažu standardne metode rješavanja planimetrijskih problema uz pomoć afinih transformacija i omoguće zainteresiranom čitatelju rješavanje problema za samostalan rad navedenih na kraju članka

Inverzija

Autor prezentira osnovne informacije o inverziji u planimetriji

Diferenciranje i integriranje pod znakom integrala

U članku se prezentiraju neke tehnike rješavanja integrala koristeći rezultate o diferenciranju i integriranju pod znakom integrala. http://e.math.hr/math_e_article/br18/glogic_silja

Murder on the Einstein express and other stories

This collection of stories touches upon many genres: Normed Trek is a clever and witty Alice-in-Wonderland-type narrative set in the realm of mathematical analysis, The Cantor Trilogy is a dystopia about the consequences of relying upon computer-based mathematical proofs, In Search of Future Time bears the flavor of Tales from Arabian Nights set in the future, and – last but not least - Murder on the Einstein Express is a short, non-technical primer on probabilities and modern classical physics, disguised as a detective story. Written primarily for an audience with some background or a strong interest in mathematics, physics and computer science (in particular artificial intelligence), these stories explore the boundaries between science and fiction in a refreshingly unconventional fashion. In the Afterthoughts the author provides some further insights and annotations. Harun Šiljak got his BoEE and MoEE degrees at the Department of Control and Electronics, University of Sarajevo and his PhD in Signal Processing at the Electrical and Electronics Engineering Department, International Burch University, Sarajevo, where he is currently an assistant professor. He has been working in basic sciences (mathematics and physics) since elementary school, qualifying twice for the International Mathematical Olympiad and once for the International Physics Olympiad. Some of his science fiction and popular science stories have been published in the Mathematical Intelligencer and in the Journal of Humanistic Mathematics