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Wybrane publikacje

  • Quantum structure in competing lizard communities


    Almost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing...

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  • Crystallization of space: Space-time fractals from fractal arithmetic

    Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...

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  • Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

    Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

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Uzyskane stopnie/tytuły naukowe

  • 1994-11-17

    Nadanie stopnia naukowego

    Uniwersytet Gdański Wydział Matematyki i Fizyki

wyświetlono 810 razy