Moiré phenomena of different types are frequently encountered in electronic imaging. Most common are moiré effects that occur between periodic structures. These effects have been intensively investigated in the past, and their mathematical theory is today fully understood. The same is true for moiré effects between repetitive layers (i.e., between geometric transformations of periodic layers). ...

The fermionic, bosonic and supersymmetric variants of the colour-flavour transformation are derived for the orthogonal group. These transformations are then used to calculate the ensemble averages of characteristic polynomials of real random matrices. 1 Statement of main results Since the pioneering work of Wigner, many physical systems have been successfully studied with the help of random mat...

By applying the Lie symmetry method, group-invariant solutions are constructed for axially loaded Euler beams. The corresponding mathematical models of beams formulated. After introducing infinitesimal transformations, determining equations proposed via point transformations acting on original equations. generators symmetries systems presented with Maple. vector fields given to span subalgebra ...

The hierarchical algebraic decomposition of finite state automata (Krohn-Rhodes Theory) has been a mathematical theory without any computational implementations until the present paper, although several possible and promising practical applications, such as automated object-oriented programming in software development [5], formal methods for understanding in artificial intelligence [6], and a w...

We present a complete classification of all possible sets of classical reversible gates acting on bits, in terms of which reversible transformations they generate, assuming swaps and ancilla bits are available for free. Our classification can be seen as the reversible-computing analogue of Post’s lattice, a central result in mathematical logic from the 1940s. It is a step toward the ambitious g...

We apply our own software package and its extensions ([16, 14, 15, 18]) for visualisations and animations in mathematics to the graphical representation of neighbourhoods in certain relative and weak topologies that arise in the theories of dual spaces of sequence spaces and of matrix transformations between FK spaces. The paper contains a short introduction to some of the main concepts of our ...

Abstract. Black-box mathematical models are powerful tools in classification and regression problems. Thanks to the use of (unknown) transformations of the inputs, the outcome can be estimated, improving performance in comparison to standard statistical models. A disadvantage of these complex models however, is their lack of interpretability. This work illustrates how advanced methods can be ma...

Based on a mathematical model involving Radon measure explicit computations on convolution integrals defining continuous (integral) wavelet transformations are carried out. The study shows that the truncated Morlet wavelet significantly depends on a rotation parameter and thus lay a foundation of edge detection in pattern recognition and image processing using rotational (directional) wavelets....

In this paper, we introduce some mathematical features of the concentration factor, a method to extract the information of the conditions of student mental models by analyzing the distributions of students’ responses on multiple-choice questions. We discuss the state density of the concentration factor, the random attractor of SC states, and the transformations between the concentration factor ...

Graph transformation provides an intuitive mechanism for capturing model transformations. In the current paper, we investigate and compare various graph transformation tools using a compact practical model transformation case study carried out as part of the AGTIVE 2007 Tool Contest [22]. The aim of this case study is to generate formal CSP processes from high-level UML activity diagrams, which...