Search results for "Mathematica"
showing 10 items of 7971 documents
A new approach for geological faults detection
2004
This paper will introduce a new approach, mainly based on wavelets transform and mathematical morphology, for the detection of geological faults in satellite and aerial photos. This can be useful for territorial analysis, digital cartography and the use of geographical information systems. The proposed method is fast enough and unsupervised. Different techniques will be compared and some examples on real data will be presented to indicate the applicability of these methods.
Wyzwalanie dziecięcej aktywności matematycznej w trakcie rozwiązywania zadań
2018
Aktywność ucznia ma ogromne znaczenie w kształtowaniu i rozwijaniu abstrakcyjnych pojęć matematycznych. Jednak aktywność ta nie powinna ograniczać się jedynie do aktywności zewnętrznej, często jedynie pozornej, ale przede wszystkim powinna być to aktywność umysłowa ucznia. Zachowania i postawy specyficzne dla aktywności matematycznej można bowiem rozwijać u ucznia jedynie w toku jego aktywności poznawczej (intelektualnej). W opracowaniu podjęto próbę ukazania możliwości stymulowania i rozwijania oraz przejawy aktywności matematycznej uczniów w wieku wczesnoszkolnym w trakcie rozwiązywania zadań.
Relaxation of a weakly discontinuous functional depending on one control function
2008
The paper considers an optimal control problem of the typewhere the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.
Deformation Quantization in White Noise Analysis
2007
We define and present an example of a deformation quantization product on a Hida space of test functions endowed with a Wick product.
Modelling and analysing oriented fibrous structures
2014
Abstract. A mathematical model for fibrous structures using a direction dependent scaling law is presented. The orientation of fibrous nets (e.g. paper) is analysed with a method based on the curvelet transform. The curvelet-based orientation analysis has been tested successfully on real data from paper samples: the major directions of fibrefibre orientation can apparently be recovered. Similar results are achieved in tests on data simulated by the new model, allowing a comparison with ground truth. peerReviewed
First and second order rational solutions to the Johnson equation and rogue waves
2018
Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the cases N = 1 and N = 2 which are given in the following. We study the evolution of the solutions by constructing the patterns of their modulus in the (x, y) plane, and this for different values of parameters.
The defocusing NLS equation : quasi-rational and rational solutions
2022
Quasi-rational solutions to the defocusing nonlinear Schrödinger equation (dNLS) in terms of wronskians and Fredholm determinants of order 2N depending on 2N − 2 real parameters are given. We get families of quasi-rational solutions to the dNLS equation expressed as a quotient of two polynomials of degree N (N + 1) in the variables x and t. We present also rational solutions as a quotient of determinants involving certain particular polynomials.
Solutions to the Gardner equation with multi-parameters and the rational case
2022
We construct solutions to the Gardner equation in terms of trigonometric and hyperbolic functions, depending on several real parameters. Using a passage to the limit when one of these parameters goes to 0, we get, for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 3. We easily deduce solutions to the mKdV equation in terms of wronskians as well as rational solutions depending on 2N real parameters.
Properties of zeros of solutions to third order nonlinear differential equations
2013
We investigate the behavior of zeros of solutions to the certain type of third order nonlinear differential equations. We show that the behavior of zeros may be rather different and depend on the nature of nonlinearity in the equation. Main results in the paper are illustrated with a number of examples.
On the Amount of Nonconstructivity in Learning Recursive Functions
2011
Nonconstructive proofs are a powerful mechanism in mathematics. Furthermore, nonconstructive computations by various types of machines and automata have been considered by e.g., Karp and Lipton [17] and Freivalds [11]. They allow to regard more complicated algorithms from the viewpoint of much more primitive computational devices. The amount of nonconstructivity is a quantitative characterization of the distance between types of computational devices with respect to solving a specific problem. In the present paper, the amount of nonconstructivity in learning of recursive functions is studied. Different learning types are compared with respect to the amount of nonconstructivity needed to lea…