The problems of unattainable infinity and infinitesimal are discussed. Limitations connected with the absolute zero of temperature and the maximal velocity are considered, as well as the consequences of these limitati...The problems of unattainable infinity and infinitesimal are discussed. Limitations connected with the absolute zero of temperature and the maximal velocity are considered, as well as the consequences of these limitations. A geometric approach is proposed as an alternative to the wave-particle duality to explain the anomalous motion of micro objects. The basis of the geometric approach is a comparison between two geometries differing from each other in the metric of infinitesimal. The interconnection of these geometries is possible through the direct and inverse Weierstrass transformation. The application of this transformation allows one to explain diffraction effects.展开更多
In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational int...In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational interpolation.展开更多
Modern but not entirely coordinated foundations of quantum physics are described in the book “The Quantum Challenge”. The difficulties and philosophical problems of this area of science are discussed. Discussions of...Modern but not entirely coordinated foundations of quantum physics are described in the book “The Quantum Challenge”. The difficulties and philosophical problems of this area of science are discussed. Discussions of many great scientists who paved the foundations of the physics of micro-world are described. These discussions are still urgent. The diversity of interpretations of the wave function, light interference, uncertainty principle, complementarity and completeness of micro-world description are stressed in this book. Difficulties and problems of quantum mechanics described in this book allowed the author of the present communication to propose a new approach based on the infinitely small metrics The difference of infinitesimals in two geometries allows one to explain W. Heisenberg’s uncertainty principle. Interconnection of the images in these geometries is possible with the help of Weierstrass integral transform. This approach allows one to describe the interference of light behind the screen with slits as a sum of the corpuscular component (Weierstrass transform) and the wave component (Fourier transform).展开更多
Through adjusting the order of interpolation nodes, we gave a kind of modified Thiele-Werner rational interpolation. This interpolation method not only avoids the infinite value of inverse differences in constructing ...Through adjusting the order of interpolation nodes, we gave a kind of modified Thiele-Werner rational interpolation. This interpolation method not only avoids the infinite value of inverse differences in constructing the Thiele continued fraction interpolation, but also simplifies the interpolating polynomial coefficients with constant coefficients in the Thiele-Werner rational interpolation. Unattainable points and determinantal expression for this interpolation are considered. As an extension, some bivariate analogy is also discussed and numerical examples are given to show the validness of this method.展开更多
Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In ...Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In this paper,several general frames are established by introducing multiple parameters and they are extensions and improvements of those for the general frames studied by Tan and Fang.Numerical examples are given to show the effectiveness of the results in this paper.展开更多
文摘The problems of unattainable infinity and infinitesimal are discussed. Limitations connected with the absolute zero of temperature and the maximal velocity are considered, as well as the consequences of these limitations. A geometric approach is proposed as an alternative to the wave-particle duality to explain the anomalous motion of micro objects. The basis of the geometric approach is a comparison between two geometries differing from each other in the metric of infinitesimal. The interconnection of these geometries is possible through the direct and inverse Weierstrass transformation. The application of this transformation allows one to explain diffraction effects.
基金The NNSF (10471055) of China and the National Grand Fundamental Research 973 Program (2004CB318000) of China.
文摘In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational interpolation.
文摘Modern but not entirely coordinated foundations of quantum physics are described in the book “The Quantum Challenge”. The difficulties and philosophical problems of this area of science are discussed. Discussions of many great scientists who paved the foundations of the physics of micro-world are described. These discussions are still urgent. The diversity of interpretations of the wave function, light interference, uncertainty principle, complementarity and completeness of micro-world description are stressed in this book. Difficulties and problems of quantum mechanics described in this book allowed the author of the present communication to propose a new approach based on the infinitely small metrics The difference of infinitesimals in two geometries allows one to explain W. Heisenberg’s uncertainty principle. Interconnection of the images in these geometries is possible with the help of Weierstrass integral transform. This approach allows one to describe the interference of light behind the screen with slits as a sum of the corpuscular component (Weierstrass transform) and the wave component (Fourier transform).
基金Supported by the National Natural Science Foundation of China (Grant No.60473114)the Natural Science Foundation of Anhui Province (Grant No.070416227)
文摘Through adjusting the order of interpolation nodes, we gave a kind of modified Thiele-Werner rational interpolation. This interpolation method not only avoids the infinite value of inverse differences in constructing the Thiele continued fraction interpolation, but also simplifies the interpolating polynomial coefficients with constant coefficients in the Thiele-Werner rational interpolation. Unattainable points and determinantal expression for this interpolation are considered. As an extension, some bivariate analogy is also discussed and numerical examples are given to show the validness of this method.
基金the National Natural Science Foundation of China (No.60473114)the Anhui Provincial Natural Science Foundation (No.070416227)the Key Project Foundation of the Department of Education of Anhui Province (No.KJ2008A027)
文摘Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In this paper,several general frames are established by introducing multiple parameters and they are extensions and improvements of those for the general frames studied by Tan and Fang.Numerical examples are given to show the effectiveness of the results in this paper.
