On continuity of the entropy-based differently implicational algorithm

summary:Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity. To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous t-norms are employed. Furthermore, four numerical fuzzy inference examples are provided, and it is found that the entropy-based differently implicational algorithm can obtain more reasonable solution in contrast with the fuzzy entropy full implication algorithm. Finally, in the entropy-based differently implicational algorithm, we point out that the first fuzzy implication reflects the effect of rule base, and that the second fuzzy implication embodies the inference mechanism

Testing deviations from the \u39bCDM model with electromagnetic and gravitational waves

The \u39bCDM model has been extensively tested over the past decades and has been established as the standard model of cosmology. Despite its huge successes, it faces some serious theoretical problems, especially related to the nature of dark matter and dark energy. Different possible modifications and extensions have been considered in the past in order to solve these problems, and a question of central importance is how these modifications can be tested and experimentally distinguished from the standard case. The aim of this thesis is twofold. First, it presents two different modifications of the dark sector. A model in which dark matter forms a Bose-Einstein condensate in high density regions and in the process forms a non-minimal coupling to the metric is considered as a possible deviation from the cold dark matter scenario, while the possibility that dark energy is inhomogeneous in space is discussed as a possible deviation from a pure cosmological constant scenario. Second, it examines ways to test these possibilities via two main observational channels - gravitational waves and electromagnetic waves. The gravitational wave event GW170817 is used to test the dark matter model and to put constraints on the mass of the dark matter field and the strength of the nonminimal coupling. The luminosity distance and the redshift of light are highlighted as important observables for dark energy, and generalised theoretical formulae for these observables are derived for conformally FLRW and perturbed FLRW spacetimes. The luminosity distance and the redshift are finally used to test for possible anisotropies of the accelerated expansion of the universe

Comparing Features of Three-Dimensional Object Models Using Registration Based on Surface Curvature Signatures

This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison

Approximation Theory and Related Applications

In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics