Search results for "Discrete Mathematics"
showing 10 items of 1728 documents
From Lattice Valued Theories to Lattice Valued Analysis
2015
We claim and justify that the future of a fuzzy logic is in the interconnection of various well-developed theories. We are focused on a lattice valued analysis that unifies the treatments of atomic elements, sets of atomic elements, functions between sets of atomic elements and their properties. We clarify the relationship between a fuzzy function and its ordinary core. We discuss the property of continuity of a fuzzy function in a lattice valued topology.
2-Groups with few rational conjugacy classes
2011
Abstract In this paper we prove the following conjecture of G. Navarro: if G is a finite 2-group with exactly 5 rational conjugacy classes, then G is dihedral, semidihedral or generalized quaternion. We also characterize the 2-groups with 4 rational classes.
The Kuratowski convergence and connected components
2012
International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.
Two-view “cylindrical decomposition” of binary images
2001
This paper describes the discrete cylindrical algebraic decomposition (DCAD) construction along two orthogonal views of binary images. The combination of two information is used to avoid ambiguities for image recognition purposes. This algorithm associates an object connectivity graph to each connected component, allowing a complete description of the structuring information. Moreover, an easy and compact representation of the scene is achieved by using strings in a five letter alphabet. Examples on complex digital images are also provided. © 2001 Elsevier Science Inc.
?-constraint with respect to a Fitting class
1986
Orbits of bounded bijective operators and Gabor frames
2020
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are often used in applications. More precisely, the paper deals with a question posed in the last years by Christensen and Hasannasab about the existence of overcomplete Gabor frames, with some ordering over $\mathbb{Z}$, which are orbits of bounded operators on $L^2(\mathbb{R})$. Two classes of overcomplete Gabor frames which cannot be ordered over $\mathbb{Z}$ and represented by orbits of operators in $GL(L^2(\mathbb{R}))$ are given. Some results about opera…
Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infin…
2016
In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddl…
Fuzzy logic approach to predict vehicle crash severity from acceleration data
2015
Vehicle crash is a complex behavior to be investigated as a challenging topic in terms of dynamical modeling. On this aim, fuzzy logic can be utilized to analyze the crash dynamics rapidly and simply. In this paper, the experimental data of the frontal crash is recorded using an accelerometer located at the centre of the gravity of the vehicle. The acceleration signal was the raw data from which the collision intensity expressed by the kinetic energy and the jerk were derived. The fuzzy logic model was then developed from the two inputs namely kinetic energy and jerk. The output variable is the crash severity expressed as the dynamic crash. The result shows that the jerk contributes much to…
Computing Euclidean Steiner trees over segments
2020
In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superse…
Probabilistic interpretation of the Calderón problem
2017
In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calderon's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes. This probabilistic interpretation comes in three equivalent formulations which open up novel perspectives on the classical question of unique determinability of conductivities from boundary data. We aim to make this work accessible to both readers with a background in stochastic process theory as well as researchers working on deterministic methods in inverse problems.