Search results for " space"
showing 10 items of 4562 documents
A Learning-Automata Based Solution for Non-equal Partitioning: Partitions with Common GCD Sizes
2021
The Object Migration Automata (OMA) has been used as a powerful tool to resolve real-life partitioning problems in random Environments. The virgin OMA has also been enhanced by incorporating the latest strategies in Learning Automata (LA), namely the Pursuit and Transitivity phenomena. However, the single major handicap that it possesses is the fact that the number of objects in each partition must be equal. Obviously, one does not always encounter problems with equally-sized groups (When the true underlying problem has non-equally-sized groups, the OMA reports the best equally-sized solution as the recommended partition.). This paper is the pioneering attempt to relax this constraint. It p…
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…
Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets
2014
The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to …
Invariant approximation results in cone metric spaces
2011
Some sufficient conditions for the existence of fixed point of mappings satisfying generalized weak contractive conditions is obtained. A fixed point theorem for nonexpansive mappings is also obtained. As an application, some invariant approximation results are derived in cone metric spaces.
A product space reformulation with reduced dimension for splitting algorithms
2021
AbstractIn this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra’s classical reformulation with a different decomposition, which results in a reduction of the dimension of the outcoming product Hilbert space. We discuss the case of not necessarily convex feasibility and best approximation problems. By applying existing splitting methods to the proposed reformulation we obtain new parallel variants of them with a reduction in the number of variables. The convergence of the new algorithms is straightforwardly derived with no further assump…
On the Applicability of the Space Syntax Methodology for the Determination of Street Lighting Classes
2020
Street lighting plays a crucial role in a city’s night landscape and in urban traffic management, influencing users’ comfort and safety. To contain costs of public street lighting systems and to avoid energy waste, illuminance levels on road surfaces must be adequate to fit actual traffic volumes, as prescribed by regulations. This is true not only for motorized roads but also for sidewalks, paths, and pedestrian areas. Regulations in force establish a relationship between road traffic volumes and minimum illuminance levels through the lighting classes selection procedure. Lighting classes selection is based on various para meters among which traffic volume is the most difficult to evaluate…
Approximations of Parabolic Equations at the Vicinity of Hyperbolic Equilibrium Point
2014
This article is devoted to the numerical analysis of the abstract semilinear parabolic problem u′(t) = Au(t) + f(u(t)), u(0) = u 0, in a Banach space E. We are developing a general approach to establish a discrete dichotomy in a very general setting and prove shadowing theorems that compare solutions of the continuous problem with those of discrete approximations in space and time. In [3] the discretization in space was constructed under the assumption of compactness of the resolvent. It is a well-known fact (see [10, 11]) that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value prob…
Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations
2012
We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.
On Boundary Conditions for Wedge Operators on Radial Sets
2008
We present a theorem about calculation of fixed point index for k-$\psi$-contractive operators with 0 < k <1 defined on a radial set of a wedge of an infinite dimensional Banach space. Then results on the existence of eigenvectors and nonzero fixed points are obtained.
Development of Point-to-Point Path Control in Actuator Space for Hydraulic Knuckle Boom Crane
2020
This paper presents a novel method for point-to-point path control for a hydraulic knuckle boom crane. The developed path control algorithm differs from previous solutions by operating in the actuator space instead of the joint space or Cartesian space of the crane. By operating in actuator space, almost all the parameters and constraints of the system become either linear or constant, which greatly reduces the complexity of both the control algorithm and path generator. For a given starting point and endpoint, the motion for each actuator is minimized compared to other methods. This ensures that any change in direction of motion is avoided, thereby greatly minimizing fatigue, jerky motion,…