Search results for "Bounded function"
showing 10 items of 508 documents
Large Eddy Simulations of Rough Turbulent Channel Flows Bounded by Irregular Roughness: The Role of Geometrical Parameters
2020
Almost all bounded flows, in nature and industry, are bounded by rough boundaries. Important efforts have been made, in fact, to analyse the physics of the fluids over such geometries. Basically, rough walls strongly influence the total energy dissipation, with important consequences in the form of higher costs especially in industrial applications.
Implementation of a two stage fully-blind self-adapted spectrum sensing algorithm
2017
In this paper, an experimental validation of a combined two-stage detector called 2EMC is carried out. The detector is proposed in [1]. The 2EMC is composed of energy detector as a primary stage and maximum-minimum eigenvalue detector as a secondary stage. The 2EMC outperforms the two individual detectors in terms of the probability of detection for the same probability of false alarm. Regarding the complexity measured in the sensing time, the 2EMC sensing time is bounded by the sensing times of the two individual detectors. 2EMC incorporates noise estimation that is used by the energy detector, which makes it fully-blind and self-adapted detector. The noise estimator performance is express…
Homomorphisms on spaces of weakly continuous holomorphic functions
1999
Let X be a Banach space and let $X^{\ast }$ be its topological dual space. We study the algebra ${\cal H}_{w^\ast}(X^{\ast})$ of entire functions on $X^{\ast }$ that are weak-star continuous on bounded sets. We prove that every m-homogeneous polynomial of finite type P on $X^*$ that is weak-star continuous on bounded sets can be written in the form $P=\textstyle\sum\limits _{j=1}^q x_{1j}\cdots x_{mj}$ where $x_{ij} \in X$ , for all i,j. As an application, we characterize convolution homomorphisms on ${\cal H}_{w^\ast}(X^{\ast})$ and on the space ${\cal H}_{wu}(X)$ of entire functions on X which are weakly uniformly continuous on bounded subsets of X, assuming that X * has the approximation…
Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
1994
We use Morse theory to estimate the number of positive solutions of an elliptic problem in an open bounded setΩ ∉ ℝN. The number of solutions depends on the topology ofΩ, actually onP t (Ω), the Poincare polynomial ofΩ. More precisely, we obtain the following Morse relations: $$\sum\limits_{u \in K} {t^{\mu \left( u \right)} } = tP_t \left( \Omega \right) + t^2 [P_t \left( \Omega \right) - 1] + t\left( {1 + t} \right)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{O} \left( t \right)$$ , where $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{O} \left( t \right)$$ is a polynomial with non-negative integer coefficients,K is the set of positive solutions …
Infinite orbit depth and length of Melnikov functions
2019
Abstract In this paper we study polynomial Hamiltonian systems d F = 0 in the plane and their small perturbations: d F + ϵ ω = 0 . The first nonzero Melnikov function M μ = M μ ( F , γ , ω ) of the Poincare map along a loop γ of d F = 0 is given by an iterated integral [3] . In [7] , we bounded the length of the iterated integral M μ by a geometric number k = k ( F , γ ) which we call orbit depth. We conjectured that the bound is optimal. Here, we give a simple example of a Hamiltonian system F and its orbit γ having infinite orbit depth. If our conjecture is true, for this example there should exist deformations d F + ϵ ω with arbitrary high length first nonzero Melnikov function M μ along…
Learning of regular expressions by pattern matching
1995
We consider the problem of restoring regular expressions from good examples. We describe a natural learning algorithm for obtaining a “plausible” regular expression from one example. The algorithm is based on finding the longest substring which can be matched by some part of the so far obtained expression. We believe that the algorithm to a certain extent mimics humans guessing regular expressions from the same sort of examples. We show that for regular expressions of bounded length successful learning takes time linear in the length of the example, provided that the example is “good”. Under certain natural restrictions the run-time of the learning algorithm is polynomial also in unsuccessf…
Pseudo-abelian integrals: Unfolding generic exponential case
2009
The search for bounds on the number of zeroes of Abelian integrals is motivated, for instance, by a weak version of Hilbert's 16th problem (second part). In that case one considers planar polynomial Hamiltonian perturbations of a suitable polynomial Hamiltonian system, having a closed separatrix bounding an area filled by closed orbits and an equilibrium. Abelian integrals arise as the first derivative of the displacement function with respect to the energy level. The existence of a bound on the number of zeroes of these integrals has been obtained by A. N. Varchenko [Funktsional. Anal. i Prilozhen. 18 (1984), no. 2, 14–25 ; and A. G. Khovanskii [Funktsional. Anal. i Prilozhen. 18 (1984), n…
Varieties of special Jordan algebras of almost polynomial growth
2019
Abstract Let J be a special Jordan algebra and let c n ( J ) be its corresponding codimension sequence. The aim of this paper is to prove that in case J is finite dimensional, such a sequence is polynomially bounded if and only if the variety generated by J does not contain U J 2 , the special Jordan algebra of 2 × 2 upper triangular matrices. As an immediate consequence, we prove that U J 2 is the only finite dimensional special Jordan algebra that generates a variety of almost polynomial growth.
The behavior of solutions of a parametric weighted (p, q)-laplacian equation
2021
<abstract><p>We study the behavior of solutions for the parametric equation</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ -\Delta_{p}^{a_1} u(z)-\Delta_{q}^{a_2} u(z) = \lambda |u(z)|^{q-2} u(z)+f(z,u(z)) \quad \mbox{in } \Omega,\, \lambda &gt;0, $\end{document} </tex-math></disp-formula></p> <p>under Dirichlet condition, where $ \Omega \subseteq \mathbb{R}^N $ is a bounded domain with a $ C^2 $-boundary $ \partial \Omega $, $ a_1, a_2 \in L^\infty(\Omega) $ with $ a_1(z), a_2(z) &gt; 0 $ for a.a. $ z \in \Omega $, $ p, q \in (1, \infty) $ and $ \Delta_{p}^{a_1}, \Delta_{q}^{a_2} $ are weighted …
Estimates for the first and second Bohr radii of Reinhardt domains
2004
AbstractWe obtain general lower and upper estimates for the first and the second Bohr radii of bounded complete Reinhardt domains in Cn.