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About 10,000 papers for “Bounded function”

ITERATED FUNCTION SYSTEMS ON FUNCTIONS OF BOUNDED VARIATION

Davide La Torre, Franklin Mendivil, Edward R. Vrscay · Fractals · 2016

We show that under certain hypotheses, an iterated function system on mappings (IFSM) is a contraction on the complete space of functions of bounded variation (BV). It then possesses a unique attractor of BV. Some BV-based inverse problems based on the Collage Theorem for contraction maps are considered.

Cited by 3

Bounded PSO Vmax Function in Neural Network Learning

Y. S. Lee, Siti Mariyam Shamsuddin, Haza Nuzly Abdull Hamed · 2008

Typically, back propagation (BP) algorithm is the most widespread technique in Artificial Neural Network (ANN learning). However, major disadvantages of BP are due to its convergence rate sluggishness and always being trapped at the local minima. Consequently, Particle Swarm Optimization(PSO) is chosen and applied in feed forward neural network to enhance the network learning. In conventional PSO, maximum velocity Vmax is exploited to serve as a constraint that controls the maximum global exploration ability of PSO. By setting these values too small cause the limitation of maximum global exploration. Hence, PSO will always favor for a local search regardless the values of weight inertia. However, by setting to a large maximum velocity, PSO can have a large range of exploration ability. Therefore, in this study, we proposed different bounded functions of PSO Vmax to control the global exploration of particles. The results show that bounded Vmax of hyperbolic tangent function furnish promising outcomes compared to bounded Vmax sigmoid function and standard Vmax function.

Cited by 10

Structure-function scaling of bounded two-dimensional turbulence

Werner Krämer, Geert Keetels, H. J. H. Clercx et al. · Physical Review E · 2011

Statistical properties of forced two-dimensional turbulence generated in two different flow domains are investigated by numerical simulations. The considered geometries are the square domain and the periodic channel domain, both bounded by lateral no-slip sidewalls. The focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no-slip boundaries. The scaling exponents of the velocity and the vorticity structure functions are compared to the classical Kraichnan-Batchelor-Leith (KBL) theory, which assumes isotropy, homogeneity, and self-similarity for turbulence scales between the forcing and dissipation scale. Our investigation reveals that in the interior of the flow domain, turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range, but it is weakly intermittent. However, the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the KBL theory predicts. Near the walls the turbulence is strongly anisotropic at all flow scales.

Cited by 8Open access

Abstract Bounded Blending for Function-based Shape Modeling

G. Pasko, A. Pasko, T. Kunii · 2008

We propose new analytical formulations of bounded blending operations for the function-based constructive shape modeling. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional arbitrary bounding solid also defined by a realvalued function. The proposed blending using a bounding solid can be applied to a single selected edge, a vertex, or another blend. We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend. We show that the proposed operations can replace pure settheoretic operations in the solid model without rebuilding the entire construction tree data structure. The proposed blending is shown to have versatile applications in interactive design. Influence of all parameters on the blend shape and location is illustrated. Keywords: Geometric modeling, shape, blending, implicit surfaces, R-functions 1.

Cited by 0

Properties of bounded variation function of two variables

Indah Dwi Murdianingsih, Susilo Hariyanto, Titi Udjiani et al. · AIP conference proceedings · 2023

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Indah Dwi Murdianingsih, Susilo Hariyanto, Titi Udjiani, Yusephus D. Sumanto, Idha Sihwaningrum; Properties of bounded variation function of two variables. AIP Conference Proceedings 25 January 2023; 2554 (1): 020004. https://doi.org/10.1063/5.0104246 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

Cited by 0

SINGULAR INNER FUNCTION AND ANALYTIC BOUNDED POINT EVALUATION

Kifah Y. Al-hami · International Journal of Pure and Apllied Mathematics · 2015

In Section 1, I constructed a singular inner function which is an upper bound for a given outer function, i.e. replacing an outer function with a constant multiple of a singular inner In Section 2, I proved how unit disk containment is not effected for the analytic bounded point evaluation by a restricted measure.

Cited by 0Open access

Integer function of a bounded l-m-index

Abuarabi Shukri · OpenGrey (Institut de l'Information Scientifique et Technique) · 1992

It is necessary to obtain various analogs of Frike-Shakh-Sisarchik theoem for integer fonctions of a bounded l-M-index. Some criteria of the integer function l-M-index boundedness have been proved both in terms of M(f) growth and in terms of f-function Teilor coefficients decrease. Results may find their field of application in general theory of analytical functions

Cited by 0Open access

Absolutely continuous function and functions of bounded variation

Filip Hladký · Digital Repository (National Repository of Grey Literature) · 2013

In this thesis we will study relationship between space of absolutely continuous func- tions and space of functions with bounded variation. In first three chapters we will study properties of absolutely continuous functions and functions with bounded variation and we will show nessesary and sufficient condition for functions with bounded variation to be absolutely continuous. Moreover we will show one part of fundamental theorem of calculus for Lebesgue's integral. In the last chapter we will study relationship between absolutely continuous mappings and mappings with bounded variation from Rn to Rm. 1

Cited by 0

Constraining Logits by Bounded Function for Adversarial Robustness

Sekitoshi Kanai, Masanori Yamada, Shin’ya Yamaguchi et al. · arXiv (Cornell University) · 2020

We propose a method for improving adversarial robustness by addition of a new bounded function just before softmax. Recent studies hypothesize that small logits (inputs of softmax) by logit regularization can improve adversarial robustness of deep learning. Following this hypothesis, we analyze norms of logit vectors at the optimal point under the assumption of universal approximation and explore new methods for constraining logits by addition of a bounded function before softmax. We theoretically and empirically reveal that small logits by addition of a common activation function, e.g., hyperbolic tangent, do not improve adversarial robustness since input vectors of the function (pre-logit vectors) can have large norms. From the theoretical findings, we develop the new bounded function. The addition of our function improves adversarial robustness because it makes logit and pre-logit vectors have small norms. Since our method only adds one activation function before softmax, it is easy to combine our method with adversarial training. Our experiments demonstrate that our method is comparable to logit regularization methods in terms of accuracies on adversarially perturbed datasets without adversarial training. Furthermore, it is superior or comparable to logit regularization methods and a recent defense method (TRADES) when using adversarial training.

Cited by 0Open access

Simple criteria for bounded turning of an analytic function

Nikola Tuneski, Maslina Darus, Elena Gelova · Goce Delchev University Repository (Goce Delčev University of Štip) · 2012

Let f be an analytic function in the open unit disk and normalized such that f(0) = f′(0) − 1 = 0. In this work, by means of the theory of differential subordinations, we study the the expression � � f'(z) + � �f(z)/z and receive results over the modulus and the real parts of f'(z) and f(z)/z, that lead to simple criteria for bounded turning of an analytic function.

Cited by 0

Function Spaces for Uniformly Locally Bounded Quasi-Uniform Spaces

Philipp Sünderhauf, Fachbereich Mathematik, Technische Hochschule Darmstadt · 1995

In a previous paper [Sun95b], we described a function space constructor for complete totally bounded quasi-uniform spaces. The present paper generalizes this construction to the wider class of uniformly locally bounded spaces, which is contained in the class of all completable spaces. Based on this, a refined function space construction is introduced. The latter seems more appropriate for the uniform case and for certain applications in programming semantics. The constructions are well-behaved with regard to uniform local boundedness and completability. Introduction This paper is part of the program [Smy88, Smy91, Sun95b, FK96] of developing a quantitative version of domain theory, that is to provide the theory of quasi-uniformities or related structures with constructions and notions from (ordinary) domain theory [AJ94]. Specifically, we consider the question of supplying suitable function space constructors, a question which is also of interest in the general theory of quasi-uniform...

Cited by 0