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About 6,192 papers for “Real-valued function”
Lan Li · 2007
The definition of bounded variation function and Dini derivations was given,together with a lemma.Proof was given for the sufficient condition for the differentiability of real-valued functions.Almost everywhere differentiability of real-valued functions was discussed and proved by bounded variation function.
Cited by 0
Peter L. Bartlett, Sanjeev R. Kulkarni, Steven E. Posner · IEEE Transactions on Information Theory · 1997
We find tight upper and lower bounds on the growth rate for the covering numbers of functions of bounded variation in the /spl Lscr//sub 1/ metric in terms of all the relevant constants. We also find upper and lower bounds on covering numbers for general function classes over the family of /spl Lscr//sub 1/(dP) metrics in terms of a scale-sensitive combinatorial dimension of the function class.
Cited by 52
Gane Samb Lô, Lois Chinwendu Okereke, Fatimatou Doumbia · arXiv (Cornell University) · 2019
The like-Lebesgue integral of real-valued measurable functions (abbreviated as \textit{RVM-MI})is the most complete and appropriate integration Theory. Integrals are also defined in abstract spaces since Pettis (1938). In particular, Bochner integrals received much interest with very recent researches. It is very commode to use the \textit{RVM-MI} in constructing Bochner integral in Banach or in locally convex spaces. In this simple not, we prove that the Bochner integral and the \textit{RVM-MI} with respect to a finite measure $m$ are the same on $\mathbb{R}$. Applications of that equality may be useful in weak limits on Banach space.
Cited by 0Open access
Ajay Kumar Bhurjee, Pankaj Kumar · AIP conference proceedings · 2022
In the classical optimization problem, parameters are generally estimated by using the probability theory or fuzzy theory. In the past few decades, such parameters are also assessed in the form of an interval, and correspondingly the interval optimization problem is imminent in existence. In this paper, the calculus for an interval-valued function is developed using partial ordering and non-standard difference to deal with such a situation. Further, the convexity for the interval-valued function is defined in terms of its mean and spread function; and several convexity results for the function are proved. All the developed concepts are illustrated through numerical examples.
Cited by 1Open access
A. Jiménez-Vargas, Moisés Villegas-Vallecillos · Topology and its Applications · 2009
Cited by 2
Kazumi Nakano · Fundamenta Mathematicae · 1972
Cited by 0Open access
Savitha Ramasamy, Suresh Sundaram, N. Sundararajan et al. · Neurocomputing · 2011
Cited by 62
Yoshiyuki Matsumura, Kazuhiro Ohkura, Kanji UEDA · 2007
The effect of multi-parent recombination on Evolution Strategies(ES) is empirically investigated on a set of real-valued test functions. The multiparent versions of intermediate recombination, discrete recombination and global combined discrete recombination are applied to both objective variables and strategy parameters. Computer simulations of the multi- recombinant ES((///,h)-ES) are conducted using Gaussian mutation for two different dimensions of test functions. Of the many formulations of ES, Classical-ES(CES) and Robust-ES(RES) are adopted for the observation.
Cited by 0
John Shawe‐Taylor · ePrints Soton (University of Southampton) · 1999
Cited by 0
Yiwei Guan, T.G. Clarkson, John G. Taylor et al. · UCL Discovery (University College London) · 1993
A learning algorithm for a pRAM-based network is presented in which the neural network learns real-valued functions by a stochastic reinforcement rule with linear reverse interpolation. The algorithm uses the output spike trains to approximate function values and to update memory contents. The algorithm is hardware realisable. It finds applications in areas which involve real-time learning, such as robotics and control.
Cited by 1
K. BHARATHI,M. NAGARAJ · SHILAP Revista de lepidopterología · 2015
Cited by 0Open access
I. RAMABHADRASARMA,S. KATRAGADDA · SHILAP Revista de lepidopterología · 2015
Cited by 0Open access
Roger C. Alperin, Kenneth N. Moss · Journal of the London Mathematical Society · 1985
Cited by 31
Jagat Krishna Pokhrel · Tribhuvan University Journal · 2017
By the maximum values of a function f (x) in calculus, we do not necessarily mean the absolutely greatest value attainable by the function. A function f (x) is said to be maximum for a value c of x, provided f (c) is greater than every other value assumed by f (x) in the immediate neighbourhood of x = c. Similarly a minimum value of f (x) is defined to be the value which is less than other values in the immediate neighbourhood.
Cited by 1Open access
Yoko Matsumura, Kazuhiro Ohkura, Kazushi Ueda · 2003
Evolutionary programming (EP) constitutes a class of general optimization algorithms based on the model of natural evolution. Real-valued function optimization has also been included in this domain since the early 90's. One of the main features is that the mutation size is self-adaptively controlled by additional parameters (strategy parameters). However, it was found that the mutation size control is not "sufficiently" self-adaptive: EP often practically stops its genetic search before reaching a global optimum, due to the tendency that strategy parameters converge in the early generations, with the result that the population cannot move to another place. In the paper, in order to overcome this burdensome character, an extended EP that utilizes the genetic drift as another source of changing strategy parameters is proposed. Computer simulations were conducted using several test functions in order to evaluate the performance of the proposed method.
Cited by 11
Messerschmitt, David G, Author · UC Berkeley
The optimization problem of maximizing or minimizing some real-valued objective function of a complex variable (or vector of complex variables) arises often in signal processing. For example, the mean-square error is such a function. A challenge that arises is that such a function is often not analytic, and thus not differentiable using the ordinary tools of complex variable theory. This tutorial report shows how this challenge can be bypassed by reformulationg the problem as a function of two real variables (the real and imaginary parts), finding the solution, and then relating this back to complex variables
Cited by 10
BOSI, GIANNI, ISLER R. · ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/) · 1997
Cited by 0
Zhu, Shinin · Human Biology · 1998
Cited by 0
Amar Jyoti Dutta, Binod Chandra Tripathy · Proyecciones (Antofagasta) · 2014
In this articlewehavedefined statistically pre-Cauchy sequence of fuzzy real numbers defined by Orlicz function. We have proved a necessary and sufficient condition for a sequence X =(Xk) of fuzzy real numbers to be statistically pre-Cauchy. We have also established some other results.
Cited by 15Open access
Nam Le, Michael O’Neill, David Fagan et al. · 2017
Drawing on a rich literature concerning social learning in animals, this paper presents a variation of Grammatical Evolution (GE) which incorporates one of the most powerful forms of social learning, namely imitation learning. This replaces the traditional method of `communication' between individuals in GE - crossover - which is drawn from an evolutionary metaphor. The paper provides an introduction to social learning, describes the proposed variant of GE, and tests on a series of benchmark symbolic regression problems. The results obtained are encouraging, being very competitive when compared with canonical GE. It is noted that the literature on social learning provides a number of useful meta-frameworks which can be used in the design of new search algorithms and to allow us to better understand the strengths and weaknesses of existing algorithms. Future work is indicated in this area.
Cited by 2