This paper presents a new method for optimizing continuous complex functions based on a learning automaton. This method can be considered as active learning permitting to select on-line the most significant data sampl...
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This paper presents a new method for optimizing continuous complex functions based on a learning automaton. This method can be considered as active learning permitting to select on-line the most significant data samples in order to quickly converge to a quasi global optimum of the functions to be optimized with a fewer number of tests or calculations. Like other stochastic optimization algorithms, it aims at finding a compromise between exploitation and exploration, i.e. converging to the nearest local optima and exploring the function behavior in order to discover global optimal regions. During the optimization procedure, this method enhances local search in interesting regions or intervals and reduces the whole searching space by removing useless regions or intervals. (C) 2004 Elsevier Inc. All rights reserved.
We investigate the existence of algebraic structures in the set of continuous, unbounded and integrable functions in [0, infinity), continuing the work initiated by Calderon-Moreno et al. (J. Math. Anal. Appl. 470:348...
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We investigate the existence of algebraic structures in the set of continuous, unbounded and integrable functions in [0, infinity), continuing the work initiated by Calderon-Moreno et al. (J. Math. Anal. Appl. 470:348-359, 2019). We explore the stricter notions of (alpha, beta)-lineability/spaceability and pointwise lineability/spaceability, which were recently introduced. For example, we prove that the aforementioned set is pointwise spaceable, in particular, spaceable. On the other hand, negative results are also obtained. For instance, we prove the non (N-0, c)-spaceability of the family of unbounded, continuous and integrable functions.
A notion of ''continuous'' functions on digital pictures has been introduced by Rosenfeld. As an extension of this concept to fuzzy cases, we define ''continuous'' functions on fuzzy di...
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A notion of ''continuous'' functions on digital pictures has been introduced by Rosenfeld. As an extension of this concept to fuzzy cases, we define ''continuous'' functions on fuzzy digital pictures. Various properties analogous to those on crisp digital pictures are shown. Especially, it is shown that a function f on fuzzy digital pictures is continuous iff it takes (fuzzy) connected sets into (fuzzy) connected sets.
We explore the existence of rational-valued approximation processes by continuous functions of two variables, such that the output continuously depends of the imposed error-bound. To this sake, we prove that the theor...
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We explore the existence of rational-valued approximation processes by continuous functions of two variables, such that the output continuously depends of the imposed error-bound. To this sake, we prove that the theory of densely ordered sets with generic predicates is aleph(0)-categorical. A model of the theory and a particular continuous choice-function is constructed. This function transfers to all other models by the respective isomorphisms. If some common-sense conditions are fulfilled, the processes are computable. As a by-product, other functions with surprising properties can be constructed.
We find all subsets of N which occur as the set of possible cardinalities of preimages of a continuous function. We also study and answer this question for various subclasses of continuous functions. (c) 2021 Elsevier...
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We find all subsets of N which occur as the set of possible cardinalities of preimages of a continuous function. We also study and answer this question for various subclasses of continuous functions. (c) 2021 Elsevier B.V. All rights reserved.
The epsilon-delta definition of continuity has a natural analog for functions that take lattice points into lattice points. It turns out that a function f is ‘continuous’ if and only if it takes neighbors into neigh...
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The epsilon-delta definition of continuity has a natural analog for functions that take lattice points into lattice points. It turns out that a function f is ‘continuous’ if and only if it takes neighbors into neighbors, i.e., if Q is a neighbor of P , then f ( Q ) = f ( P ) or is a neighbor of f ( P ) (diagonal neighbors not allowed). Some basic properties of such ‘continuous’ functions are established. In particular, we show that a ‘continuous’ function from a finite block of lattice points into itself has an ‘almost-fixed’ point P such that f ( P ) is a neighbor of P (diagonal neighbors allowed). We also show that a function is one-to-one and continuous if and only if it is a combination of translations, rotations by multiples of 90°, or reflections in a horizontal, vertical, or diagonal line.
Let F(X),F(Y) be sufficiently large sets of nonnegative continuous real-valued functions defined on completely regular spaces X,Y, respectively. Let Φ:F(X)→F(Y) be a surjective map satisfying that f∨g>0⟺Φ(f)∨...
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Let C [0;1] be the Banach algebra of real valued continuous functions on [0, 1], provided with the supremum norm. For f;g is an element of C [0;1] and balls B-f, B-g with center f and g, respectively, it is not necess...
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Let C [0;1] be the Banach algebra of real valued continuous functions on [0, 1], provided with the supremum norm. For f;g is an element of C [0;1] and balls B-f, B-g with center f and g, respectively, it is not necessarily true that f . g is in the interior of B-f . B-g. In the present paper we characterize those pairs f, g where this is the case. The problem is illustrated by using a suitable translation. One studies walks in a landscape with hills and valleys where an accompanying dog can move in a certain prescribed way.
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