Conditions for the existence of the total differential of an arbitrary continuous function

1980 ◽  
Vol 31 (6) ◽  
pp. 577-578
Author(s):  
F. M. Diab
Keyword(s):  
Continuous Function ◽  
Arbitrary Continuous Function ◽  
Total Differential

scholarly journals A Single Hidden Layer Feedforward Network with Only One Neuron in the Hidden Layer Can Approximate Any Univariate Function

2016 ◽  
Vol 28 (7) ◽  
pp. 1289-1304 ◽  
Author(s):  
Namig J. Guliyev ◽  
Vugar E. Ismailov
Keyword(s):  
Continuous Function ◽  
Finite Interval ◽  
Activation Function ◽  
Feedforward Network ◽  
Arbitrary Continuous Function ◽  
The Real ◽  
Univariate Function ◽  
Constructive Approximation ◽  
Hidden Layer ◽  
Sigmoidal Activation Function

The possibility of approximating a continuous function on a compact subset of the real line by a feedforward single hidden layer neural network with a sigmoidal activation function has been studied in many papers. Such networks can approximate an arbitrary continuous function provided that an unlimited number of neurons in a hidden layer is permitted. In this note, we consider constructive approximation on any finite interval of [Formula: see text] by neural networks with only one neuron in the hidden layer. We construct algorithmically a smooth, sigmoidal, almost monotone activation function [Formula: see text] providing approximation to an arbitrary continuous function within any degree of accuracy. This algorithm is implemented in a computer program, which computes the value of [Formula: see text] at any reasonable point of the real axis.

Solution of the problem of forecasting based on neural networks

2020 ◽  
pp. 45-48
Author(s):  
E.V. Kuliev ◽  
N.V. Grigorieva ◽  
M.A. Dovgalev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Life Cycle ◽  
Continuous Function ◽  
Human Brain ◽  
Arbitrary Continuous Function ◽  
The Neural Network ◽  
Nonlinear Neural Networks

This article is about prediction using neural networks. Neural networks are used to solve problems that require analytical calculations similar to those carried out by the human brain. Inherently nonlinear neural networks allow to approximate an arbitrary continuous function with any degree of accuracy, regardless of the absence or presence of any periodicity or cyclicality. Today, neural networks are one of the most powerful forecasting mechanisms. This article discusses the General principles of training and operation of the neural network, the life cycle, the solution of forecasting problems using the approximation of the function.

scholarly journals The expansion of continuous functions in series of integrals of orthonormal functions

1972 ◽  
Vol 13 (1) ◽  
pp. 29-38 ◽  
Author(s):  
H. C. Finlayson
Keyword(s):  
Continuous Function ◽  
Specific Problem ◽  
Continuous Functions ◽  
Partial Answer ◽  
Arbitrary Continuous Function ◽  
In Series

This paper deals with the following problem: Can an arbitrary continuous function on [0, 1], which vanishes at the origin, be represented in some sense as a series of constant multiples of indefinite integrals of a complete orthonormal set of functions on [0,1]? Four contexts in which this problem arises naturally will be given in the introduction and the remainder of the paper will be devoted to giving a partial answer to the specific problem formulated in one of these contexts.

Generalized ʎ-Closed Sets and (ʎ-ʏ)*-Continuous Function

2017 ◽  
Vol 4 (ICBS Conference) ◽  
pp. 1-17 ◽  
Author(s):  
Alias Khalaf ◽  
Sarhad Nami
Keyword(s):  
Continuous Function ◽  
Closed Sets

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

Limit of Simply Continuous Function

1992 ◽  
Vol 18 (1) ◽  
pp. 270 ◽  
Author(s):  
Borsík
Keyword(s):  
Continuous Function
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