scholarly journals On basicity of the degenerate trigonometric system with excess

2017 ◽  
Vol 21 (2) ◽  
pp. 249-257
Author(s):  
Aydin Sh. Shukurov
Keyword(s):  
Weight Function ◽  
Schauder Basis ◽  
Trigonometric System ◽  
Lp Space

The basis properties (completeness, minimality and Schauder basicity) of systems of the form {ω(t)φn(t)}, where {φn(t)} is an exponential or trigonometric (cosine or sine) systems, have been investigated in several papers. Concrete examples of the weight function ω(t) are known for which the system itself is not complete and minimal but has excess – becomes complete and minimal in corresponding Lp space only after elimination of some of its elements. The aim of this paper is to show that if ω(t) is any measurable weight function such that the system {ω(t) sin nt}n∊ℕ has excess, then neither this system itself, nor a system obtained from it by elimination of an element, is not a Schauder basis.

On the Form of Decision Weight Function

2002 ◽  
Author(s):  
Shyhnan Liou ◽  
Chung-Ping Cheng
Keyword(s):  
Weight Function

SCHAUDER BASIS DETERMINING PROPERTIES

1992 ◽  
Vol 12 (1) ◽  
pp. 89-97
Author(s):  
Qiyuan Na
Keyword(s):  
Schauder Basis

Multi Disease-Prediction Framework Using Hybrid Deep Learning: An Optimal Prediction Model (Preprint)

2020 ◽  
Author(s):  
Anusha Ampavathi ◽  
Vijaya Saradhi T
Keyword(s):  
Feature Extraction ◽  
Big Data ◽  
Deep Learning ◽  
Weight Function ◽  
Optimization Algorithm ◽  
Large Scale ◽  
Heuristic Algorithms ◽  
Disease Prediction ◽  
Health Care Decisions ◽  
Proposed Model

UNSTRUCTURED Big data and its approaches are generally helpful for healthcare and biomedical sectors for predicting the disease. For trivial symptoms, the difficulty is to meet the doctors at any time in the hospital. Thus, big data provides essential data regarding the diseases on the basis of the patient’s symptoms. For several medical organizations, disease prediction is important for making the best feasible health care decisions. Conversely, the conventional medical care model offers input as structured that requires more accurate and consistent prediction. This paper is planned to develop the multi-disease prediction using the improvised deep learning concept. Here, the different datasets pertain to “Diabetes, Hepatitis, lung cancer, liver tumor, heart disease, Parkinson’s disease, and Alzheimer’s disease”, from the benchmark UCI repository is gathered for conducting the experiment. The proposed model involves three phases (a) Data normalization (b) Weighted normalized feature extraction, and (c) prediction. Initially, the dataset is normalized in order to make the attribute's range at a certain level. Further, weighted feature extraction is performed, in which a weight function is multiplied with each attribute value for making large scale deviation. Here, the weight function is optimized using the combination of two meta-heuristic algorithms termed as Jaya Algorithm-based Multi-Verse Optimization algorithm (JA-MVO). The optimally extracted features are subjected to the hybrid deep learning algorithms like “Deep Belief Network (DBN) and Recurrent Neural Network (RNN)”. As a modification to hybrid deep learning architecture, the weight of both DBN and RNN is optimized using the same hybrid optimization algorithm. Further, the comparative evaluation of the proposed prediction over the existing models certifies its effectiveness through various performance measures.

scholarly journals Operators constructed by means of basic sequences and nuclear matrices

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ahmed Morsy ◽  
Nashat Faried ◽  
Samy A. Harisa ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Banach Spaces ◽  
Compact Operators ◽  
Schauder Basis ◽  
Countable Number ◽  
Nuclear Operator ◽  
Approximation Numbers ◽  
Infinite Dimensional ◽  
Dimensional Matrix ◽  
Nuclear Operators

AbstractIn this work, we establish an approach to constructing compact operators between arbitrary infinite-dimensional Banach spaces without a Schauder basis. For this purpose, we use a countable number of basic sequences for the sake of verifying the result of Morrell and Retherford. We also use a nuclear operator, represented as an infinite-dimensional matrix defined over the space $\ell _{1}$ℓ1 of all absolutely summable sequences. Examples of nuclear operators over the space $\ell _{1}$ℓ1 are given and used to construct operators over general Banach spaces with specific approximation numbers.

On the weight function for the wedge (or notch)

1994 ◽  
Vol 70 (5) ◽  
pp. 297-301 ◽  
Author(s):  
Xanthippi Markenscoff
Keyword(s):  
Weight Function

Theory of Boundary Eigensolutions in Engineering Mechanics

2000 ◽  
Vol 68 (1) ◽  
pp. 101-108 ◽  
Author(s):  
A. R. Hadjesfandiari ◽  
G. F. Dargush
Keyword(s):  
Weight Function ◽  
Mixed Boundary ◽  
Traditional Approach ◽  
Mixed Boundary Conditions ◽  
Boundary Element Methods ◽  
Positive Weight ◽  
Nonsmooth Problems ◽  
Integral Equation Methods ◽  
Potential Problems ◽  
Engineering Mechanics

A theory of boundary eigensolutions is presented for boundary value problems in engineering mechanics. While the theory is quite general, the presentation here is restricted to potential problems. Contrary to the traditional approach, the eigenproblem is formed by inserting the eigenparameter, along with a positive weight function, into the boundary condition. The resulting spectra are real and the eigenfunctions are mutually orthogonal on the boundary, thus providing a basis for solutions. The weight function permits effective treatment of nonsmooth problems associated with cracks, notches and mixed boundary conditions. Several ideas related to the convergence characteristics are also introduced. Furthermore, the connection is made to integral equation methods and variational methods. This paves the way toward the development of new computational formulations for finite element and boundary element methods. Two numerical examples are included to illustrate the applicability.

Convergence of greedy approximation for the trigonometric system

2005 ◽  
Vol 31 (2) ◽  
pp. 85-115 ◽  
Author(s):  
S. V. Konyagin ◽  
V. N. Temlyakov
Keyword(s):  
Trigonometric System ◽  
Greedy Approximation
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