scholarly journals Time fractional problem via ınner product including weighted function

2022 ◽  
Vol 24 (1) ◽  
pp. 91-99
Author(s):  
Süleyman ÇETİNKAYA ◽  
Ali DEMİR
Keyword(s):  
Inner Product ◽  
Weighted Function

Sequential space fractional diffusion equation’s solutions via new inner product

2020 ◽  
pp. 2150121
Author(s):  
Suleyman Cetinkaya ◽  
Ali Demir
Keyword(s):  
Fourier Series ◽  
Initial Conditions ◽  
Separation Of Variables ◽  
Analytic Solutions ◽  
Dirichlet Boundary Conditions ◽  
Inner Product ◽  
Sequential Space ◽  
Weighted Function ◽  
Sturm Liouville ◽  
Fractional Differential

In this study, we determine the analytic solutions of sequential space fractional differential equations with Dirichlet boundary conditions and initial conditions in one dimension. We constructed a Fourier series solution for the eigenfunctions of a corresponding Sturm–Liouville eigenvalue problem, including fractional derivative in Caputo sense using the separation of variables. We defined a new inner product with a weighted function to get coefficients in the Fourier series.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

scholarly journals Active Contour Model with Adaptive weighted function for Robust Image Segmentation under Biased Conditions

2021 ◽  
pp. 114811
Author(s):  
Aditi Joshi ◽  
Mohammed Saquib Khan ◽  
Asim Niaz ◽  
Farhan Akram ◽  
Hyun Chul Song ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Active Contour ◽  
Active Contour Model ◽  
Weighted Function ◽  
Contour Model ◽  
Robust Image

scholarly journals Fuzzy Inner Product Space: Literature Review and a New Approach

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida
Keyword(s):  
Literature Review ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Comprehensive Overview ◽  
New Approach ◽  
Inner Product Spaces ◽  
Product Function ◽  
Suitable Definition

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

scholarly journals Identification of coexisting dynamics in boundary layer flows through proper orthogonal decomposition with weighting matrices

Meccanica ◽  
2021 ◽  
Author(s):  
Matteo Dellacasagrande ◽  
Dario Barsi ◽  
Patrizia Bagnerini ◽  
Davide Lengani ◽  
Daniele Simoni
Keyword(s):  
Experimental Data ◽  
Proper Orthogonal Decomposition ◽  
Fourier Transforms ◽  
Free Stream ◽  
Numerical Test ◽  
Separated Flow ◽  
Orthogonal Decomposition ◽  
Inner Product ◽  
Test Case ◽  
Proper Orthogonal

AbstractA different version of the classic proper orthogonal decomposition (POD) procedure introducing spatial and temporal weighting matrices is proposed. Furthermore, a newly defined non-Euclidean (NE) inner product that retain similarities with the POD is introduced in the paper. The aim is to emphasize fluctuation events localized in spatio-temporal regions with low kinetic energy magnitude, which are not highlighted by the classic POD. The different variants proposed in this work are applied to numerical and experimental data, highlighting analogies and differences with respect to the classic and other normalized variants of POD available in the literature. The numerical test case provides a noise-free environment of the strongly organized vortex shedding behind a cylinder. Conversely, experimental data describing transitional boundary layers are used to test the capability of the procedures in strongly not uniform flows. By-pass and separated flow transition processes developing with high free-stream disturbances have been considered. In both cases streaky structures are expected to interact with other vortical structures (i.e. free-stream vortices in the by-pass case and Kelvin–Helmholtz rolls in the separated type) that carry a significant different amount of energy. Modes obtained by the non-Euclidean POD (NE-POD) procedure (where weighted projections are considered) are shown to better extract low energy events sparse in time and space with respect to modes extracted by other variants. Moreover, NE-POD modes are further decomposed as a combination of Fourier transforms of the related temporal coefficients and the normalized data ensemble to isolate the frequency content of each mode.

Mackey Continuity of Characteristic Functionals

2002 ◽  
Vol 9 (1) ◽  
pp. 83-112
Author(s):  
S. Kwapień ◽  
V. Tarieladze
Keyword(s):  
Product Space ◽  
Locally Convex Space ◽  
Inner Product ◽  
Nuclear Space ◽  
Probability Measures ◽  
Linear Kernel ◽  
Characteristic Functional ◽  
Initial Space ◽  
Radon Probability Measure ◽  
Locally Convex

Abstract Problems of the Mackey-continuity of characteristic functionals and the localization of linear kernels of Radon probability measures in locally convex spaces are investigated. First the class of spaces is described, for which the continuity takes place. Then it is shown that in a non-complete sigmacompact inner product space, as well as in a non-complete sigma-compact metizable nuclear space, there may exist a Radon probability measure having a non-continuous characteristic functional in the Mackey topology and a linear kernel not contained in the initial space. Similar problems for moment forms and higher order kernels are also touched upon. Finally, a new proof of the result due to Chr. Borell is given, which asserts that any Gaussian Radon measure on an arbitrary Hausdorff locally convex space has the Mackey-continuous characteristic functional.

Sign in / Sign up

Export Citation Format

Share Document