Research Article
A Matrix Model for Adaptive Graph Filtering Using a Generalized Mean-sets Theory’s Approach
Issue:
Volume 9, Issue 1, June 2025
Pages:
1-15
Received:
27 March 2025
Accepted:
8 April 2025
Published:
6 May 2025
DOI:
10.11648/j.engmath.20250901.11
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Abstract: Integrating Mean-sets theory employing generalized graph or group-theoretic tools and techniques into adaptive graph filtering can lead to more effective resilient filtering processes, particularly in challenging environments with clutter or uncertainty. In this paper, we show that under some crucial smoothing assumptions, the generalized Mean-sets theory developped for negatively curved convex combination Polish metric spaces following the formal Means-sets probability theory’s approach from Natalia Mosina, provides a new useful system for some secure adaptive graph filtering processes. We use convex combination operations (in the sense of Terán and Molchanov) on both individual input graph signals and filters. Individual adaptive graph filters being independently adapted by space (dataset)-valued random variables, while the convexification operator on the underlying dataset acts as a flexible theoretical instrument for preserving some good features of the standard scheme, like privacy of their informative trends, and looks more robust to changes. We exhibit a graph matrix model from a system of convex combination of two adaptive finite impulse response (FIR) graph filters processing a sampled-weighted mean-set (expectation) of some transversal graph signals with finite length N ≥ 2.
Abstract: Integrating Mean-sets theory employing generalized graph or group-theoretic tools and techniques into adaptive graph filtering can lead to more effective resilient filtering processes, particularly in challenging environments with clutter or uncertainty. In this paper, we show that under some crucial smoothing assumptions, the generalized Mean-sets...
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Research Article
Effect of Parabolically Varying Non-Homogeneity on Thermally Induced Vibration of Orthotropic Trapezoidal Plate with Thickness Varies Linearly in One Direction and Parabolically in Other Direction
Amit Sharma
,
Pragati Sharma*,
Geeta
Issue:
Volume 9, Issue 1, June 2025
Pages:
16-25
Received:
1 August 2025
Accepted:
14 August 2025
Published:
3 September 2025
DOI:
10.11648/j.engmath.20250901.12
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Abstract: The present paper deals with the effect of parabolically varying non-homogeneity on thermally induced vibration of orthotropic trapezoidal plate with thickness varies linearly in one direction and parabolically in other direction. The two term deflection function corresponding to clamped-simply supported clamped-simply supported (C-S-C-S) boundary condition is defined by the product of the equation of the prescribed continuous piecewise boundary shape. The non-homogeneity of the plate varies parabolically. Rayleigh-Ritz method is used to solve the governing differential equation for maximum strain energy and maximum kinetic energy for orthotropic trapezoidal plate. The effect of frequencies for first and second mode investegated with the variations in structural parameters such as taper constant, non-homogeneity constant, aspect ratio and thermal gradient respectively. Results are calculated with great accuracy and compare the present model with the other in literature with the help of tables and graphs. All the results presented here are new and are not found elsewhere.
Abstract: The present paper deals with the effect of parabolically varying non-homogeneity on thermally induced vibration of orthotropic trapezoidal plate with thickness varies linearly in one direction and parabolically in other direction. The two term deflection function corresponding to clamped-simply supported clamped-simply supported (C-S-C-S) boundary ...
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