Results 101 to 110 of about 4,701,227 (283)

Solution and Stability of a Multi-Quadratic Functional Equation

Mathematics
In this paper, we characterize the general solution to a system of functional equations with respect to the multi-quadratic mappings by proving that any such mapping can be uniquely represented via a 2n-additive pairwise symmetric mapping.
Jae-Hyeong Bae, Won-Gil Park
doaj   +1 more source

Stability for the Mixed Type of Quartic and Quadratic Functional Equations

Journal of Function Spaces, 2014
We establish the general solutions of the following mixed type of quartic and quadratic functional equation: f(2x+y)+f(2x-y)=4f(x+y)+4f(x-y)+2f(2x)-8f(x)-6f(y).
Young-Su Lee, Soomin Kim, Chaewon Kim
doaj   +1 more source

Stability of a 3-variable quadratic functional equation

, 2008
In this paper, the authors discuss the general solution and the stability of a 3-variable quadratic functional equation f(x+y,z+w,u+v)+ f(x-y,z-w,u-v)= 2f(x, z,u)+ 2f(y,w,v).
M. Arunkumar ,, K. Ravi,
core  

Thermodynamics of Concomitant Charge‐Transfer, Antiferromagnetic, and Isostructural Phase Transitions in Barocaloric ACu3Fe4O12 Quadruple Perovskites

Advanced Science, EarlyView.
A copper‐iron charge transfer instability drives concomitant electronic, magnetic, and isostructural phase transitions in ACu3Fe4O12${\rm ACu}_3{\rm Fe}_4{\rm O}_{12}$, with an inverse barocaloric effect. A minimal Landau theory ties these thermodynamic signatures together, revealing a pressure‐independent transition entropy with comparable charge and ...
Jefferson Delgado‐Quesada, Gian Giacomo Guzmán‐Verri   +1 more
wiley   +1 more source

Lipschitz stability of the K-quadratic functional equation

, 2018
Let N be the set of all positive integers, G an Abelian group with a metric d and E a normed space. For any f : G → E we define the k-quadratic difference of the function f by the formula Qk ƒ(x; y) := 2ƒ(x) + 2k2ƒ(y) - f(x + ky) - f(x - ky) for x; y ∈ G
Chahbi, Abdellatif, Kabbaj, Samir, EL-Fassi, Iz-iddine   +2 more
core  

Solid Harmonic Wavelet Bispectrum for Image Analysis

Advanced Science, EarlyView.
The Solid Harmonic Wavelet Bispectrum (SHWB), a rotation‐ and translation‐invariant descriptor that captures higher‐order (phase) correlations in signals, is introduced. Combining wavelet scattering, bispectral analysis, and group theory, SHWB achieves interpretable, data‐efficient representations and demonstrates competitive performance across texture,
Alex Brown, Mathilda Avirett‐Mackenzie, Carolin Villforth, Georgios Exarchakis   +3 more
wiley   +1 more source

A FIXED POINT APPROACH TO THE FUZZY STABILITY OF A QUADRATIC-QUARTIC FUNCTIONAL EQUATION

, 2012
Using fixed point method, we prove the Hyers-Ulam stability of the following quadratic-quartic functional equation f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + 2f(2y) - 8f(y) in fuzzy Banach ...
Dong Yun Shin, Shin, Dong Yun, Lee, Jung Rye, Park, Choonkil, Choonkil Park, Jung Rye Lee   +5 more
core   +1 more source

Overcoming Artificial Structures in Resolution‐Enhanced Hi‐C Data by Signal Decomposition and Multi‐Scale Attention

Advanced Science, EarlyView.
Deep‐learning‐based signal enhancement is an effective way to recover high‐resolution details from a low‐resolution chromatin contact map. However, due to computational challenges, existing methods commonly divide up the contact map into small patches and create artificial discontinuities at patch boundaries.
Qinyao Li, Kelly Yichen Li, Chiara Nicoletti, Stephen Kwok‐Wing Tsui, Pier Lorenzo Puri, Qin Cao, Kevin Y. Yip   +6 more
wiley   +1 more source

Interpretable Machine Learning Framework for Nb─Si Based Alloy Design with Enhanced Fracture Toughness

Advanced Science, EarlyView.
An interpretable machine learning framework integrating SHAP and PDP analysis identifies critical design descriptors from 139 physicochemical features for Nb─Si alloys. The framework achieves <7% prediction error and guides the discovery of Nb38.5Ti38.5Si3Zr18V2 alloy with 22.791 MPa·m1/2 fracture toughness, breaking the 20 MPa·m1/2 barrier.
Dezhi Chen, Chao Xu, Jingyue Yu, Qi Wang, Hongze Fang, Shuo Yin, Turab Lookman, Ruirun Chen   +7 more
wiley   +1 more source

Measure zero stability problem of a new quadratic functional equation

, 2016
Let R be the set of real numbers, Y a Banach space and f:R→Y. We prove the Ulam-Hyers stability theorem for the new quadratic functional equation∑j=2k(f(x1+xj)+f(x1-xj))=2(k-1)f(x1)+2∑j=2kf(xj) for all (x1,., xk)∈Γ, where Γ⊂Rk is of Lebesgue measure 0 ...
Chung, J., Rassias, J.M.
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