Results 1 to 10 of about 4,380,008 (160)
A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms
Annales Mathematicae Silesianae, 2022 Let S be a semigroup, and let φ, ψ: S → S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation f(xϕ(y))+f(ψ(y)x)=2f(x)f(y), x,y ∈ S,
Akkaoui Ahmed +2 more
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Remarks on the Conditional Quadratic and the Conditional D’Alembert Functional Equations on Particular Normed Spaces [PDF]
Abstract and Applied Analysis, 2013 Let be a real normed space with dimension greater than 2 and let be a real functional defined on . Applying some ideas from the studies made on the conditional Cauchy functional equation on the restricted domain of the vectors of equal norm and the ...
Margherita Fochi, Gabriella Viola
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Variational approach to multimode nonlinear optical fibers. [PDF]
NanophotonicsAbstract We analyze the spatiotemporal solitary waves of a graded‐index multimode optical fiber with a parabolic transverse index profile. Using the nonpolynomial Schrödinger equation approach, we derive an effective one‐dimensional Lagrangian associated with the Laguerre–Gauss modes with a generic radial mode number p and azimuthal index m.
Lorenzi F, Salasnich L.
europepmc +2 more sources
The D’Alembert Inevitability Theorem [PDF]
MathematicsWe study functions satisfying the composition law F(xy)+F(x/y)=P(F(x),F(y)) with a symmetric polynomial combiner P. We prove that symmetry together with a quadratic degree bound on P forces a composition law of d’Alembert type.
Jonathan Washburn +2 more
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The superstability of d’Alembert’s functional equation on the Heisenberg group
Applied Mathematics Letters, 2010 B. Bouikhalene, E. Elqorachi, J. Rassias
exaly +2 more sources
On the superstability of generalized d'Alembert harmonic functions
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2016 The aim of this paper is to study the superstability problem of the d'Alembert type functional equation f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) for all x,y,z ∈ G, where G is an abelian group and σ: G → G is an endomorphism such that ...
Iz-iddine EL-Fassi
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Variant of D'alembert functional equation on compact homogeneous space
, 2018 In this work, we introduce a new functional equation on compact homogeneous spaces based on the d'Alembert functional equation on compact groups. We solve the functional equation by using tools from harmonic analysis.
Sorawit Viwanthananut
semanticscholar +1 more source
A Variant of D’alembert’s Matrix Functional Equation
Annales Mathematicae Silesianae, 2020 The aim of this paper is to characterize the solutions Φ : G → M2(ℂ) of the following matrix functional equations Φ(xy)+Φ(σ(y)x)2=Φ(x)Φ(y), x,y,∈G,{{\Phi \left( {xy} \right) + \Phi \left( {\sigma \left( y \right)x} \right)} \over 2} = \Phi \left( x \
Y. Aissi, D. Zeglami, M. Ayoubi
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Coherent Comparison as Information Cost: Axiomatic Foundations for Discrete Ledger Dynamics
FoundationsWe develop an information-theoretic, cost-first framework for discrete dynamics in which the primitive operation is ratio-based comparison. Given two quantities compared via their ratio x=a/b, we assign a cost F(x) measuring deviation from equilibrium (x=
Sebastian Pardo-Guerra +3 more
doaj +1 more source
Computer Graphics Forum, EarlyView.Abstract We introduce mixed super‐circles, a position‐curvature formulation of the original dynamic 2D super‐helix model. Compared to the latter, purely curvature‐based model – the so‐called chained formulation –, the mixed formulation that we propose here drastically reduces the algorithmic complexity of the solving scheme – from quadratic to quasi ...
Emile Hohnadel +2 more
wiley +1 more source