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On the superstability of generalized d'Alembert harmonic functions [PDF]
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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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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Uniqueness of the Canonical Reciprocal Cost
MathematicsWe study a rigidity problem for functions F:R>0→R≥0 that penalize deviation of a positive ratio from equilibrium x=1. Assuming (i) a d’Alembert-type composition law on R>0, and (ii) a single quadratic calibration at the identity (in logarithmic ...
Jonathan Washburn, Milan Zlatanović
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The D’Alembert Inevitability Theorem
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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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
Human‐Induced Vibration of Long‐Span Multi‐Layer Composite Beams—Analytical Calculation Method
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 8, August 2026.ABSTRACT The finite element method (FEM) provides a general framework for analyzing virtually all types of structures under various loading conditions. Nevertheless, in certain situations, designers may identify that the structural system exhibits predominantly beam‐like behavior, allowing the use of analytical theories.
Markku Heinisuo +2 more
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Weak Solutions for a Class of Nonlocal Singular Problems Over the Nehari Manifold
Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12360-12378, 30 July 2026.ABSTRACT In this paper, we consider a nonlocal model of dilatant non‐Newtonian fluid with a Dirichlet boundary condition. By using the Nehari manifold and fibering map methods, we obtain the existence of at least two weak solutions, with sign information.
Zhenfeng Zhang +2 more
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A Matrix‐Free, Scalable, and Robust Implicit Material Point Method
International Journal for Numerical Methods in Engineering, Volume 127, Issue 14, 30 July 2026.ABSTRACT An implicit material point method is presented using a new dynamic relaxation solver, allowing for a simple and efficient quasi‐static formulation that may be readily implemented in existing explicit‐dynamic codes. The use of dynamic relaxation and aggregation is shown to produce an extremely robust material point method scheme, with good ...
Sam J. V. Sutcliffe +5 more
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Fortschritte der Physik, Volume 74, Issue 6, June 2026.ABSTRACT We present a clear, step‐by‐step method for counting degrees of freedom and identifying constraints in general field theories. This approach, grounded in the works of Einstein, Hilbert, Cartan, Kuranishi, and, more recently, Seiler, is neither Lagrangian nor Hamiltonian in nature. Instead, it applies directly to the field equations. We offer a
Lavinia Heisenberg
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Photon‐Sphere Modes in Curved Optical Microcavities: A Black‐Hole Analogue Laser
Advanced Science, Volume 13, Issue 28, 18 May 2026.An optical analogue of a Schwarzschild black hole is realized using curved microcavities that preserve light‐like geodesics. A new family of laser modes confined around the photon sphere is identified alongside conventional whispering‐gallery modes. Analytical theory, numerical simulations, and experiments reveal curvature‐induced confinement, enabling
Chenni Xu +9 more
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