Results 41 to 50 of about 94 (83)
Self‐Similar Blowup for the Cubic Schrödinger Equation
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1831-1918, August 2026.ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
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Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
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A note on the monomiality principle and generalized polynomials.
Rendiconti di Matematica e delle Sue Applicazioni, 2001 Summary: The monomiality principle is used to state generalized forms of the division algorithm and of the remainder theorem for families of polynomials written as linear combination of Hermite polynomials.
G. DATTOLI +2 more
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When is the graph of a random 0/1 polytope a clique?
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract We study graph‐theoretic properties of random 0/1$0/1$ polytopes. Specifically, let Qpn⊆{0,1}n$Q_p^n \subseteq \lbrace 0,1\rbrace ^n$ be a random subset where each point is included independently with probability p$p$, and consider the graph Gp$G_p$ of the polytope conv(Qpn)$\operatorname{conv}(Q_p^n)$.
Catherine Babecki +2 more
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International Journal for Numerical Methods in Engineering, Volume 127, Issue 14, 30 July 2026.ABSTRACT Numerous mesh‐distortion‐insensitive Petrov‐Galerkin finite element formulations have been developed for the simulation of elastostatic problems. This contribution presents initial results on how these formulations can be extended to linear elastodynamics. In this context, three different approaches are examined, building upon an established 8‐
Felix Zähringer, Peter Betsch
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New Bell–Sheffer Polynomial Sets
Axioms, 2018 In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them, have been studied. The method used in previous articles, and even in the present one, traces back to preceding
Pierpaolo Natalini, Paolo Emilio Ricci
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The Monomiality Principle Applied to Extensions of Apostol-Type Hermite Polynomials
European Journal of Pure and Applied MathematicsIn this research paper, we present a class of polynomials referred to as Apostol-type Hermite-Bernoulli/Euler polynomials $\mathcal{U}_\nu(x,y;\rho;\mu)$, which can be given by the following generating function\begin{equation*} \displaystyle \frac{2-\mu+\frac{\mu}{2}\xi}{\rho e^{\xi}+(1-\mu)}e^{x \xi+y \xi^2} =\displaystyle\sum\limits_{\nu=0 ...
Stiven Díaz +4 more
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Surface and Boundary Corrections in Peridynamics Using Optimized Nodal Influence Weights
International Journal for Numerical Methods in Engineering, Volume 127, Issue 14, 30 July 2026.ABSTRACT Peridynamics (PD), similarly to some other nonlocal continuum theories, exhibits truncated interaction horizons near free surfaces, cracks, and voids in bounded domains. This loss of neighbors causes artificial surface effects and inconsistencies in the derivative and energy operators that persist under discretization refinement, limiting PD ...
Arman Shojaei +5 more
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Truncated-exponential-based Frobenius–Euler polynomials
Advances in Difference Equations, 2019 In this paper, we first introduce a new family of polynomials, which are called the truncated-exponential based Frobenius–Euler polynomials, based upon an exponential generating function.
Wiyada Kumam +4 more
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Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver
International Journal for Numerical Methods in Fluids, Volume 98, Issue 7, Page 804-839, July 2026.A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
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