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Let Ω ⊂ RN, N ≥ 2, be a bounded connected domain, and let u(t) = et∆D 1 be the Dirichlet heat evolution of the constant initial temperature. We prove that if the exterior normal derivative ∂νu(·,tj) is constant on ∂Ω along a sequence tj ↓ 0, then Ω is a ball, assuming only ∂Ω ∈ C2. This answers, in the classical curvat...
A novel inner approximation algorithm is proposed for dynamic optimization problems to ensure strict satisfaction of path constraints. Distinct from traditional methods relying on interval analysis, the proposed algorithm leverages the convex hull property of Bernstein polynomials to tightly bound the polynomial compon...
Optimization and Control (math.OC)Optimization and ControlFOS: Mathematicsmathematics
Maurin-Dupuis, Camille · Briandet, Romain · Chateau, Alice
Bacillus cereus is a ubiquitous spore-forming pathogen that represents a persistent challenge for the food industry due to its ability to rapidly colonize abiotic surfaces and develop highly resistant biofilms. These structures act as reservoirs for spores and may promote the persistence and expression of virulence det...
Quorum sensing[SDV.AEN] Life Sciences [q-bio]/Food and NutritionBiofilmSpore
We study the two-color distinct-part series \(S_1(q)\), equivalently Andrews' generating function \(v_d(q)\) for strictly concave compositions, and its odd and even companions \(T_o(q)\) and \(T_e(q)\). We determine the coefficients of \(S_1(q)\) modulo \(4\) and obtain a complete criterion for the resulting Ramanujan-...
We give an asymptotic formula for the number of rational points of bounded height on algebraic varieties defined by systems of multihomogeneous diagonal equations. The proof uses the Hardy-Littlewood circle method and the hyperbola method developed by Blomer and Brüdern.
Number TheoryFOS: MathematicsNumber Theory (math.NT)mathematics
Yubexi Correa · Vera Cebrián-Lloret · Patricia López-Sánchez · Juan Carlos Martínez · y 7 más
Seaweeds are increasingly recognized as sustainable and nutritious candidates to support future food systems, yet the mechanisms governing their digestibility remain poorly understood. In this work, we show that the cell walls of Nori seaweed (Porphyra umbilicalis) are highly resistant to gastric digestion, with protei...
agricultural biotechnologyagricultural and veterinary sciences640
In this paper, we present a rigorous long-time stability analysis of a second-order explicit exponential Runge--Kutta (ERK2) method for the Cahn--Hilliard equation. By employing Fourier spectral collocation in space and a two-stage ERK2 scheme in time, we construct a fully discrete numerical method and establish an ene...
Zefan Du · Shuwen Kan · Samuel A. Stein · Zhiding Liang · y 2 más
As quantum processors scale, monolithic architectures face growing challenges due to limited qubit density, heterogeneous error profiles, and restricted connectivity. Modular quantum systems, enabled by chip-to-chip coupler-connected modular architectures, provide a scalable alternative. However, existing quantum compi...
Quantum PhysicsFOS: Physical sciencesengineering and technologyQuantum Physics (quant-ph)
Carlo De Paolis Robles · Andrés Tomás-Martín · Ignacio Egido · Aurelio García-Cerrada
The gradual substitution of conventional synchronous generators by converter-interfaced renewable energy sources raises concerns about the reduction of conventional inertia in electric power systems and the ensuing threat to their stability. In this regard, grid-forming voltage source converters have been proposed as a...
engineering and technologySystems and Control (eess.SY)Systems and Control
Tongtong Jin · Anirudh Subramanyam · D. Adrian Maldonado
This paper introduces a framework based on Large Deviation Theory (LDT) to accurately and efficiently compute the rare probabilities of voltage collapse. We formulate the problem as finding the most probable failure point (the instanton) on the stability boundary and derive both first-order and second-order approximati...
Optimization and Control (math.OC)Optimization and ControlFOS: Mathematicsengineering and technology
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