Results 41 to 50 of about 157,970 (240)
On the approximation of algebraic numbers by algebraic integers [PDF]
Journal of the Australian Mathematical Society, 1963 In his Topics in Number Theory, vol. 2, chapter 2 (Reading, Mass., 1956) W. J. LeVeque proved an important generalisation of Roth's theorem (K. F. Roth, Mathematika 2,1955, 1—20).Let ξ be a fixed algebraic number, σ a positive constant, and K an algebraic number field of degree n.
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Tropical Solution of Discrete Best Approximation Problems
MathematicsWe consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input–output pairs of an unknown function defined on a
Nikolai Krivulin
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International Journal of Adaptive Control and Signal Processing, EarlyView.This work introduces an adaptive human pilot model that captures pilot time‐delay effects in adaptive control systems. The model enables the prediction of pilot–controller interactions, facilitating safer integration and improved design of adaptive controllers for piloted applications.
Abdullah Habboush, Yildiray Yildiz
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On the approximation to algebraic numbers by algebraic numbers
Glasnik Matematicki, 2009 Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number e, there are infinitely many algebraic numbers α of degree at most n such that |ξ−α| < H(α)−n−1+e, where H(α) denotes the naive height of α. We sharpen this result by replacing e by
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On the approximation of π by special algebraic numbers [PDF]
Glasgow Mathematical Journal, 1980 Suppose that m0 is an integer, m0≥3, ρ = exp(2πi/m0), K = ℚ(ρ, i), v denotes the degree of K, ξ∈K has degree N over ℚ. The length, where is the (irreducible) minimal polynomial for with ξ relatively prime integer coefficients. Feldman [2, p. 49] proved that there is an absolute constant c0>0 such thatFrom [2, p. 49, Notes 1 and 2] we know that v =
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Advanced Engineering Materials, EarlyView.A numerical model resulting from irreversible thermodynamics for describing transport processes is introduced, focusing on thermodynamic activity gradients as the actual driving force for diffusion. Implemented in CUDA C++ and using CalPhaD methods for determining the necessary activity data, the model accurately simulates interdiffusion in aluminum ...
Ulrich Holländer +3 more
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Chromatic homotopy theory is asymptotically algebraic
, 2019 Inspired by the Ax--Kochen isomorphism theorem, we develop a notion of categorical ultraproducts to capture the generic behavior of an infinite collection of mathematical objects.
Barthel, Tobias +2 more
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Demonstration of an All‐Optical AND Gate Mediated by Photochromic Molecules
Advanced Functional Materials, EarlyView.A logic AND gate that runs on photons is demonstrated. It relies on two spatially separated photochromic molecules that work in tandem. Abstract The realization of a photonic logic AND gate, i.e. a logic AND gate that runs on photons rather than electrons, and where all steps are controlled by light, is demonstrated. In a proof‐of‐principle experiment,
Heyou Zhang +7 more
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Diophantine approximation of Mahler numbers
, 2015 Suppose that $F(x)\in\mathbb{Z}[[x]]$ is a Mahler function and that $1/b$ is in the radius of convergence of $F(x)$. In this paper, we consider the approximation of $F(1/b)$ by algebraic numbers.
Bell, Jason +2 more
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Advanced Robotics Research, EarlyView.This work presents a state‐adaptive Koopman linear quadratic regulator framework for real‐time manipulation of a deformable swab tool in robotic environmental sampling. By combining Koopman linearization, tactile sensing, and centroid‐based force regulation, the system maintains stable contact forces and high coverage across flat and inclined surfaces.
Siavash Mahmoudi +2 more
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