Results 51 to 60 of about 157,970 (240)
Report on some recent advances in Diophantine approximation [PDF]
, 2009 A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as
Waldschmidt, Michel
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On approximation of p-adic numbers by p-adic algebraic numbers
Journal of Number Theory, 2005 18 ...
Beresnevich, V. +2 more
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Spatial‐Wavelength Multiplexing Error‐Controlled Photonic Analog Computing System
Advanced Science, EarlyView.A novel photonic integrated circuit prototype implementing the concept of general‐purpose analog computing and demonstrate its capability in radio frequency applications. The chip features a multichannel architecture and performs fully optical analog computation with frequency‐domain parallel processing. An FPGA‐based error‐correction algorithm aims to
Tao Zhu +15 more
wiley +1 more source
A Perspective on Interactive Theorem Provers in Physics
Advanced Science, EarlyView.Into an interactive theorem provers (ITPs), one can write mathematical definitions, theorems and proofs, and the correctness of those results is automatically checked. This perspective goes over the best usage of ITPs within physics and motivates the open‐source community run project PhysLean, the aim of which is to be a library for digitalized physics
Joseph Tooby‐Smith
wiley +1 more source
Diophantine approximation by conjugate algebraic integers
, 2003 Building on work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel'fond's transcendence criterion which provides a sufficient condition for a complex or $p$-adic number $\xi$ to be algebraic in terms of the ...
Roy, Damien, Waldschmidt, Michel
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On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree [PDF]
Acta Arithmetica, 1999 Define the absolute height of an algebraic number \(\beta\) by \(H(\beta)=|a_0|\prod_{i=1}^t\max (1,|\beta^{(i)}|)^{1/t}\), where \(t\) is the degree of \(\beta\), \(a_0\) is the leading coefficient of its minimal polynomial, and where \(\beta^{(1)}\ldots \beta^{(t)}\) are its conjugates. \textit{E. Wirsing} [Number Theory Institute 1969, Proc.
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Physical Origin of Temperature Induced Activation Energy Switching in Electrically Conductive Cement
Advanced Science, EarlyView.The temperature‐induced Arrhenius activation energy switching phenomenon of electrical conduction in electrically conductive cement originates from structural degradation within the biphasic ionic‐electronic conduction architecture and shows percolation‐governed characteristics: pore network opening dominates the low‐percolation regime with downward ...
Jiacheng Zhang +7 more
wiley +1 more source
Advanced Science, EarlyView.This study investigates how CTCs survive varying shear stress during hematogenous metastasis. We uncover a self‐protection mechanism, by which non‐adherent CTCs adapt to high shearing milieu through accumulated cytoplasmic myosin‐mediated disruption of myosin‐actin binding, attenuating force transmission into chromatin to protect CTCs from shear ...
Cunyu Zhang +10 more
wiley +1 more source
Effective approximation to complex algebraic numbers by algebraic numbers of bounded degree
Transactions of the American Mathematical SocietyWe establish the first effective improvements on the Liouville inequality for approximation to complex non-real algebraic numbers by complex algebraic numbers of degree at most 4 4 .
Bajpai, Prajeet, Bugeaud, Yann
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Distinct Biotypes of Visual Perception in Major Depressive Disorder
Advanced Science, EarlyView.In a discover dataset (272 acute MDD patients), this work identifies a novel depression biotype characterized by impaired visual motion perception, using machine learning clustering. An independent dataset confirms the robustness of this biotype through cross‐validation and demonstrates its generalizability.
Zhuoran Cai +13 more
wiley +1 more source