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Laura Luzzi Stefano Marmi Hitoshi Nakada Rie Natsui 《Journal of Approximation Theory》2010,162(1):24-41
For given, we consider the one-parameter family of -continued fraction maps, which include the Gauss map (), the nearest integer () and by-excess () continued fraction maps. To each of these expansions and to each choice of a positive function on the interval we associate a generalized Brjuno function . When or , and , these functions were introduced by Yoccoz in his work on linearization of holomorphic maps.We compare the functions obtained with different values of and we prove that the set of -Brjuno numbers does not depend on the choice of provided that . We then consider the case , and we prove that is a Brjuno number (for ) if and only if both and are Brjuno numbers for . 相似文献
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María F. Natale Eduardo A. Santillan Marcus Domingo A. Tarzia 《Nonlinear Analysis: Real World Applications》2010,11(3):1946-1952
We consider a one-dimensional solidification of a pure substance which is initially in liquid state in a bounded interval . Initially, the liquid is above the freezing temperature, and cooling is applied at while the other end is kept adiabatic. At the time , the temperature of the liquid at comes down to the freezing point and solidification begins, where is the position of the solid–liquid interface. As the liquid solidifies, it shrinks () or expands () and appears a region between and , with . Temperature distributions of the solid and liquid phases and the position of the two free boundaries ( and ) in the solidification process are studied. For three different cases, changing the condition on the free boundary (temperature boundary condition, heat flux boundary condition and convective boundary condition) an explicit solution is obtained. Moreover, the solution of each problem is given as a function of a parameter which is the unique solution of a transcendental equation and for two of the three cases a condition on the parameter must be verified by data of the problem in order to have an instantaneous phase-change process. In all the cases, the explicit solution is given by a representation of the similarity type. 相似文献
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We give a parameterization of the algebraic points of given degree over on the curve This result extends a previous result of E.F. Schaefer who described in Schaefer (1998) [1] the set of algebraic points of degree ?3 over . 相似文献
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For any positive integers , we present formulae for the number of irreducible polynomials of degree n over the finite field where the coefficients of , and are zero. Our proofs involve counting the number of points on certain algebraic curves over finite fields, a technique which arose from Fourier-analysing the known formulae for the base field cases, reverse-engineering an economical new proof and then extending it. This approach gives rise to fibre products of supersingular curves and makes explicit why the formulae have period 24 in n. 相似文献
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Lola Thompson 《Journal of Number Theory》2012,132(5):1038-1053
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Aysel Erey 《Discrete Mathematics》2018,341(5):1419-1431
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In this Note, we give sufficient conditions for the regularity of Leray–Hopf weak solutions to the Navier–Stokes equation. We prove that, if one of three conditions (i) where and , (ii) where and , or (iii) where and , is satisfied, then the solution is regular. These conditions improve earlier results on the conditional regularity of the Navier–Stokes equations. To cite this article: I. Kukavica, M. Ziane, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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In this paper, by using Picard–Fuchs equations and Chebyshev criterion, we study the upper bounds of the number of limit cycles given by the first order Melnikov function for discontinuous differential systems, which can bifurcate from the periodic orbits of quadratic reversible centers of genus one (r19): , , and (r20): , , and the periodic orbits of the quadratic isochronous centers , , and , . The systems (r19) and (r20) are perturbed inside the class of polynomial differential systems of degree n and the system and are perturbed inside the class of quadratic polynomial differential systems. The discontinuity is the line . It is proved that the upper bounds of the number of limit cycles for systems (r19) and (r20) are respectively and counting the multiplicity, and the maximum numbers of limit cycles bifurcating from the period annuluses of the isochronous centers and are exactly 5 and 6 (counting the multiplicity) on each period annulus respectively. 相似文献