Approximation of the Lebesgue Constant of a Lagrange Polynomial by a Logarithmic Function with Shifted Argument

2021 ◽  
Vol 252 (3) ◽  
pp. 445-452
Author(s):  
I. A. Shakirov
2010 ◽  
Author(s):  
Sanjeev Agarwal ◽  
Indu Bhuria ◽  
R. B. Patel ◽  
B. P. Singh

2013 ◽  
Vol 12 (08) ◽  
pp. 1350055
Author(s):  
SONIA L'INNOCENTE ◽  
FRANÇOISE POINT ◽  
CARLO TOFFALORI

Given a compact linear Lie group G, we form a natural expansion of the theory of the reals where G and the graph of a logarithm function on G live. We prove its effective model-completeness and decidability modulo a suitable variant of Schanuel's Conjecture.


2016 ◽  
Vol 06 (03) ◽  
pp. 1650019 ◽  
Author(s):  
V. M. Ishchuk ◽  
D. V. Kuzenko

The paper presents results of experimental study of the dielectric constant relaxation during aging process in Pb(Zr,Ti)O3based solid solutions (PZT) after action of external DC electric field. The said process is a long-term one and is described by the logarithmic function of time. Reversible and nonreversible relaxation process takes place depending on the field intensity. The relaxation rate depends on the field strength also, and the said dependence has nonlinear and nonmonotonic form, if external field leads to domain disordering. The oxygen vacancies-based model for description of the long-term relaxation processes is suggested. The model takes into account the oxygen vacancies on the sample's surface ends, their conversion into [Formula: see text]- and [Formula: see text]-centers under external effects and subsequent relaxation of these centers into the simple oxygen vacancies after the action termination. [Formula: see text]-centers formation leads to the violation of the original sample's electroneutrality, and generate intrinsic DC electric field into the sample. Relaxation of [Formula: see text]-centers is accompanied by the reduction of the electric field, induced by them, and relaxation of the dielectric constant, as consequent effect.


2020 ◽  
Vol 126 (3) ◽  
pp. 559-567
Author(s):  
Megumi Kirihata ◽  
Makoto Yamashita

We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map), and functional calculus by operator monotone functions defined on the positive real numbers instead of the logarithmic function.


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