Parabolic methods for ultraspherical interpolation inequalities

Berry-ess Een-type Inequalities for Ultraspherical Expansions

This paper contains several variants of Berry-Ess een-type inequalities for ultraspher-ical expansions of probability measures on 0; ]. Similar to the classical results on IR , proofs will be based in some cases on ultraspherical analogues of Fej er-kernels. The inequalities in this paper in particular lead to relations between the spherical-cap-distance of probability measures on unit spheres ...

Four point parabolic interpolation

Lachance. M.A. and A.J. Schwartz. Four point parabolic interpolation, Computer Aided Geometric Design 8 (1991) 143-149. We show that four points in the plane may be interpolated by one or two parabolas or possibly by no parabola, depending on the configuration of points. We provide methods for distinguishing the cases and constructing the parabolas.

Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences∗

This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincaré, logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities. The connection between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere is emphasized. The authors ad...

islanding detection methods for microgrids

امروزه استفاده از منابع انرژی پراکنده کاربرد وسیعی یافته است . اگر چه این منابع بسیاری از مشکلات شبکه را حل می کنند اما زیاد شدن آنها مسائل فراوانی برای سیستم قدرت به همراه دارد . استفاده از میکروشبکه راه حلی است که علاوه بر استفاده از مزایای منابع انرژی پراکنده برخی از مشکلات ایجاد شده توسط آنها را نیز منتفی می کند . همچنین میکروشبکه ها کیفیت برق و قابلیت اطمینان تامین انرژی مشترکان را افزایش ...

Notes on Interpolation Inequalities