BERNSTEIN'S FIRST SUMMABLE OPERATORS ON THE SPECIAL REAL ORTHOGONAL GROUP SO(n)

We study the structure of Bernstein's first summable operators and show that they con- verge uniformly to continuons functions on the special real orthogonal group SO(n)in this paper.In addition,we have also discussed the approximation degree to a class of function Lipα(0<α≤1)on SO(n).

THE KAKEYA MAXIMAL OPERATOR WITH A SPECIAL BASE to the memory of Professor Ruilin Long

Let M f be the Kakeya maximal function in d-dimensional Euclidean space, with same base consisting of cylinders of eccentricity N. The inequality shoum for a base satisfying a direction condition, where ?and c are constants depending only on d.

War and Peace in Ukraine.A Legal-Linguistic Perspective

The current research overlaps a linguistic and a legal analysis of public international law in the Ukrainian case.Based on both official documents and public declarations,it explains the grounds for the wide range of understandings that the two common concepts-peace and war-may be bearing depending of the angle of looking at the matter and depending on the actor invoking them.The study develops the reasons likely to have been considered by President Putin when insisting to refer to the Russian military action started in Ukraine in February 2022 as“special military operation”instead of“war”and the cardinal difference in terms of legal impact for such a linguistic choice.It also builds on the elements which could serve as a basis for achieving a deal in obtaining peace in Ukraine,while tackling on the possible geopolitical,public communication and diplomatic hurdles,and offering clues for strategic analysis of the matter.

Guest editorial:special section on energy storage systems and operational flexibility in power systems

The energy storage system(ESS) is becoming an important component in power systems to mitigate the adverse impact of intermittent renewable energy resources and improve power grid reliability and efficiency.However,storage devices driven by different technologies can have specific grid impacts.This special section is dedicated to reflecting the

Design of low-noise photodetector with a bandwidth of130 MHz based on transimpedance amplification circuit

A low-noise photodetector is a basic tool for the research of quantum information processing. We present a specially designed low-noise photoelectric detector with a bandwidth of 130 MHz, using a transimpedance amplification circuit. Based on the detailed calculation of the dependence on each parameter of the detector,a useful method of how to design a low-noise and broadband photodetector is provided. When the optical power is between 1.0 and 16 m W, the photodetector has a good linear response to the injected light. Its electronics noise power is below-77 d Bm, which is within the whole bandwidth. When the incident light power is 2 m W, the output noise powers are 10.0, 8.0, and 6.0 d B higher than the corresponding electronics noise within the bandwidth of 1–50, 50–90, and 90–130 MHz, respectively, which is in good agreement with the theoretical prediction.Thus, this photoelectric detector could have good application prospects in quantum communication and an optical cavity locking system.