Zongsheng Gao

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Let A and B be bounded linear operators on a Hilbert space satisfying A ≥ B ≥ 0. The well-known Furuta inequality is given as follows: Let r ≥ 0 and p > 0; then A r 2 Amin{1,p}A r 2 ≥ (A r 2 BpA r 2 ) min{1,p}+r p+r . In order to give a self-contained proof of it, Furuta (1989) proved that if 1 ≥ r ≥ 0, p > p0 > 0 and 2p0 + r ≥ p > p0, then (A r 2 Bp0A r 2(More)
Consider a random k-conjunctive normal form F k (n, rn) with n variables and rn clauses. We prove that if the probability that the formula F k (n, rn) is satisfiable tends to 0 as n→∞, then r ⩾ 2.83, 8.09, 18.91, 40.81, and 84.87, for k = 3, 4, 5, 6, and 7, respectively. SAT 问题是第一个被证明的 NP 完全问题, 是理论计算机科学研究的核心问题之一。 自从上世纪九十年代初发现 NP 完全问题存在相变现象以来, 随机 k-SAT(More)
In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire(More)
This paper discusses some spectral properties of class wF(p,r,q) operators for p > 0, r > 0, p + r ≤ 1, and q ≥ 1. It is shown that if T is a class wF(p,r,q) operator, then the Riesz idempotent Eλ of T with respect to each nonzero isolated point spectrum λ is selfadjoint and Eλ = ker(T − λ)= ker(T − λ)∗ . Afterwards, we prove that every class wF(p,r,q)(More)