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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)
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 A min{1,p} A r 2 ≥ (A r 2 B p A 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 > p 0 > 0 and 2p 0 + r ≥ p > p 0 , then (A r 2 B p(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)
We will study meromorphic functions that share a small function, and prove the following result: let f (z) and g(z) be two transcendental meromorphic functions in the complex plane and let n ≥ 11 be a positive integer. Assume that a(z)( ≡ 0) is a common small function with respect to f (z) and g(z). If f n f ′ and gng ′ share a(z) CM, then either f n(z) f ′(More)