设{X_n}为i.i.d.r.v.s.,EX_1=0,EX_1~2=1,S_n=sum from i=1 to n(X_i),H(x)>0 (x≥0)为非降连续函数,对某γ>0和x_0>0,当x≥x_0时,x^(-2-γ)H(x)非降,x^(-1)logH(x)非增,且x^(-1)logH(x)→0(x→∞),则有一标准Wiener过程{W(t),...设{X_n}为i.i.d.r.v.s.,EX_1=0,EX_1~2=1,S_n=sum from i=1 to n(X_i),H(x)>0 (x≥0)为非降连续函数,对某γ>0和x_0>0,当x≥x_0时,x^(-2-γ)H(x)非降,x^(-1)logH(x)非增,且x^(-1)logH(x)→0(x→∞),则有一标准Wiener过程{W(t),t≥0},使得 S_n-W(n)=O(invH(n))a.s.(n→∞)的充分必要条件是:对任何t>0有EH(t|X_1|)<∞。展开更多
Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universalit...Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies,time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle(SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.展开更多
文摘设{X_n}为i.i.d.r.v.s.,EX_1=0,EX_1~2=1,S_n=sum from i=1 to n(X_i),H(x)>0 (x≥0)为非降连续函数,对某γ>0和x_0>0,当x≥x_0时,x^(-2-γ)H(x)非降,x^(-1)logH(x)非增,且x^(-1)logH(x)→0(x→∞),则有一标准Wiener过程{W(t),t≥0},使得 S_n-W(n)=O(invH(n))a.s.(n→∞)的充分必要条件是:对任何t>0有EH(t|X_1|)<∞。
文摘Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies,time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle(SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.
