Under the influence of a one-dimensional stationary outfield with the equilibrium between kinetic and potential energy produced by it,a modified Sch(?)rdinger equation in the form i((?)ψ/(?)t)t=a (?)~2ψ/ax^2-ib (?),...Under the influence of a one-dimensional stationary outfield with the equilibrium between kinetic and potential energy produced by it,a modified Sch(?)rdinger equation in the form i((?)ψ/(?)t)t=a (?)~2ψ/ax^2-ib (?),where b=b_o(?)T/(?)x,is used to describe the behavior of the probability wave on the six-month departure charts at the 500 hPa level.It is found that C=2πa/L-b_o(?)T/ax and when L→∞,then C= -b_o(?)T/(?)x,where C is wave velocity,a and b are constants,and L is wavelength.The motion direction of probability waves is against the outfield temperature gradient,and their velocity is related to the absolute value of temperature gradient.The motion of waves shrinks in heat sinks and expands in heat sources,which have been verified in practice.Finally the six-month departure probability wave and the modified Sch(?)rdinger equation are used in the MOS predictions of temperature and rainfall in spring-summer 1981-1985 in Jilin Province and the accuracy for trend predictions is equal to 80%.展开更多
We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of...We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of(X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that(X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by products which are interesting in their own right.展开更多
文摘Under the influence of a one-dimensional stationary outfield with the equilibrium between kinetic and potential energy produced by it,a modified Sch(?)rdinger equation in the form i((?)ψ/(?)t)t=a (?)~2ψ/ax^2-ib (?),where b=b_o(?)T/(?)x,is used to describe the behavior of the probability wave on the six-month departure charts at the 500 hPa level.It is found that C=2πa/L-b_o(?)T/ax and when L→∞,then C= -b_o(?)T/(?)x,where C is wave velocity,a and b are constants,and L is wavelength.The motion direction of probability waves is against the outfield temperature gradient,and their velocity is related to the absolute value of temperature gradient.The motion of waves shrinks in heat sinks and expands in heat sources,which have been verified in practice.Finally the six-month departure probability wave and the modified Sch(?)rdinger equation are used in the MOS predictions of temperature and rainfall in spring-summer 1981-1985 in Jilin Province and the accuracy for trend predictions is equal to 80%.
基金supported by the National Science Foundation of the United States (Grant No. CMMI-1435864)
文摘We consider the random difference equations S =_d(X + S)Y and T =_dX + TY, where =_ddenotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right hand side are independent of(X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that(X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by products which are interesting in their own right.
