In this paper,by using monotone function,integral average technique and matrix inequalities,some new oscillation criteria for second order differential system with damping term(P(t)Y′(t))′+D(t)Y′(t)+Q(t)Y(t)=0,t∈[t_0,∞)are established,which generalize and improve some known oscillation ctiteria is literature.
Let f be a nonnegative operator monotone function on [0,∞). Then for all non-commutative Banach function space norms, we obtain that‖f(A)X-Xf(B)‖54‖f(|AX-XB|)‖,where A,B are τ-measurable positive operators, X is a contraction.
With the increase of specimens′ average grain,the acoustic parameters of rock isn′t a monotone function,and they reduce firstly and then increase,what′s more,the changeable scope of dynamic Poisson′s Ratio is higher than one of other acoustic parameters,and so it can′t show the deformation property of rock as the mechanical parameter of material.
In this paper, a quite general method to construct singular monotone function has been given here, and the relation between singular monotone functions and probabilistic properties of the generalized binary expansions of real numbers is also revealed in this method.
The necessary and sufficient conditions for a Boolean function to be 1-monotone function are presented using spectral methods by M. G. Kavpovsky. This paper points out some errors in the Karpovsky's theory. The correct spectral methods for identification of 1-monotone Boolean functions and their proofs are given.
In this paper,the relation between the strong law of large numbers of Markov chains and the singular monotone functions has been revealed,and a general approach to construct singular monotone functions has been put forward.