We consider FLRW cosmological models for perfect fluid (with ρ as the energy density) in the frame work of the f(ρ) modified theory of gravity [V. N. Tunyak, Russ. Phys. J. 21, 1221 (1978); J. R. Ray, L. L. Smalley, Phys. Rev. D. 26, 2615 (1982)]. This theory, with total Lagrangian R-f(ρ), can be considered as a cousin of the F(R) theory of gravity with total Lagrangian F(R)-ρ. We can pick proper function forms f(ρ) to achieve, as the F(R) theory does, the following 4 specific goals, 1) producing a non-singular cosmological model (Ricci scalar and
This paper is concerned with the relationship between maximum
principle and dynamic programming in zero-sum stochastic
differential games. Under the assumption that the value function is enough
smooth, relations among the adjoint processes, the generalized Hamiltonian
function and the value function are given. A portfolio optimization problem
under model uncertainty in the financial market is discussed to show the
applications of our result.
In this paper, we shall study the uniqueness problems of meromorphic
functions of differential polynomials sharing two values IM. Our results improve
or generalize many previous results on value sharing of meromorphic functions.