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- (a) Find a conjugacy C between G(x) = 4x(1-x) and g(x)=2-x^2 . (b) Show that g(x) has chaotic orbits.Give a recursive definition (with initial condition(s)) of (an) where (n = 1, 2, 3, . . . )Consider the following configuration of solar photovoltaic arrays consisting of crystalline silicon solar cells. There are two subsystems connected in parallel, each one containing two cells. In order for the system to function, at least one of the two parallel subsystems must work. Within each subsystem, the two cells are connected in series, so a subsystem will work only if all cells in the subsystem work. Consider a particular lifetime value t0, and suppose we want to determine the probability that the system lifetime exceeds t0.Let Ai denote the event that the lifetime of cell i exceeds t0(i = 1, 2, , 4). We assume that the Ai's are independent events (whether any particular cell lasts more than t0 hours has no bearing on whether or not any other cell does) and that P(Ai) = 0.6 for every i since the cells are identical. Using P(Ai) = 0.6, the probability that system lifetime exceeds t0 is easily seen to be 0.5904. To what value would 0.6 have to be changed in order to increase…
- Consider the following configuration of solar photovoltaic arrays consisting of crystalline silicon solar cells. There are two subsystems connected in parallel, each one containing two cells. In order for the system to function, at least one of the two parallel subsystems must work. Within each subsystem, the two cells are connected in series, so a subsystem will work only if all cells in the subsystem work. Consider a particular lifetime value to, and suppose we want to determine the probability that the system lifetime exceeds t0. Let Ai denote the event that the lifetime of cell i exceeds t0 (i = 1, 2, , 4). We assume that the Ai's are independent events (whether any particular cell lasts more than t0 hours has no bearing on whether or not any other cell does) and that P(Ai) = 0.6 for every i since the cells are identical. Using P(Ai) = 0.6, the probability that system lifetime exceeds t0 is easily seen to be 0.5904. To what value would 0.6 have to be changed in order to increase…Suppose that g = g(q, p, t), and that H is the Hamiltonian. Show that:a) (See the Figure)b) if any quantity does not explicitly depend on time and its Poisson parenthesis with the Hamiltonian is null, such quantity is a constant of motion for the system.Find the generating functions a(x) and b(x) with system of recurrent relationships:
- The Hamiltonian operator of a system is H=-(d2f/dx2) +x2 . Show that Nx exp (-x2/2) is an eigenfunction of H and determine the eigenvalue. Also evaluate N by normalization of the function.Consider two points (x0, y0) and (x1, y1). Prove that the first order Langrange polynonial is equivalent to linear interpolation.Find x1, x2, x3 with gauss jordan