Use Stokes' theorem to compute the circulation

F · dr

where F =

8xyz, 2y²z, 5yz

and C is the boundary of the portion of the plane

2x + 3y + z = 6

in the first octant. Here C is positively oriented with respect to the plane whose orientation is upward.

Briefly define the following terms and discuss their role in molecular modelling a. Periodic boundary conditions b. Steepest descents minimization c. Force field parameterisation d. Bonded potential e. Cross terms f. Harmonic potential g. Morse potential

Briefly define the following terms and discuss their role in molecular modelling

a. Periodic boundary conditions

b. Steepest descents minimization

c. Force field parameterisation

d. Bonded potential

e. Cross terms

f. Harmonic potential

g. Morse potential

The boundary of a lamina consists of the semicircles

y =

and y =

together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin.

Solve the Boundary Value Problem, PDE: U_tt-a²u_xx=0, 0≤x≤1, 0≤t<∞

BCs: u(0,t)=0

u(1,t)=cos(t)

u(x,0)=0

u_t(x,0)=0

1. Consider the set of real numbers S=[-1,0)U{1/n:n=1,2,3,...}. Give the explicit set for each of the

1. The complement of S,
2. The closure of S,
3. The boundary points of S,
4. The limit points of S,
5. The isolated points of S,
6. The interior of S, and
7. The exterior of S.

1. [9 marks] Consider the boundary-value problem,
y′′ +2εy1/2 = 0, y(0) = 1,y(1) = 3/2.
Letting y = y0 + εy1 + ε2y2 + . . . , find y0 and y1 and hence y with error O(ε2).

hello Mr\Mrs
My question is about Security again.
1)What are security and its adjacent consepts ?
2) What is the disciplinary boundary of International Securit Studies ?
3) The Western-centrism conundrum (needs some brief explanation).
thanks in advance :)

What would have you done differently to successfully contain and solve the crisis in each of these three countries? USA, UK, and Germany?