2]]/2EI] Rd[theta] (3) where: A = cross sectional area of wall E = Young's Modulus of beam material [alpha] = thermal expansion coefficient I = second moment of area, cross section of wall L = length of straight section of the wall R = Radius of curvature of bend [DELTA]T = Temperature change [theta] = Angle measured from the point of tangency between bend and straight section of wall The boundary condition at B requires that the horizontal deformation of the wall at this location be zero.

On the other hand, if profitable pooling were to occur at a point of tangency, or where the HH-type indifference curve is steeper than the LL-type, then both types could be attracted to a profitable alternative that is also incentive compatible with respect to the HL-types.

There are interesting frictions and incongruities in these places and, often, if you stand at the point of tangency, you can see both sides better than if you were in the middle of either" (Fadiman, p.

1) The mission history of nineteenth-century India, indisputably full of frictions and incongruities, suggests exactly that-standing at the point of tangency between Hinduism and Christianity could be transformative and sometimes was.

Starting from the point of tangency between the IMF's indifference curve and the government's reaction function, there exist unexploited mutual welfare gains for the IMF and the recipient government.

Domestic investment, inclusive of that part funded by foreign saving, rises to the point where the marginal product of capital, reflected in the slope of the dashed portion of the investment opportunities frontier in Figure 1, equals the prevailing world interest rate, as earlier specified in equation (8), at the point of tangency.

From the points of intersection of the tangents with the extension of the diameter, he then produces parallel lines, in any direction, whose length is equal to the distance from the point of tangency to the extension of the diameter.

Given a production possibilities curve and a state indifference curve or preference function, the point of tangency would indicate the coordinates of the plan.