A life insurer exhibiting this degree of risk aversion would choose the free asset portfolio located at the

tangency point of the upper indifference curve and the solid black frontier.

The cevians joining the vertices of a triangle to the points of

tangency of the opposite sides with the corresponding excircles are concurrent.

However, in the realistic case, the choice of the maximum product is the closest approximation to such

tangency that could be, or should be, achieved.

Let us denote [epsilon] as the weight of the lending

tangency portfolio and (1 - [epsilon]) as the weight of the borrowing

tangency portfolio used to construct a third portfolio on the envelope of minimum variance portfolios for a given expected return.

Right-angled triangles have appeared because any radius meeting a point of

tangency is perpendicular to the tangent.

The utility-maximizing equilibrium for our individual as an entrepreneur is at the

tangency point E.

Prove: the point E lies on the chord ML--the chord connecting the points of

tangency.

In [CL13], we also study the

tangency graphs of Boyd-Maxwell ball packings and enumerate level-2 Coxeter systems.

For one can indeed contrive points of

tangency among the three writers, some of them deliberately oblique, triangulating what are otherwise quite different fictional and authorial projects.

Because OO' incorporates a marginal tax rate of 50 percent, its smaller gradient implies

tangency with the beneficiary's indifference curve IC2 at a point ([E.

1,2] change depending on the location of the

tangency points [P.

NC is referred to as a

tangency method because the resulting sound level is determined by

tangency to criteria curves in each octave band without regard to the shape of the sound spectrum.

which leads to a theory of

tangency and theorems dealing with the relationships between great circles and sets of parallel lesser circles.

His topics include the possibility of classifying part surfaces, an analytical method based on second fundamental forms of the contacting part surfaces, indicatrix of conformity of two smooth regular surfaces in the first order of

tangency, and general considerations and special cases for generating enveloping surfaces.

Located at the point of

tangency of three important geopolitical and geo-economic zones-Europe, Central Asia and Middle East--the Black Sea region is a main energy transit bridge and at the same time, an important stage on which the risk factors and outbreaks of conflict have a strong impact on the security of South-East Europe and therefore NATO.