Since such a point cannot lie on the positive

real axis, there is no scope for a physical phase transition in a finite system.

Notice the position of the two solutions; they are no longer on the

real axis.

which are two asymptotically periodic meromorphic functions along the

real axis. Referring the graph of [absolute value of cot k] to [31], there are vertical lines in C passing through the

real axis at which [absolute value of cot k] = 0 and then strictly increases to 1 or at which [absolute value of cot k] = 0 and strictly decreases to 1, as [absolute value of JK] goes to infinity.

pair complex critical points do not reach the

real axis. Typical Spectrum Curves are presented in Figure 15(c).

Suppose that [B.sub.n] is a set which is bounded, symmetric with the respect of the

real axis and which the boundary coincides with the segment [-i, i] and the arc given by the polar equation [rho] = r([theta])[e.sup.i[theta]], where

If [phi] = 0, we say that D is convex in the direction of the

real axis. The following theorem due to Clunie and Sheil-Small [8] is often referred to as the shear construction and will be critical to our minimal surface constructions.

where ([[GAMMA].sub.+]) is the upper part of r when split by the

real axis, and I(Z) denotes the imaginary part of Z.

The higher the [Q.sub.L] of the poles ([Q.sub.L] (p) = [??] (p)/R (p)) is, the nearer the [??] ([Y.sub.osc] + [Y.sub.res]) cross over the

real axis will be to the oscillation frequency.

Tangent of the angle of inclination of the

real axis in the other (scaled) coordinates is Y/X = 0.14796/60.9097 = 0.00242917.

The US, Israel and India are the

real axis of evil since the three have imperialist and expansionist designs, are intolerant, ruthless and anti-Islam and believe in exporting terrorism.

Nature 3: if [X.sub.1] = (a,b) and [X.sub.2] = (c,d) are two intervals in the

real axis, [X.sub.2] [subset] [X.sub.1], and no common endpoints, then for any x, has a correlation function:

For obvious reasons the x-axis is called the

real axis and the y-axis is called the imaginary axis.