real axis


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real axis

[′rēl ′ak·səs]
(mathematics)
The horizontal axis of the Cartesian coordinate system for the euclidean or complex plane.
References in periodicals archive ?
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.