This implies that [f.sub.N](z) is analytic in any region of the

complex plane that has no partition function zeros.

Some modes have cut on frequencies the same as in case of being surrounded by vacuum instead, and the wavenumbers demonstrate symmetry with respect to the axes of the

complex plane.

Let us consider

complex plane articulation linkage of the fourth class (Figure), that consists of driving link 1, which is connected to a stand-pipe 0 and other driven links 2...5, among which links 2...4 are connecting rods, 5--rocker arm.

For any 0 < r [less than or equal to] 1, consider the punctured

complex plane at z = 1 with the interval [1, [infinity]) removed:

A (complete) hyperbolic surface ([summation], G) is called elementary if it is conformally equivalent with a simply connected or doubly connected regular domain (a regular domain D [subset] C is called doubly connected if its complement in the Riemann sphere has two connected components, which happens iff [[pi].sub.1](D) [equivalent] Z) contained in the

complex plane. This amounts to the condition that the uniformizing surface group [GAMMA] of ([summation], G) is the trivial group or a cyclic subgroup of PSL(2, R) of parabolic or hyperbolic type.

Hence, we can choose a sequence of points [{[[lambda].sub.n]}.sup.[infinity].sub.n=1] in the

complex plane as follows:

The main result of this paper is the classified C*-algebra generated by the Toeplitz operators with bounded vertical symbols with limits at -[infinity] and [infinity] acting over poly-Fock space in the

complex plane.

Let a and b be two distinct finite values and f be a meromorphic function in the

complex plane with finitely many poles.

Similarly complex numbers can be represented as points: not only on the real number line but anywhere on a plane (the

complex plane).

Let a and b be two distinct finite values, and let f be a meromorphic function in the

complex plane such that f has finitely many poles in the

complex plane.

In the second approach, the analysis is based on the root locus of its corresponding characteristic equation in the

complex plane. Unlike the temporal approach, the frequency approach can provide necessary and sufficient conditions that are not conservative.