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.