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References in periodicals archive

The quotient space T \ H can be identified with a compact Riemann surface F of a genus g [greater than or equal to] 2.

On Koyama's refinement of the prime geodesic theorem

In order to acquire the algebro-geometric solutions of systems (16), we first introduce the Riemann surface r of the hyperelliptic curve with genus N:

Algebro-Geometric Solutions for a Discrete Integrable Equation

[4]), and they found that the number of minimal reducing subspaces of [T.sub.B] equals the number of connected components of the Riemann surface of B(z) = B(w) when the order of B is 3,4,6.

Restriction of Toeplitz Operators on Their Reducing Subspaces

Consider a compact connected Riemann surface [summation] of genus g with canonical homology cycle bases [a.sub.i], [b.sub.i] for i = 1, ..., g.

Twisted Frobenius Identities from Vertex Operator Superalgebras

Along the lines of other important contributions to the development of topology--and in particular that of Felix Klein--Hermann Weyl has pointed out this feature of Riemann's work, by arguing "that it is always the Riemann surface, not the analytic form, which is regarded as the given object" (2010: 157).

The surface and the abyss/Rethinking topology

Let [GAMMA]\H be a hyperbolic Riemann surface of finite area.

On the Modulus of the Selberg Zeta-Functions in the Critical Strip

In the case of multi-valued analytic functions of a single complex variable, the proposed solution is called "The Riemann Surface'.

Software tools for visualizing multivalued functions

Hence if, conversely, a map A from a simply connected Riemann surface [summation] into ([h.sup.2n+1]) satisfying (3.5) is given, then a solution to [[phi].sup.-1]ld[phi] = Bdz + [bar.B]d[bar.z] exists and defines a harmonic map from [summation] into [H.sup.2n+1].

Weierstrass representation formula in Heisenberg group [H.sup.2n+1]

Another interesting instance is that of a Riemann surface endowed with the Poincare metric.

Stability of Gromov hyperbolicity

The function g[lambda] has branch points at [z.sup.+.sub.[lambda]] and [z.sup.-.sub.[lambda]] and its natural domain of definition is the two-sheeted Riemann surface [R.sub.[lambda]] defined by the relation

From Taylor to quadratic Hermite-Pade polynomials

For any Riemann surface S of genus g [less than or equal to] 2,

On automorphism groups of maps, surfaces and Smarandache geometries (1)

This distinction is necessary because [u.sup.(p).sub.s] and [[partial]u.sup.(s).sub.s]/[partial]z are discontinuous on crossing the screen, and is taken into account in Sommerfeld's theory by "wrapping" the diffracting half plane in a semi-infinite, two-sided Riemann surface so that its positive and negative sides are distinguished by the values 2[pi] and 0 of the polar angle [PHI] in Fig.

Optical diffraction in close proximity to plane apertures, part 2, comparison of half-plane diffraction theories