simply connected space

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simply connected space

[′sim·plē kə¦nek·təd ′spās]
(mathematics)
A topological space whose fundamental group consists of only one element; equivalently, all closed curves can be shrunk to a point.
References in periodicals archive ?
For the doubly and multiply connected domains with genus greater than one, as illustrated in Figures 1(c) and 1(d), one may locate many source points in the domain.
The method can be applied to arbitrary simply and multiply connected domains with smooth boundaries.
Let [OMEGA] be the simply or multiply connected cross section of an orthotropic and linearly elastic Saint-Venant composite beam under torsion.
In a forthcoming work, this method is considered for computing conformal mapping of multiply connected domains.
We study conformal maps from multiply connected domains in the extended complex plane onto lemniscatic domains.
The contributors construct a linear Pfaff equation of Fuchs type with three singular surfaces, solve the scalar Riemann-Hilbert problem for circular multiply connected domains, and describe the behavior of solutions to the Cauchy problem for hyperbolic regularizations of conservation laws.
The Dirichlet problems for higher-order linear differential equations in multiply connected domains have not been solved yet.
In three chapters the authors first cover generalizations of the Herglotz representation theorem, von Neumann's inequality and the Sz.-Nagy dilation theorem to multiply connected domains.
Features include meshing of multiply connected regions with multiple levels of nested internal boundaries, external boundaries representing arbitrary combinations of line segments and arcs, internal points, and internal entities.
These weird shapes can be understood in terms of three-dimensional polyhedrons whose faces are glued together to create finite, multiply connected spaces.
For bounded or unbounded multiply connected domains of connectivity m+1, discretizing the boundary integral equations (2.3) and (2.5) by the Nystrom method with the trapezoidal rule yields dense and nonsymmetric (m + 1)n x (m + 1)n linear systems, where n is the number of nodes in the discretization of each boundary component.
Papers on two-dimensional algorithms address such topics as elliptic barrier-type grid generators for problems with moving boundaries, a class of quasi-isometric grids, triangle distortions under quasi-isometries, grid optimization and adaptation, moving mesh calculations in unsteady two-dimensional problems, generation of curvilinear grids in multiply connected domains of complex topology.