scholarly journals No topological condition implies equality of polynomial and rational hulls

2019 ◽  
Vol 147 (12) ◽  
pp. 5195-5207
Author(s):  
Alexander J. Izzo
Keyword(s):  
Topological Condition

Existence of Solutions to Poisson's Equation

2008 ◽  
Vol 51 (2) ◽  
pp. 229-235
Author(s):  
Mary Hanley
Keyword(s):  
Boundary Conditions ◽  
Poisson Equation ◽  
Existence Of Solutions ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
The Poisson Equation ◽  
Topological Condition ◽  
Necessary And Sufficient

AbstractLet Ω be a domain in ℝn (n ≥ 2). We find a necessary and sufficient topological condition on Ω such that, for anymeasure μ on ℝn, there is a function u with specified boundary conditions that satisfies the Poisson equation Δu = μ on Δ in the sense of distributions.

scholarly journals On Sliced Spaces: Global Hyperbolicity Revisited

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 304 ◽  
Author(s):  
Kyriakos Papadopoulos ◽  
Nazli Kurt ◽  
Basil Papadopoulos
Keyword(s):  
Shift Function ◽  
Global Hyperbolicity ◽  
Globally Hyperbolic ◽  
Topological Condition ◽  
Lapse Function

We give a topological condition for a generic sliced space to be globally hyperbolic without any hypothesis on lapse function, shift function, and spatial metric.

scholarly journals Pin(d, d) covariance of pure spinor equations for supersymmetric vacua and non-Abelian T-duality

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Aybike Çatal-Özer ◽  
Emine Diriöz
Keyword(s):  
Differential Equations ◽  
Tangent Bundle ◽  
Isometry Group ◽  
Structure Group ◽  
Type Ii ◽  
Pure Spinor ◽  
Four Dimensions ◽  
First Order ◽  
Topological Condition ◽  
First Order Differential Equations

Abstract In a supersymmetric compactification of Type II supergravity, preservation of $$ \mathcal{N} $$ N = 1 supersymmetry in four dimensions requires that the structure group of the generalized tangent bundle TM ⨁ T∗M of the six dimensional internal manifold M is reduced from SO(6) to SU(3) × SU(3). This topological condition on the internal manifold implies existence of two globally defined compatible pure spinors Φ1 and Φ2 of non-vanishing norm. Furthermore, these pure spinors should satisfy certain first order differential equations. In this paper, we show that non-Abelian T-duality (NATD) is a solution generating transformation for these pure spinor equations. We first show that the pure spinor equations are covariant under Pin(d, d) transformations. Then, we use the fact NATD is generated by a coordinate dependent Pin(d, d) transformation. The key point is that the flux produced by this transformation is the same as the geometric flux associated with the isometry group, with respect to which one implements NATD. We demonstrate our method by studying NATD of certain solutions of Type IIB supergravity with SU(2) isometry and SU(3) structure.

scholarly journals On Sliced Spaces: Global Hyperbolicity Revisited

2019 ◽  
Author(s):  
Kyriakos Papadopoulos ◽  
Nazli Kurt ◽  
Basil K. Papadopoulos
Keyword(s):  
Shift Function ◽  
Global Hyperbolicity ◽  
Globally Hyperbolic ◽  
Topological Condition ◽  
Lapse Function

We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.

scholarly journals Parametric jet interpolation for Stein manifolds with the density property

2019 ◽  
Vol 30 (08) ◽  
pp. 1950046
Author(s):  
Alexandre Ramos-Peon ◽  
Riccardo Ugolini
Keyword(s):  
Finite Number ◽  
Stein Manifold ◽  
Density Property ◽  
Stein Manifolds ◽  
Topological Condition ◽  
Holomorphic Flexibility

Given a Stein manifold with the density property, we show that under a suitable topological condition it is possible to prescribe derivatives at a finite number of points to automorphisms depending holomorphically on a Stein parameter. This is an Oka property of the manifold and is related to its holomorphic flexibility.

Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions

1980 ◽  
Vol 32 (3) ◽  
pp. 657-685 ◽  
Author(s):  
F. Dashiell ◽  
A. Hager ◽  
M. Henriksen
Keyword(s):  
Continuous Functions ◽  
Topological Properties ◽  
Order Convergence ◽  
Sequential Order ◽  
Compact Spaces ◽  
Lattice Group ◽  
Vector Lattices ◽  
Topological Condition ◽  
Bounded Continuous Functions ◽  
Tychonoff Spaces

This paper studies sequential order convergence and the associated completion in vector lattices of continuous functions. Such a completion for lattices C(X) is related to certain topological properties of the space X and to ring properties of C(X). The appropriate topological condition on the space X equivalent to this type of completeness for the lattice C(X) was first identified, for compact spaces X, in [6]. This condition is that every dense cozero set S in X should be C*-embedded in X (that is, all bounded continuous functions on S extend to X). We call Tychonoff spaces X with this property quasi-F spaces (since they generalize the F-spaces of [12]).In Section 1, the notion of a completion with respect to sequential order convergence is first described in the setting of a commutative lattice group G.

ALMOST KÄHLER 4-MANIFOLDS, L2-SCALAR CURVATURE FUNCTIONAL AND SEIBERG–WITTEN EQUATIONS

2004 ◽  
Vol 15 (06) ◽  
pp. 573-580 ◽  
Author(s):  
MITSUHIRO ITOH
Keyword(s):  
Scalar Curvature ◽  
Topological Condition ◽  
Witten Theory ◽  
Almost Kähler ◽  
Scalar Curvature Functional

We show in this paper by applying the Seiberg–Witten theory developed by Taubes and LeBrun that a compact almost Kähler–Einstein 4-manifold of negative scalar curvature s is Kähler–Einstein if and only if the L2-norm satisfies ∫Ms2dv=32π2(2χ+3τ)(M). The Einstein condition can be weakened by the topological condition (2χ+3τ)(M)>0.

Thin sequences in the corona of H ∞

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Dimcho Stankov ◽  
Tzonio Tzonev
Keyword(s):  
Shilov Boundary ◽  
Interpolating Sequence ◽  
Topological Condition ◽  
Discrete Sequences

AbstractIn this paper we consider several conditions for sequences of points in M(H ∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $$M(H^\infty )\backslash \mathbb{D}$$ of H ∞ is a thin sequence for H ∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ∞ necessarily satisfy the same condition.

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