scholarly journals A note on stable complex structures on real vector bundles over manifolds

2015 ◽  
Vol 189 ◽  
pp. 1-9 ◽  
Author(s):  
Huijun Yang
Keyword(s):  
Vector Bundles ◽  
Stable Complex ◽  
Complex Structures ◽  
Real Vector

STRING EQUATIONS OF MOTION FROM VANISHING CURVATURE

1991 ◽  
Vol 06 (08) ◽  
pp. 1319-1333 ◽  
Author(s):  
MARK J. BOWICK ◽  
KONG-QING YANG
Keyword(s):  
Vector Bundles ◽  
Adiabatic Approximation ◽  
Equations Of Motion ◽  
Bosonic String ◽  
Complex Structures ◽  
Closed Bosonic String

The equations of motion for the massless modes of the closed bosonic string are obtained in the adiabatic approximation from the requirement of the vanishing of the curvature of appropriate vector bundles over the space of complex structures Diff S1/S1. This vanishing is required for physical states to be independent of string parametrization.

On complex structures in 8-dimensional vector bundles

1998 ◽  
Vol 95 (1) ◽  
pp. 323-330 ◽  
Author(s):  
Martin Čadek ◽  
Jiří Vanžura
Keyword(s):  
Vector Bundles ◽  
Complex Structures ◽  
Dimensional Vector

scholarly journals On the emergence of structural complexity in RNA replicators

2017 ◽  
Author(s):  
Carlos G. Oliver ◽  
Vladimir Reinharz ◽  
Jérôme Waldispühl
Keyword(s):  
Large Scale ◽  
Computational Study ◽  
Rna World ◽  
Gc Content ◽  
Structural Complexity ◽  
Molecular Structures ◽  
Stable Complex ◽  
Complex Structures ◽  
Branched Structures ◽  
Stable Structures

AbstractThe RNA world hypothesis relies on the ability of ribonucleic acids to spontaneously acquire complex structures capable of supporting essential biological functions. Multiple sophisticated evolutionary models have been proposed for their emergence, but they often assume specific conditions. In this work we explore a simple and parsimonious scenario describing the emergence of complex molecular structures at the early stages of life. We show that at specific GC-content regimes, an undirected replication model is sufficient to explain the apparition of multi-branched RNA secondary structures – a structural signature of many essential ribozymes. We ran a large scale computational study to map energetically stable structures on complete mutational networks of 50-nucleotide-long RNA sequences. Our results reveal that the sequence landscape with stable structures is enriched with multi-branched structures at a length scale coinciding with the appearance of complex structures in RNA databases. A random replication mechanism preserving a 50% GC-content may suffice to explain a natural enrichment of stable complex structures in populations of functional RNAs. By contrast, an evolutionary mechanism eliciting the most stable folds at each generation appears to help reaching multi-branched structures at highest GC content.

Sums of stably trivial vector bundles

1980 ◽  
Vol 87 (1) ◽  
pp. 97-107 ◽  
Author(s):  
Jacques Allard
Keyword(s):  
Vector Bundle ◽  
Line Bundle ◽  
Vector Bundles ◽  
Real Vector

We say that a real vector bundle ξ over a finite C.W. complex X is stably trivial of type (n, k) or, simply, of type (n, k) if ξ ⊕ kε ≅ nε, where ε denotes a trivial line bundle. The following theorem is an immediate corollary (see (12)) of a theorem of T. Y. Lam ((9), theorem 2).

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