Search results for "topological [string]"

On a topological interpretation of electronic and vibrational molecular energies

1998

Abstract A relationship between Randic's connectivity index and various quantum mechanical parameters derived from the Huckel Molecular Orbital (HMO) approach is demonstrated. When applied to conjugated hydrocarbons, this index represents the measure of the global π electron molecular energy and, therefore, of the resonance energy. Moreover, the development of the procedure, allows the introduction of a new definition of the bond order which, in turn, makes possible a better prediction not only for bond lengths of naphtalene but also for the resonance integral and conjugation energy for butadiene. Also, a corrected value for the Randic index is deduced, which allows for the reduction of the…

Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions

2017

Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.

Catalyst-free vapour-solid technique for deposition of Bi2Te3 and Bi2Se3 nanowires/nanobelts with topological insulator properties.

2015

We present a simple two-stage vapour–solid synthesis method for the growth of bismuth chalcogenide (Bi2Te3, Bi2Se3) topological insulator nanowires/nanobelts by using Bi2Se3 or Bi2Te3 powders as source materials. During the first stage of the synthesis process nanoplateteles, serving as “catalysts” for further nanowire/nanobelt growth, are formed. At a second stage of the synthesis, the introduction of a N2 flow at 35 Torr pressure in the chamber induces the formation of free standing nanowires/nanobelts. The synthesised nanostructures demonstrate a layered single-crystalline structure and Bi : Se and Bi : Te ratios 40 : 60 at% for both Bi2Se3 and Bi2Te3 nanowires/nanobelts. The presence of…

Modular fluxes, elliptic genera, and weak gravity conjectures in four dimensions

2019

We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory compactifications with N=1 supersymmetry. Extending our previous work on nearly tensionless heterotic strings in six dimensions, we show that under certain assumptions a tower of asymptotically massless states arises in the limit of vanishing coupling of a U(1) gauge symmetry coupled to gravity. This tower contains super-extremal states whose charge-to-mass ratios are larger than those of certain extremal dilatonic Reissner-Nordstrom black holes, precisely as required by the Weak Gravity Conjecture. Unlike in six dimensions, the tower of super-extremal states does not always populate a charge sub-lattice. The main t…

On Słowikowski, Raíkov and De Wilde Closed Graph Theorems

1986

Publisher Summary This chapter focuses on the Slowikowski, Raikov and De Wilde closed graph theorems. The vector spaces used in the chapter, are defined over the field Ղ of real or complex numbers. The term, “space” means separated topological vector space, unless the contrary is specifically stated. If Ω is a non-empty open subset of the n -dimensional euclidean space, then the Schwartz space ҟ′(Ω) endowed with the strong topology belongs to this class. The chapter also studies the classes of spaces related with this conjecture. The class of Slowikowski spaces contains the F-spaces and it is stable with respect to the operations that include: countable topological direct sums, closed subsp…

Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

2016

Three-dimensional topological semimetals come in different variants, either containing Weyl points or Dirac lines. Here we describe a more complicated momentum-space topological defect where several separate Dirac lines connect with each other, forming a momentum-space equivalent of the real-space nexus considered before for helium-3. Close to the nexus the Dirac lines exhibit a transition from type I to type II lines. We consider a general model of stacked honeycomb lattices with the symmetry of Bernal (AB) stacked graphite and show that the structural mirror symmetries in such systems protect the presence of the Dirac lines, and also naturally lead to the formation of the nexus. By the bu…

Generalized fuzzy topology versus non-commutative topology

2011

The paper introduces a modification of the notions of generalized fuzzy topological space of Demirci and quantal space of Mulvey and Pelletier, suitable to explore interrelations between point-set lattice-theoretic topology and non-commutative topology developed in the framework of C^*-algebras or (more recently) of quantales. As a consequence of the new approach, a generalization of the concept of topological system of Vickers arises. Moreover, the currently dominating variable-basis topological setting in the fuzzy community, due to Rodabaugh, appears to be ''fixed-basis''.

On i-topological spaces: generalization of the concept of a topological space via ideals

2006

[EN] The aim of this paper is to generalize the structure of a topological space, preserving its certain topological properties. The main idea is to consider the union and intersection of sets modulo “small” sets which are defined via ideals. Developing the concept of an i-topological space and studying structures with compatible ideals, we are concerned to clarify the necessary and sufficient conditions for a new space to be homeomorphic, in some certain sense, to a topological space.

THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES

2013

Graph Topology Learning and Signal Recovery Via Bayesian Inference

2019

The estimation of a meaningful affinity graph has become a crucial task for representation of data, since the underlying structure is not readily available in many applications. In this paper, a topology inference framework, called Bayesian Topology Learning, is proposed to estimate the underlying graph topology from a given set of noisy measurements of signals. It is assumed that the graph signals are generated from Gaussian Markov Random Field processes. First, using a factor analysis model, the noisy measured data is represented in a latent space and its posterior probability density function is found. Thereafter, by utilizing the minimum mean square error estimator and the Expectation M…