Narrow Results

We provide a classification and an explicit realization of all simple Gelfand–Tsetlin modules of the complex Lie algebra $𝔰𝔩(3)$. The realization of these modules, including those with infinite-dimensional weight spaces, is given via regular and derivative Gelfand–Tsetlin tableaux. Also, we show that all simple Gelfand–Tsetlin $𝔰𝔩(3)$-modules can be obtained as subquotients of localized Gelfand–Tsetlin $E_{21}$-injective modules.

Brillouin spectroscopy is a powerful tool for measuring the mechanical properties of materials without contact. The sensitivity to mechanical changes that a Brillouin spectrometer can detect is determined by the precision to which a spectral peak can be localized. The localization precision is however fundamentally limited by the low number of photons within a Brillouin measurement, as well as by intrinsic noise of the setup. Here, we present a method to improve the spectral sensitivity of Brillouin measurements by exploiting the autocorrelation function of the spectrum. We show that by performing a localization process on the autocorrelation function nearly 20% increase in localization precision can be obtained. This result is consistent between our theoretical treatment, numerical simulation and experimental results. We further study the effect of background noise on the precision improvement for realistic scenarios.

The aim here is to show an example for localization and relevant low-dimensional superfluids in nuclear system. Due to a particular property of tensor force originating from the One-Pion-Exchange (OPE) between two nucleons, dense nuclear medium undergoes a layer confinement of the nucleons on one hand and also pion condensation (PC) for pion field mediating two-nucleon interaction on the other hand. The localization is characterized by a layered structure with a specific spin-isospin ordering. In that situation, the pairing problem has a two-dimensional (2D) character, i.e., low-dimensional superfluid realized in the hadronic matter with strong interactions. The pairing description suitable to the 2D nature is presented and possible realization of superfluidity in neutron stars is discussed, togeter with its effect on the cooling scenarios.

It is well known that the metal-insulator transition in two dimensions for non-interacting fermions takes place at infinitesimal disorder. In contrast, the superconductor-to-insulator transition takes place at a finite critical disorder (on the order of V_c ~ 2t), where V is the typical width of the distribution of random site energies and t is the hopping scale. In this article we compare the localization/delocalization properties of one and two particles. Whereas the metal-insulator transition is a consequence of single-particle Anderson localization, the superconductor-insulator transition (SIT) is due to pair localization – or, alternatively, fluctuations of the phase conjugate to pair density. The central question we address is how superconductivity emerges from localized single-particle states. We address this question using inhomogeneous mean field theory and quantum Monte Carlo techniques and make several testable predictions for local spectroscopic probes across the SIT. We show that with increasing disorder, the system forms superconducting blobs on the scale of the coherence length embedded in an insulating matrix. In the superconducting state, the phases on the different blobs are coherent across the system whereas in the insulator long-range phase coherence is disrupted by quantum fluctuations. As a consequence of this emergent granularity, we show that the single-particle energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT despite a robust single-particle gap.

We study reduced matrix models obtained by the dimensional reduction of quiver Chern-Simons theories on S³ and show that, around a certain multiple fuzzy sphere background, the reduced models are equivalent to the original theories in the large-N limit. This is regarded as a large-N reduction on S³. By using the localization technique, we prove the large-N equivalence with respect to supersymmetric observables.

We study the 1/2 BPS condition of Wilson loop on squashed three-sphere, and find that the solution becomes torus knot or unknot. We also calculate the expectation value of 1/2 BPS Wilson loops by using localization technique with the gauge group U(2) and Wilson loop as fundamental representation. And it completely matches with known results.

To date, there are little reliable data on the position, velocity and acceleration characteristics of Unidentified Aerial Phenomena (UAP). The dual hardware and software system described in this document provides a means to address this gap. We describe a weatherized multi-camera system which can capture images in the visible, infrared and near infrared wavelengths. We then describe the software we will use to calibrate the cameras and to robustly localize objects-of-interest in three dimensions. We show how object localizations captured over time will be used to compute the velocity and acceleration of airborne objects.

China–Africa cooperation in recent years has been marked by two distinct trends, localization and internationalization, which have allowed a variety of actors and stakeholders to be part of Africa’s development story. But even as African development takes on more nongovernmental and multilateral characteristics, inadequate social participation and lack of coordination between major donor countries still pose significant challenges that must be addressed before localization and internationalization can help further boost aid effectiveness on the continent. The Forum on China–Africa Cooperation (FOCAC) as the premium platform for China–Africa cooperation holds great promise for advancing Africa’s economic, social, and human development, on the one hand, and forging closer multilateral coordination, on the other. In addition, a more complex geopolitical landscape has also underscored the forum’s strategic and practical value for top Chinese policymakers and their African counterparts, as both seek more predictable and productive relations to meet an increasing number of common challenges and are making new efforts to build a more open and inclusive FOCAC in order to advance the Belt and Road Initiative (BRI) and fulfill Beijing’s commitment to multilateralism and international cooperation.

In this paper, we introduce Dirac equation, the hole theory of positive and negative matter, and Anderson localization theory briefly. We analyze physical conditions of localization: $L_{\phi }>L>\xi >\ell$ inequality relation. On this basis, we try to put forward the physical mode of production of free positron and electron. In this model, when $\gamma$ rays travel through a vacuum, due to the action in which quantum superfluid rushes to the heat source ($\gamma$ ray), the quantum superfluid polymerization, local disorder, two-model quantum superfluid shunt, quantum superfluid in a vacuum is localized by the electro-vector and magnetic-vector in the electromagnetic field of the $\gamma$ ray to form electrons and positrons; in essence, the electro-vector and magnetic-vector are components of $\gamma$ quantum in the electromagnetic field ($\gamma$ ray); and the spin of the $\gamma$ ray is composed of two components. After localization, positive and negative polarities whose phases are opposite are formed. The positron and electron charges produced in this model have the same quantum numbers such as the mass, spin and average lifetime, and the additive quantum numbers such as charge, baryon number, lepton number, and singularity number should be equal but opposite, the magnetic moment direction of the positive and negative particles are opposite when their spin directions are the same. We can take experimental verification of this model. Once verified, the localization theory also seems to open a door for us to study the structure of sub-quarks and lepton, and also provides a theoretical basis for harnessing the enormous energy generated by the annihilation of positive and negative matter.

A growing literature employs distance-based measures of localization to assess the spatial distribution of firms with a focus on manufacturing across a country. We analyse the spatial concentration of a variety of consumer services firms in the Phoenix, AZ area using geo-referenced Yelp data from over 29,000 establishments. Results from a K-density approach indicate substantial localization and service differentiation among localised firms. Firm concentration varies across service cost and quality; higher quality/cost establishments tend to cluster. Our results further understanding of the modern urban landscape as cities are increasingly centres of consumption.

We study an index for three-dimensional supersymmetric gauge theories placed on a sphere and immersed in external magnetic fields — in fact topologically twisted. We find an exact non-perturbative formula for this index, applying supersymmetric localization techniques. The index, different from the more common superconformal index, counts Landau-level ground states of the theories in magnetic field. It has physical applications: to the study of non-perturbative dualities, of moduli spaces, of Chern-Simons theory and Verlinde algebras, of wrapped branes in string theory and the quantum entropy of black holes; as well as mathematical applications: to quantum cohomology and its K-theoretic generalization.