Equalities and Inequalities for Norms of Block Imaginary Circulant Operator Matrices

Circulant, block circulant-type matrices and operator norms have become effective tools in solving networked systems. In this paper, the block imaginary circulant operator matrices are discussed. By utilizing the special structure of such matrices, several norm equalities and inequalities are presented. The norm τ in consideration is the weakly unitarily invariant norm, which satisfies τA=τ(UAV). The usual operator norm and Schatten p-norm are included. Furthermore, some special cases and examples are given

A Service Restoration Method for Active Distribution Network

AbstractFor a large scale of distributed generations being connected to the power distribution network, the traditional service restoration methods cannot meet the demand of the distributed generation's large access which facing significant challenges. Service restoration of active distribution network (ADN) is a multi-objective, multiple-constraint, and complex optimization problem. Considering the user priority level, the load amounts restored, the counts of switch operation, the network loss after the power restoration, and the operation of power sources, this article establishes a restoration model based on grid actual situation, which is more realistic for the ADN. As a different dimension of different objective, this article proposes the generalized model in order to compare those solutions conveniently, the paper uses genetic algorithm to get recovery scheme. Results of case study show that the proposed model is effective

VLBA 24 and 43 GHz observations of massive binary black hole candidate PKS 1155+251

PKS 1155+251 is a radio-loud quasar source at z=0.203. Observations using very long baseline interferometry (VLBI) at ~2, 5, 8 and 15 GHz show that the structure of the radio source is quite complicated on parsec scales and that the outer hot spots are apparently undergoing a significant contraction. Because these results cannot be fully explained based on the compact symmetric object (CSO) scenario with a radio core located between the northern and southern complexes, we made observations with the Very Long Baseline Array (VLBA) at 24 and 43 GHz to search for compact substructures and alternative interpretations. The results show that the radio core revealed in the previous VLBI observations remains compact with a flat spectrum in our sub-milli-arcsecond--resolution images; the northern lobe emission becomes faint at 24 GHz and is mostly resolving out at 43 GHz; the southern complex is more bright but has been resolved into the brightest southern-end (S1) and jet or tail alike components westwards. Explaining the southern components aligned westward with a standard CSO scenario alone remains a challenge. As for the flatter spectral index of the southern-end component S1 between 24 and 43 GHz in our observations and the significant 15 GHz VLBA flux variability of S1, an alternative scenario is that the southern complex may be powered by a secondary black hole residing at S1. But more sensitive and high-resolution VLBI monitoring is required to discriminate the CSO and the binary black hole scenarios.Comment: 7 pages, 3 figures, accepted by MNRA

Imaging and variability studies of CTA~102 during the 2016 January γ\gamma-ray flare

The $\gamma$-ray bright blazar CTA 102 is studied using imaging (new 15 GHz and archival 43 GHz Very Long Baseline Array, VLBA data) and time variable optical flux density, polarization degree and electric vector position angle (EVPA) spanning between 2015 June 1 and 2016 October 1, covering a prominent $\gamma$-ray flare during 2016 January. The pc-scale jet indicates expansion with oscillatory features upto 17 mas. Component proper motions are in the range 0.04 - 0.33 mas/yr with acceleration upto 1.2 mas followed by a slowing down beyond 1.5 mas. A jet bulk Lorentz factor $\geq$ 17.5, position angle of 128.3 degrees, inclination angle $\leq$ 6.6 degrees and intrinsic half opening angle $\leq$ 1.8 degrees are derived from the VLBA data. These inferences are employed in a helical jet model to infer long term variability in flux density, polarization degree, EVPA and a rotation of the Stokes Q and U parameters. A core distance of $r_{\rm core,43 \ GHz}$ = 22.9 pc, and a magnetic field strength at 1 pc and the core location of 1.57 G and 0.07 G respectively are inferred using the core shift method. The study is useful in the context of estimating jet parameters and in offering clues to distinguish mechanisms responsible for variability over different timescales.Comment: 20 pages, 7 figures, 3 tables; accepted for publication in Ap

Algorithms for Finding Inverse of Two Patterned Matrices over Z

Circulant matrix families have become an important tool in network engineering. In this paper, two new patterned matrices over Zp which include row skew first-plus-last right circulant matrix and row first-plus-last left circulant matrix are presented. Their basic properties are discussed. Based on Newton-Hensel lifting and Chinese remaindering, two different algorithms are obtained. Moreover, the cost in terms of bit operations for each algorithm is given

Learning to Compose and Reason with Language Tree Structures for Visual Grounding

Grounding natural language in images, such as localizing "the black dog on the left of the tree", is one of the core problems in artificial intelligence, as it needs to comprehend the fine-grained and compositional language space. However, existing solutions rely on the association between the holistic language features and visual features, while neglect the nature of compositional reasoning implied in the language. In this paper, we propose a natural language grounding model that can automatically compose a binary tree structure for parsing the language and then perform visual reasoning along the tree in a bottom-up fashion. We call our model RVG-TREE: Recursive Grounding Tree, which is inspired by the intuition that any language expression can be recursively decomposed into two constituent parts, and the grounding confidence score can be recursively accumulated by calculating their grounding scores returned by sub-trees. RVG-TREE can be trained end-to-end by using the Straight-Through Gumbel-Softmax estimator that allows the gradients from the continuous score functions passing through the discrete tree construction. Experiments on several benchmarks show that our model achieves the state-of-the-art performance with more explainable reasoning.Comment: Accepted to IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI

Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers

Circulant matrix family is used for modeling many problems arising in solving various differential equations. The RSFPLR circulant matrices and RSLPFL circulant matrices are two special circulant matrices. The techniques used herein are based on the inverse factorization of polynomial. The exact determinants of these matrices involving Perrin, Padovan, Tribonacci, and the generalized Lucas number are given, respectively

Application of Biomass-Based Nanomaterials in Energy

The utilization of biomass as a sustainable and renewable resource for nanomaterial synthesis has received considerable attention in recent years. Through the efficient utilization of biomass waste, opportunities for energy production, energy conversion, and the fabrication of nanomaterials can be maximized. The combination of biomass-based nanomaterials with additional nanomaterials makes the composite system have more remarkable performance, which further facilitates the transformation procedure of biomass-based nanomaterials for applications. This comprehensive review provides an overview of the preparation and applications of biomass-based nanomaterials. The preparation section covers a range of methods for synthesizing biomass-based nanomaterials, including biomass-based carbonaceous nanomaterials, biomass-based carbon nitride nanomaterials, nanomaterials derived from biomass templates, biomass-based nanomaterials as carriers, and the use of biomass for metal ion reduction. The applications section explores the diverse applications of biomass-based nanomaterials, such as hydrogen production, carbon dioxide reduction, batteries, and supercapacitors. The unique properties and advantages of biomass-based nanomaterials in each application are discussed. The conclusion summarizes the current progress and presents future perspectives for the development and utilization of biomass-based nanomaterials. This review emphasizes the potential of biomass as a valuable and sustainable source for nanomaterial synthesis, opening up promising opportunities in various fields