Four-class Skew-symmetric Association Schemes

An association scheme is called skew-symmetric if it has no symmetric adjacency relations other than the diagonal one. In this paper, we study 4-class skew-symmetric association schemes. In J. Ma [On the nonexistence of skew-symmetric amorphous association schemes, submitted for publication], we discovered that their character tables fall into three types. We now determine their intersection matrices. We then determine the character tables and intersection numbers for 4-class skew-symmetric pseudocyclic association schemes, the only known examples of which are cyclotomic schemes. As a result, we answer a question raised by S. Y. Song [Commutative association schemes whose symmetrizations have two classes, J. Algebraic Combin. 5(1) 47-55, 1996]. We characterize and classify 4-class imprimitive skew-symmetric association schemes. We also prove that no 2-class Johnson scheme can admit a 4-class skew-symmetric fission scheme. Based on three types of character tables above, a short list of feasible parameters is generated.Comment: 12 page

Numerical analysis of flow structures and bed entrainment in turbulent open-channel flow

PhDThe results from a Direct Numerical Simulation (DNS) and a Large Eddy Simulation (LES) are employed to study the large-scale coherent structures and bed entrainment in the turbulent open-channel flow. The gravel bed is represented by a hexagonal arrangement of uniform spheres. The large-scale coherent structures are composed of a group of quasistreamwise vortices and asymmetric hairpin vortices. The meandering structures are shown to be longer than the length of the computational box, more than 20 times the effective flow depth in this study, and the width tends to be one order of magnitude smaller than the length. The signature of the large-scale motion is elongated local maximum of streamwise velocity. It is also found that these structures contribute substantially to both of the Reynolds Stress (RS) and the Turbulent Kinetic Energy (TKE). The entrainment of bed gravels is investigated by the three-dimensional analysis of the relationship between near-wall coherent structures and the force moments exerted on the particles. It is found that the spanwise drag moment (MD2) is of the same order of magnitude compared with the streamwise drag moment (MD1). The majority of MD2 originates from pressure whilst the viscous force plays as an important role as pressure for MD1. The contributions of the forces at different heights of the particle to MD1 and MD2 are explored. The quasi-streamwise vortices are strongly associated with MD2 and the ejections are shown to be more favorable for bed entrainment than the sweeps in this bed condition

Fissioned triangular schemes via sharply 3-transitive groups

AbstractIn [D. de Caen, E.R. van Dam, Fissioned triangular schemes via the cross-ratio, European J. Combin. 22 (2001) 297–301], de Caen and van Dam constructed a fission scheme FT(q+1) of the triangular scheme on PG(1,q). This fission scheme comes from the naturally induced action of PGL(2,q) on the 2-element subsets of PG(1,q). The group PGL(2,q) is one of two infinite families of finite sharply 3-transitive groups. The other such family M(q) is a “twisted” version of PGL(2,q), where q is an even power of an odd prime. The group PSL(2,q) is the intersection of PGL(2,q) and Mq(q). In this paper, we investigate the association schemes coming from the actions of PSL(2,q), Mq(q) and PML(2,q), respectively. Through the conic model introduced in [H.D.L. Hollmann, Q. Xiang, Association schemes from the actions of PGL(2,q) fixing a nonsingular conic, J. Algebraic Combin. 24 (2006) 157–193], we introduce an embedding of PML(2,q) into PML(3,q). For each of the three groups mentioned above, this embedding produces two more isomorphic association schemes: one on hyperbolic lines and the other on hyperbolic points (via an orthogonal parity) in a 3-dimensional orthogonal geometry. This embedding enables us to treat these three isomorphic association schemes simultaneously

Suborbits of a point stabilizer in the orthogonal group on the last subconstituent of orthogonal dual polar graphs

AbstractAs one of the serial papers on suborbits of point stabilizers in classical groups on the last subconstituent of dual polar graphs, the corresponding problem for orthogonal dual polar graphs over a finite field of odd characteristic is discussed in this paper. We determine all the suborbits of a point-stabilizer in the orthogonal group on the last subconstituent, and calculate the length of each suborbit. Moreover, we discuss the quasi-strongly regular graphs and the association schemes based on the last subconstituent, respectively

Layer-structured niobium oxides and their analogues for advanced hybrid capacitors

© 2019 Elsevier B.V. Niobium-based oxides including niobium oxide (Nb2O5) and their analogues with quasi-2D network of open and stable Wadsley-Roth shear crystal structure, have gained great interest for advanced hybrid supercapacitors due to their outstanding rate capability derived from the intercalation pseudocapacitive kinetics. To realize their full potential as battery-type anode electrodes for supercapacitor, various strategies have been effectively implemented to overcome the drawbacks especially the poor intrinsic electrical conductivity, including structure design, surface modification, conductivity enhancement, and electrode engineering. Here, we provide a comprehensive overview of the latest progress of Nb-based oxides for high-rate hybrid supercapacitors in the aspects of structure-performance relationship, performance-optimizing strategies, and energy storage mechanisms. We will also present our insights into the challenges and perspectives for future development and industrial applications

Porous amorphous Ge/C composites with excellent electrochemical properties

Porous amorphous germanium/carbon (Ge/C) composites, which were synthesized through the reduction/carbonization of germanium oxide/oleic acid precursors, could exhibit a high-capacity, high-rate and long-life performance due to the synergistic effect of the porous structure and carbon

Co-Loan Network of Chinese Banking System Based on Listed Companies’ Loan Data

Based on the loan data of Chinese listed companies from 2008 to 2016, this paper constructs a co-loan network of the Chinese banking system and analyzes the topological structures and corresponding evolvement characteristics from the perspective of complex network. Through the empirical studies, we find that the co-loan network always displays a core-periphery structure; for example, ten banks including four state banks and six large commercial banks are always in the core region of the Chinese banking system for nine consecutive years. Furthermore, the co-loan network is a small-world network lasting for nine years