In this study, the suspension of MoO3 nanobelts was first prepared in a hydrothermal way from Mo powders and H2O2 solution, which could be transformed into the suspension of H
x
MoO3 nanobelts under an acidic condition using N2H4·H2O as the reducing agent. Three paper-form samples made from MoO3 and H
x
MoO3 nanobelts (low or high hydrogen content) were then fabricated via a vacuum filtration method, followed by their structural comparative analysis such as FESEM, XRD, Raman spectra, and XPS, etc. The measurement of electric resistances at room temperature shows that the conductance of H
x
MoO3 nanobelts is greatly improved because of hydrogen doping. The temperature-dependent resistances of H
x
MoO3 nanobelts agree with the exponential correlation, supporting that the conducting carriers are the quasi-free electrons released from Mo5+. In addition, the formation process of H
x
MoO3 nanobelts from MoO3 nanobelts is also discussed.
Abstract. A 0-Hecke algebra is a deformation of the group algebra of a Coxeter group. Based on work of Norton and Krob-Thibon, we introduce a tableau approach to the representation theory of 0-Hecke algebras of type A, which resembles the classic approach to the representation theory of symmetric groups by Young tableaux and tabloids. We extend this approach to type B and D, and obtain a correspondence between the representation theory of 0-Hecke algebras of type B and D and quasisymmetric functions and noncommutative symmetric functions of type B and D. Other applications are also provided.
The Catalan number Cn enumerates parenthesizations of x0 * · · · * xn where * is a binary operation. We introduce the modular Catalan number C k,n to count equivalence classes of parenthesizations of x0 * · · · * xn when * satisfies a k-associative law generalizing the usual associativity. This leads to a study of restricted families of Catalan objects enumerated by C k,n with emphasis on binary trees, plane trees, and Dyck paths, each avoiding certain patterns. We give closed formulas for C k,n with two different proofs. For each n ≥ 0 we compute the largest size of k-associative equivalence classes and show that the number of classes with this size is a Catalan number.
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