Law of the iterated logarithm for random graphs

A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles.     

On subgame perfect equilibria in quantum Stackelberg duopoly with incomplete information

The Li–Du–Massar quantum duopoly model is one of the generally accepted quantum game schemes. It has applications in a wide range of duopoly problems. Our purpose is to study Stackelberg's duopoly with incomplete information in the quantum domain. The result of Lo and Kiang has shown that the correlation of players' quantities caused by the quantum entanglement enhances the first-mover advantage in the game. Our work demonstrates that there is no first-mover advantage if the players' actions are maximally correlated. Furthermore, we proved that the second mover gains a higher equilibrium payoff than the first one.     

4类图完美匹配数目的递推求法

本文研究了4类特殊图完美匹配数目的显式表达式.利用划分,求和,再递推的方法分别给出了图3-n Z4,2-n(2-C6),2-n(2-K4)和3-n(C4-C6)的完美匹配数目的计算公式.     

Ultraviolet light absorber with low surface energy: synthesis and characterization

Novel fluorine-containing ultraviolet absorbers (FBPs) with low surface energy were successfully synthesized based on 2,4-dihydroxy benzophenone (BP-1), and their structures were characterized by ¹H NMR, ¹³C NMR, FTIR, and HRMS. UV absorption of FBPs was studied in 10⁻⁴ M dichloromethane (CH₂Cl₂), which demonstrated the superior UV absorption capability of FBPs (ca. ?=1.7×10⁴ to 2.2×10⁴ at λ_max) over the matrix (?=1.7×10⁴ at λ_max). Quantum chemistry calculation was performed to investigate the stable structure and UV electronic absorption bands of FBPs. The surface chemistry information of high-chlorinated polyethylene (HCPE) coating films embedded with ultraviolet absorbers (UVAs) was given by X-ray photoelectron spectroscopy (XPS) and contact angle measurement. The results show that the surface enrichment capability of FBPs is remarkably better than traditional UVAs (including BP-1, BP-3, BP-12) because of the low surface energy properties of FBPs.     

Perfect 1‐Factorizations of a Family of Cayley Graphs

A 1‐factorization of a graph G is a decomposition of G into edge‐disjoint 1‐factors (perfect matchings), and a perfect 1‐factorization is a 1‐factorization in which the union of any two of the 1‐factors is a Hamilton cycle. We consider the problem of the existence of perfect 1‐factorizations of even order 4‐regular Cayley graphs, with a particular interest in circulant graphs. In this paper, we study a new family of graphs, denoted , which are Cayley graphs if and only if k is even or . By solving the perfect 1‐factorization problem for a large class of graphs, we obtain a new class of 4‐regular bipartite circulant graphs that do not have a perfect 1‐factorization, answering a problem posed in 7 . With further study of graphs, we prove the nonexistence of P1Fs in a class of 4‐regular non‐bipartite circulant graphs, which is further support for a conjecture made in 7 .     

Beyond Perovskite Solar Cells: Tellurium Iodide as a Promising Light‐Absorbing Material for Solution‐Processed Photovoltaic Application

Searching new light‐absorbing materials to replace toxic lead halide in solar cells is very important and highly desirable. In this research, we firstly demonstrated that tellurium iodide (TeI₄) could be used as a light‐absorbing material in solar cells due to its suitable optical band gap and the active lone‐pair electron orbital in Te⁴⁺. The best power conversion efficiency (PCE=3.56%) was achieved with a concentration of 0.9 M TeI₄ in DMF:DMSO (4 : 1, v,v) without any heat treatment or antisolvent dripping. Our study indicates the promising potential of TeI₄ for photovoltaic and optoelectronic applications.     

Design of a tuned vibration absorber for a slender hollow cylindrical structure

Abstract

In this paper, details of the design work for a tuned vibration absorber to be used on a hollow cylindrical structure is presented. The vibration problem is of resonant type and the tuned vibration absorber is designed to suppress the displacement vibration response of the free end of the slender hollow structure dominated by the contribution of its lowest transverse vibration modes. The structure is modeled using a commercial finite element software. Finite element model of the structure is verified using experimentally obtained frequency response functions and modal parameters. Effective parameters of the tuned vibration absorber design are then determined based on finite element analysis simulations of the vibration suppression performance of the tuned vibration absorber as it is used on the structure. Details of the tuned vibration absorber design are determined and a prototype is fabricated. Prototype tuned vibration absorber is then characterized experimentally both as a standalone system and also as it is used on the main structure. Vibration reduction performance of the physical prototype of the tuned vibration absorber is also compared with its vibration reduction performance estimated from finite element analysis simulations so that the analysis based design process can be validated.

Communicated by Dumitru Caruntu.     

Dual-band isotropic metamaterial absorber based on near-field interaction in the Ku band

We numerically and experimentally investigate single-band and dual-band isotropic metamaterial absorbers (IMAs) based on metallic disks. By optimizing the diameter of the metallic disks and the thickness of the dielectric substrate, the single-band IMA is observed at 16.2 GHz with absorptivity of 97%. When adding one disk-pair to the structure, the dual-band IMA is obtained at 12.8 and 15.5 GHz due to the symmetry breaking. The physical mechanics is explained by near-field coupling effect and equivalent LC circuit model. The measurement results performed in the range 12–18 GHz show a good agreement with simulation and theoretical analysis. Our findings demonstrate a new approach to achieve dual-band and multi-band IMAs.     

Passive vibration absorber effect on the machining surface quality of a flexible workpiece

This paper presents a study of the vibratory behaviour of a flexible workpiece subject to a milling end operation. Indeed, this vibratory behaviour is critical, especially when the excitation frequency is near to the resonance. For this reason, passive vibration suppression is considered in order to attenuate the dynamic response of the milled workpiece and decrease the dynamic effect on the resulting machined surface roughness and flatness. In order to confirm the efficiency of the passive vibration suppression, the vibratory behaviour and the quality (roughness and flatness) of a machined surface are studied without and with passive absorber (TMD) using a finite-element model.