Note on a conjecture for the sum of signless Laplacian eigenvalues

For a simple graph G on n vertices and an integer k with 1 ? k ? n, denote by \(\mathcal{S}^+_k\) (G) the sum of k largest signless Laplacian eigenvalues of G. It was conjectured that \(\mathcal{S}^+_k(G)\leqslant{e}(G)+(^{k+1}_{\;\;2})\) (G) ? e(G) + (k+1 2), where e(G) is the number of edges of G. This conjecture has been proved to be true for all graphs when k ∈ {1, 2, n ? 1, n}, and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all k). In this note, this conjecture is proved to be true for all graphs when k = n ? 2, and for some new classes of graphs.     

Polymorphic phase transition and thermal stability in squaric acid (H2C4O4)

Phase transformations in squaric acid (H₂C₄O₄) have been investigated by thermogravimetry and differential scanning calorimetry with different heating rates β. The mass loss in TG apparently begins at onset temperatures T_di=245±5 °C (β=5 °C min^?1), 262±5 °C (β=10 °C min^?1), and 275±5 °C (β=20 °C min^?1). A polymorphic phase transition was recognized as a weak endothermic peak in DSC around 101 °C (T_c⁺). Further heating with β=10 °C min^?1 in DSC revealed deviation of the baseline around 310 °C (T_i), and a large unusual exothermic peak around 355 °C (T_p), which are interpreted as an onset and a peak temperature of thermal decomposition, respectively. The activation energy of the thermal decomposition was obtained by employing relevant models. Thermal decomposition was recognized as a carbonization process, resulting in amorphous carbon.     

Electrical characterization of nylon-6 composite nanofibers

The electrical characteristics of nylon-6 nanofibers incorporated with TiO₂ and Fe₃O₄ nanoparticles were investigated. The resultant nanofibers exhibited good incorporation of nanoparticles. The impregnated TiO₂ and Fe₃O₄ nanoparticles into the nylon-6 nanofibers were confirmed by high resolution transmission electron microscopy (HR-TEM) and energy dispersive X-ray (EDX) spectroscopy studies. The electrical conductivity of the nylon-6 incorporated with TiO₂ and Fe₃O₄ composite nanofibers were higher than that of the pristine nylon-6 nanofibers. The impregnation of TiO₂ and Fe₃O₄ nanoparticles significantly enhanced the electrical property of the composite nanofibers. These polymeric/nanoparticles composite nanofibers structure may open a new direction for future organic electronics.     

Characterization of chaotic dynamic behavior in the gas–liquid slug flow using directed weighted complex network analysis

Understanding the nonlinear and complex dynamics underlying the gas–liquid slug flow is a significant but challenging problem. We systematically carried out gas–liquid two-phase flow experiments for measuring the time series of flow signals, which is studied in terms of the mapping from time series to complex networks. In particular, we construct directed weighted complex networks (DWCN) from time series and then associate different aspects of chaotic dynamics with the topological indices of the DWCN and further demonstrate that the DWCN can be exploited to detect unstable periodic orbits of low periods. Examples using time series from classical chaotic systems are provided to demonstrate the effectiveness of our approach. We construct and analyze numbers of DWCNs for different gas–liquid flow patterns and find that our approach can quantitatively distinguish different experimental gas–liquid flow patterns. Furthermore, the DWCN analysis indicates that slug flow shows obvious chaotic behavior and its unstable periodic orbits reflect the intermittent quasi-periodic oscillation behavior between liquid slug and large gas slug. These interesting and significant findings suggest that the directed weighted complex network can potentially be a powerful tool for uncovering the underlying dynamics leading to the formation of the gas–liquid slug flow.     

Evolutionary game on a stochastic growth network

In some real complex systems the structures are difficult to map or changing over time. To explore the evolution of strategies on these complex systems, it is not realistic enough to specify their structures or topological properties in advance. In this paper, we address the evolutionary game on a stochastic growth network adopting the prisoner’s dilemma game. We introduce a growing rate q$q$ to control the ratio of network growth to strategy evolution. A large q$q$ denotes that the network grows faster than strategy evolution. Simulation results show that a fast growing rate is helpful to promote the average payoffs of both cooperators and defectors. Moreover, this parameter also significantly influences the cooperation frequency on the resulting networks. The coexisting mechanisms in this paper may provide a beneficial insight for understanding the emergence of complex topological structures and game behaviors in numerous real systems.     

基于Heston随机波动率模型和风险偏好视角的资产负债管理

本文研究基于Heston随机波动率模型的资产负债管理问题。假设金融市场由一个无风险资产和一个风险资产构成,投资者的目标是最大化其终端财富的期望效用。应用随机控制方法,得到了该问题最优资产配置策略的解析表达式和相应值函数的解析解,通过数值算例分析了Heston模型主要参数以及债务对最优资产配置策略的影响。结果表明:配置到风险资产的比例对Heston模型中的参数非常敏感;为了对冲债务风险,负债的引入使得配置到风险资产的比例比无负债情形下的高;在风险厌恶系数变大时,无论投资者是否有负债,其投资到风险资产的比例则越来越低。     

Improved dimensional stability of Nafion membrane modified using a layer by layer self-assembly of biophilic polymers

The modification of perfluorinated proton exchange membranes (e.g. Nafion) utilizing a layer by layer (LbL) electrostatic assembly of oppositely charged biophilic polymers such as poly-l-lysine as positive layer and dsDNA as a negative layer is developed to protect the interface between the catalyst layer and the membrane in a low temperature fuel cell. Various physicochemical measurements including water uptake, proton conductivity and surface tension were investigated for both the as-received Nafion and the biopolymeric LbL modified Nafion. The smaller water contact angle and the less swelling characteristics of the biopolymer modified Nafion membrane was founded compared to that of as-received Nafion. This clearly indicates that the more hydrophilic surface of biopolymeric layers on Nafion plays an important role in the enhanced dimensional stability. In addition, a potential hypothesis explaining the higher proton conductivity from the LbL biopolymeric film coated Nafion is suggested.     

A thioester substrate binds to the enzyme Arthrobacter thioesterase in two ionization states: evidence from Raman difference spectroscopy

4‐Hydroxybenzoyl‐CoA (4‐HB‐CoA) thioesterase from Arthrobacter is the final enzyme catalyzing the hydrolysis of 4‐HB‐CoA to produce coenzyme A and 4‐hydroxybenzoic acid in the bacterial 4‐chlorobenzoate dehalogenation pathway. Using a mutation E73A that blocks catalysis, stable complexes of the enzyme and its substrate can be analyzed by Raman difference spectroscopy. Here we have used Raman difference spectroscopy, in the non‐resonance regime, to characterize 4‐HB‐CoA bound in the active site of the E73A thioesterase. In addition, we have characterized complexes of the wild‐type enzyme complexed with the unreactive substrate analog 4‐hydroxyphenacyl‐CoA (4‐HP‐CoA). Both sets of complexes show evidence for two forms of the ligand in the active site: one population has the 4‐hydroxy group protonated, 4‐OH; while the second has the group as the hydroxide, 4‐O⁻. For bound 4‐HP‐CoA, X‐ray data show that glutamate 78 is close to the 4‐OH in the complex and it is likely that this is the proton acceptor for the 4‐OH proton. Although the pK_a of the 4‐OH group on the free substrate in aqueous solution is 8.6, the relative populations of ionized and neutral 4‐HB‐CoA bound to E73A remain invariant between pH 7.3 and 9.8. The invariance with pH suggests that the 4‐OH and the ‐COO⁻ of E78 constitute a tightly coupled pair where their separate pK_a ‘s lose their individual qualities. Narrow band profiles are seen in the CO double bond and C‐S regions, suggesting that the hydrolyzable thioester group is rigidly bound in the active site in a syn gauche conformation. Copyright © 2011 John Wiley & Sons, Ltd.     

Exploring the origin of tip‐enhanced Raman scattering; preparation of efficient TERS probes with high yield

Tip‐enhanced Raman scattering (TERS) spectroscopy is a promising technique for nanoscale chemical analysis. However, there are several challenges preventing widespread application of this technology, including reproducible fabrication of efficient TERS probes. These problems reflect a lack of clear understanding of the origins of, and the parameters influencing TERS. It is believed that the coating characteristics at the apex of the tip have a major effect on the near‐field optical enhancement and thus the TERS activity of a metalized probe. Here we show that the aspect ratio of the tip can play a significant role in the efficiency of TERS probes. We argue that the electrostatic field arising from the lightning‐rod effect has a substantial role in the observed TERS effect. This argument is supported by ‘edge‐enhanced Raman scattering’ which is shown for a noble metal film. Furthermore, it is reported that an associated tip‐surface‐enhanced Raman scattering effect can be achieved by using a TERS‐inactive metalized probe on a surface‐enhanced Raman spectroscopy‐inactive roughened surface. This observation can be explained by an interparticle enhancement of the electromagnetic field. Copyright © 2011 John Wiley & Sons, Ltd.     

Optical nonlinearity measurement of 4-（N-methyl,N-hydroxyethl）amino,4＇-nitroazobenzene using a transmittance technique with a phase object（T-PO） with top-hat beams at 600-nm wavelength

The transmittance technique with a phase object（T-PO）,for measuring optical nonlinear coefficients is proposed with a top-hat beam.The sensitivity of the T-PO with a top-hat beam is a factor of 4 greater than that with a Gaussian beam.The validity of this method is verified by measuring the nonlinearity of a well-characterized liquid,CS 2 at 532-nm wavelength.The ease of use of this method has been proved by measuring a new compound 4-（N-methyl,N-hydroxyethyl）amino,4＇-nitroazobenzene（ANAB） at 600-nm wavelength,indicating that this method can be extended to the measurement of optical nonlinearities in a wide-band spectrum.