An inequality for the group chromatic number of a graph

We give an inequality for the group chromatic number of a graph as an extension of Brooks’ Theorem. Moreover, we obtain a structural theorem for graphs satisfying the equality and discuss applications of the theorem.     

Electrical characteristics of AlInN/GaN HEMTs under cryogenic operation

Electrical properties of an AlInN/GaN high-electron mobility transistor (HEMT) on a sapphire substrate are investi-gated in a cryogenic temperature range from 295 K down to 50 K. It is shown that drain saturation current and conductance increase as transistor operation temperature decreases. A self-heating effect is observed over the entire range of temperature under high power consumption. The dependence of channel electron mobility on electron density is investigated in detail. It is found that aside from Coulomb scattering, electrons that have been pushed away from the AlInN/GaN interface into the bulk GaN substrate at a large reverse gate voltage are also responsible for the electron mobility drop with the decrease of electron density.     

Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates

The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates. To investigate the origin of maximum entropy states, the inhomogeneous Helmholtz equation is modified to consider the point interaction coming from the driving oscillator. The coupling strength associated with the point interaction is characterized by a dimensionless factor α. The δ potential of the point interaction is numerically modelled by a truncated basis with an upper index N. The asymptotic behavior for the upper index N is thoroughly explored to verify that the coupling strength of α = 1.0 can make the theoretical resonant modes agree excellently with the maximum entropy states as N→∞. It is further authenticated that nearly the same resonant modes can be obtained by using a larger coupling strength α when a smaller upper index N is exploited in the calculation.     

化学氧碘激光器尾气主动冷却技术试验

使用主动冷却技术降低化学氧碘激光器（COIL）尾气的温度,是提高引射式压力恢复系统引射效率的一项关键技术。采用理论计算和数值模拟的方法,得出了满足技术指标要求的冷却器系统设计参数,并研制了一套以管翅式热交换器、液氮循环汽化提供制冷量的COIL尾气主动冷却试验装置。与激光器的对接试验结果表明,在COIL出光60 s试验中,热交换器可以使尾气温度从590 K降低到160 K,出口截面温度不均匀度小于21 K,经过热交换器的气流总压损失小于100 Pa。     

Spectral Measures Associated with the Factorization of the Lebesgue Measure on a Set via Convolution

Let \(Q\) be a fundamental domain of some full-rank lattice in \({\mathbb {R}}^d\) and let \(\mu \) and \(\nu \) be two positive Borel measures on \({\mathbb {R}}^d\) such that the convolution \(\mu *\nu \) is a multiple of \(\chi _Q\) . We consider the problem as to whether or not both measures must be spectral (i.e. each of their respective associated \(L^2\) space admits an orthogonal basis of exponentials) and we show that this is the case when \(Q = [0,1]^d\) . This theorem yields a large class of examples of spectral measures which are either absolutely continuous, singularly continuous or purely discrete spectral measures. In addition, we propose a generalized Fuglede’s Conjecture for spectral measures on \({\mathbb {R}}^1\) and we show that it implies the classical Fuglede’s Conjecture on \({\mathbb {R}}^1\) .     

Characterizations of Strength Extremal Graphs

With graphs considered as natural models for many network design problems, edge connectivity κ′(G) and maximum number of edge-disjoint spanning trees τ(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G (see Cunningham, in J ACM 32:549–561, 1985; Matula, in Proceedings of 28th Symposium Foundations of Computer Science, pp 249–251, 1987, among others). Mader (Math Ann 191:21–28, 1971) and Matula (J Appl Math 22:459–480, 1972) introduced the maximum subgraph edge connectivity \({\overline{\kappa'}(G) = {\rm max} \{\kappa'(H) : H {\rm is} \, {\rm a} \, {\rm subgraph} \, {\rm of} G \}}\) . Motivated by their applications in network design and by the established inequalities $$\overline{\kappa'}(G) \ge \kappa'(G) \ge \tau(G),$$ we present the following in this paper:

1. For each integer k > 0, a characterization for graphs G with the property that \({\overline{\kappa'}(G) \le k}\) but for any edge e not in G, \({\overline{\kappa'}(G + e) \ge k+1}\) .
2. For any integer n > 0, a characterization for graphs G with |V(G)| = n such that κ′(G) = τ(G) with |E(G)| minimized.

     

Enhancements of rate capability and cyclic performance of spinel LiNi0.5Mn1.5O4 by trace Ru-doping

The rate capability and cyclic performance of the LiNi_0.5Mn_1.5O₄ under high current density have been significantly improved by doping a small amount of ruthenium (Ru). Specifically, Li_1.1Ni_0.35Ru_0.05Mn_1.5O₄ and LiNi_0.4Ru_0.05Mn_1.5O₄ synthesized by solid state reaction can respectively deliver a discharge capacity of 108 and 117 mAh g^?1 at 10 C rate between 3 and 5 V. At 10 C charge/discharge rate, Li_1.1Ni_0.35Ru_0.05Mn_1.5O₄ and LiNi_0.4Ru_0.05Mn_1.5O₄ can respectively maintain 91% and 84% of their initial capacity after 500 cycles, demonstrating that Ru-doping could be a way to enhance the electrochemical performance of spinel LiNi_0.5Mn_1.5O₄.     

Preparative isolation of pseudolaric acids A and B,and their glucosides from the root bark of Pseudolarix kaempferi using high‐speed counter‐current chromatography

In order to provide the chemical markers for the quality control of herbal medicines, four diterpenoids, pseudolaric acids A and B (PAA and PAB), and their glucosides were isolated from the methanol extract of the Chinese herb Pseudolarix kaempferi using high‐speed counter‐current chromatography (HSCCC). The diphase solvent system was n‐hexane/EtOAc/MeOH/H₂O which was used at two ratios (5:5:5:5 and 1:9:4:6 by volume) in the separation of pseudolaric acids and their glycosides, respectively. As a result, PAA (14 mg), PAB (129 mg), PAA‐O‐β‐D ‐glucopyranoside (8 mg, PAAG), and PAB‐O‐β‐D ‐glucopyranoside (42 mg, PABG) were obtained from 0.5 g of the crude extract. Their purities were determined to be above 97% by HPLC analysis. Their chemical structures were confirmed by ¹H and ¹³C NMR analysis or HPLC comparison with the reference compounds.     

PREPARATION AND CELL COMPATIBILITY OF FUNCTIONALIZED BIODEGRADABLE POLY(DL-LACTIDE-CO-RS-Β-MALIC ACID)

In order to create a functionalized biodegradable polymer for vascular tissue engineering application,poly(DL- lactide-co-RS-β-malic acid)(PDLLMAc)was synthesized.PDLLMAc was obtained after hydrogenolysis of poly(DL- lactide-co-RS-β-benzyl malolactonate)(PDLLMA),which was from the ring-opening polymerization of DL-lactide(DLLA) and RS-β-benzyl malolactonate(MA)using stannous octoate as catalyst.The copolymers were characterized by ~1H-NMR, FTIR,GPC and DSC.The tensile strength and water uptake of the cop...