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161.
162.
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 \({\mathbb {R}}^1\) . 相似文献
163.
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:
- 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, \({\overline{\kappa'}(G + e) \ge k+1}\) .
- For any integer n > 0, a characterization for graphs G with |V(G)| = n such that κ′(G) = τ(G) with |E(G)| minimized.
164.
The rate capability and cyclic performance of the LiNi0.5Mn1.5O4 under high current density have been significantly improved by doping a small amount of ruthenium (Ru). Specifically, Li1.1Ni0.35Ru0.05Mn1.5O4 and LiNi0.4Ru0.05Mn1.5O4 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, Li1.1Ni0.35Ru0.05Mn1.5O4 and LiNi0.4Ru0.05Mn1.5O4 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 LiNi0.5Mn1.5O4. 相似文献
165.
Quan‐Bin Han Lina Wong Fanny Lai Nian‐Yun Yang Jing‐Zheng Song Chun‐Feng Qiao Hong‐Xi Xu 《Journal of separation science》2009,32(2):309-313
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. 相似文献
166.
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... 相似文献
167.
Microwave-assisted growth and characterization of water-dispersed CdTe/CdS core-shell nanocrystals with high photoluminescence 总被引:5,自引:0,他引:5
He Y Lu HT Sai LM Lai WY Fan QL Wang LH Huang W 《The journal of physical chemistry. B》2006,110(27):13370-13374
A novel microwave-assisted method of growth of high-quality CdTe/CdS core-shell nanocrystals in the aqueous phase is presented in this paper. The photoluminescence quantum yield (PLQY) is greatly enhanced by epitaxial growth of the CdS shell. Under optimum conditions, the PLQY of as-prepared nanocrystals reaches as high as 75% without any post-treatment. Furthermore, these investigations demonstrate that microwave irradiation is tremendously useful for fast epitaxial growth of nanocrystals due to its special characteristics. As a result, the microwave synthesis is sufficiently time-economizing (only five minutes are required) to obtain optimum amounts of CdTe/CdS core-shell nanocrystals in comparison to the conventional illumination method (several days are required). Therefore, this current research not only provides a rapid microwave synthesis for producing highly fluorescent CdTe/CdS core-shell nanocrystals, but also it presents some advantages of the microwave synthesis in comparison to the illumination method. 相似文献
168.
169.
Zhengjin Jiang Zhuohong Yang Roderich D. Süssmuth Norman Williams Smith Shuting Lai 《Journal of chromatography. A》2010,1217(7):1149-1156
It is believed that the enantiorecognition mechanism based on macrocyclic antibiotics involves multimodal interactions via hydrogen bonding, π–π interaction, steric hindrance, hydrophobic interaction and so on. A variety of enantiomeric N-benzoylated amino acids were separated using balhimycin (A) or its analogues bromobalhimycin (B) and dechlorobalhimycin (C) as chiral mobile phase additive using a CE method, which combined the partial filling technique with the dynamic coating technique and the co-EOF electrophoresis technique. The enantioresolution and the migration time were highly relevant to the structure of analytes, especially to the substitutions on the N-tagged benzoyl moiety of the amino acids. A steric effect and π–π interaction based mechanism is proposed in order to explain some observed enantioresolution differences between positional isomers. Notably dechlorobalhimycin exhibited the best enantioresolution for several N-benzoylated derivatives of leucine, which was rarely observed for N-dansylated amino acid derivatives. The hydrophobicity difference of the aglycone pocket among three chiral selectors was assumed to account for this behaviour. 相似文献
170.
A facile Pd-catalyzed sequential reaction has been developed for the synthesis of δ-carbolines from 2-iodoanilines and N-tosyl-enynamines. This protocol involves Larock heteroannulation/elimination/electrocyclization/oxidative aromatization cascade sequences and allows access to multisubstituted δ-carbolines in moderate to good yields. 相似文献