On the concepts of intertwining operator and tensor product module in vertex operator algebra theory

We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general be used as a replacement axiom for the Jacobi identity. We further give a sufficient condition for the commutator formula to imply the Jacobi identity in this definition. Using these results we illuminate the crucial role of the condition called the “compatibility condition” in the construction of the tensor product module in vertex operator algebra theory, as carried out in work of Huang and Lepowsky. In particular, we prove by means of suitable counterexamples that the compatibility condition was indeed needed in this theory.     

有限子集系的Sperner系

1９８０年，Ｋｏ-Ｗｅｉ Ｌｉｈ提出如下猜想：如果Ｆ是由Ｂ^ｎ中固定秩的不同元素生成的序理想，那么Ｆ是Ｓｐｅｒｎｅｒ系．本文证实了当Ｆ是由Ｘ的子集Ｙ的所有相同秩的元素生成的序理想，猜想是正确的     

大面积染料敏化太阳电池的串联阻抗特性研究

在电子扩散微分方程的基础上,研究了染料敏化太阳电池光生电流和光生电压随光照强度不同的变化关系.提出敏化太阳电池串联阻抗功率损耗模型,理论模拟了大面积电池（有效面积>1 cm²）光电转换效率随多孔薄膜有效面积宽度变化的曲线、透明导电基底膜与银栅极的比接触电阻以及在不同入射光强下银栅极体电阻对大面积染料敏化太阳电池光伏性能的影响.结果表明透明导电基底膜的方块电阻和银栅极体电阻对大面积染料敏化太阳电池的性能有很大影响,而这种影响随光强的减弱逐渐减小. 关键词： 染料敏化 太阳电池 串联阻抗 光电转换效率     

Asymptotic behavior of solutions for a class of retarded difference equations

Consider the retarded difference equationx _n −x _n−1 =F(−f(x _n )+g(x _n−k )), wherek is a positive integer,F,f,g:R→R are continuous,F andf are increasing onR, anduF(u)>0 for allu≠0. We show that whenf(y)≥g(y) (resp. f(y)≤g(y)) fory∈R, every solution of (*) tends to either a constant or −∞ (resp. ∞) asn→∞. Furthermore, iff(y)≡g(y) fory∈R, then every solution of (*) tends to a constant asn→∞. Project supported by NNSF (19601016) of China and NSF (97-37-42) of Hunan     

聚集态和陷阱对交联聚乙烯真空沿面闪络特性的影响

研究了半结晶聚合物交联聚乙烯的聚集态和陷阱等对真空沿面闪络特性的影响.交联聚乙烯(XLPE)在135℃下恒温10min后,分别经过-56℃,-25℃淬火处理,自然降温,或1℃/min,0.5℃/min慢速降温等热处理过程,测量了热处理后试样的电气性能、显微结构、陷阱分布和真空中的沿面闪络特性.实验结果表明,与未热处理试样相比,热处理试样的直流闪络电压最高提高了76%,脉冲闪络电压最高提高了19%.认为热处理改变了XLPE试样的聚集态和陷阱,从而提高了XLPE试样的真空沿面闪络性能,提出了可以通过控制半结晶聚合物的聚集态和缺陷结构提高其真空沿面闪络性能.     

表面张力-重力短峰波作用的海底边界层速度二阶解

依据最近提出的三阶表面张力-重力短峰波理论,通过求解经典的Prandtl边界层方程,给出海底边界层速度的二阶解析解,为确定海底边界层的质量输运提供了一个必备的先行理论基础.     

One-loop renormalizability of noncommutative U(1) gaugetheory with scalar fields

This paper uses the background field method to calculate one-loop divergent corrections to the gauge field propagators in noncommutative U(1) gauge theory with scalar fields. It shows that for a massless scalar field, the gauge field propagators are renormalizable to θ²-order, but for a massive scalar field they are renormalizable only to θ-order.     

A note on Schweizer–Smital chaos

In this paper, we consider a continuous map f:X→X$f:X\to X$, where X$X$ is a compact metric space, and prove that for any positive integer N$N$, f$f$ is Schweizer–Smital chaotic if and only if f^N$f^N$ is too.     

Generalized quasi-variational-like hemivariational inequalities

In this paper, we introduce and study a new class of generalized quasi-variational-like hemivariational inequalities with multi-valued η$\eta$-pseudomonotone operators in Banach spaces. Some new existence theorems of solutions for this class of generalized quasi-variational-like hemivariational inequalities are proved. The results presented in this paper generalize and extend some known results.     

An improved automatic time-of-flight picker for medical ultrasound tomography

Objective and motivationTime-of-flight (TOF) tomography used by a clinical ultrasound tomography device can efficiently and reliably produce sound-speed images of the breast for cancer diagnosis. Accurate picking of TOFs of transmitted ultrasound signals is extremely important to ensure high-resolution and high-quality ultrasound sound-speed tomograms. Since manually picking is time-consuming for large datasets, we developed an improved automatic TOF picker based on the Akaike information criterion (AIC), as described in this paper.MethodsWe make use of an approach termed multi-model inference (model averaging), based on the calculated AIC values, to improve the accuracy of TOF picks. By using multi-model inference, our picking method incorporates all the information near the TOF of ultrasound signals. Median filtering and reciprocal pair comparison are also incorporated in our AIC picker to effectively remove outliers.ResultsWe validate our AIC picker using synthetic ultrasound waveforms, and demonstrate that our automatic TOF picker can accurately pick TOFs in the presence of random noise with absolute amplitudes up to 80% of the maximum absolute signal amplitude. We apply the new method to 1160 in vivo breast ultrasound waveforms, and compare the picked TOFs with manual picks and amplitude threshold picks. The mean value and standard deviation between our TOF picker and manual picking are 0.4 μs and 0.29 μs, while for amplitude threshold picker the values are 1.02 μs and 0.9 μs, respectively. Tomograms for in vivo breast data with high signal-to-noise ratio (SNR) (∼25 dB) and low SNR (∼18 dB) clearly demonstrate that our AIC picker is much less sensitive to the SNRs of the data, compared to the amplitude threshold picker.Discussion and conclusionsThe picking routine developed here is aimed at determining reliable quantitative values, necessary for adding diagnostic information to our clinical ultrasound tomography device - CURE. It has been successfully adopted into CURE, and allows us to generate such values reliably. We demonstrate that in vivo sound-speed tomograms with our TOF picks significantly improve the reconstruction accuracy and reduce image artifacts.