On irreducible p,q-representations of gl(2)

The theory of irreducible p,q-representations of the complex Lie algebra gl(2) is developed. We construct a one variable model of irreducible p,q-representations of gl(2) in terms of p,q-derivative operator, and derive a generating function based on it.     

Solution properties of polymethyl acrylate I. Properties of PMA chain by viscometric method

Fundamental properties of polymethyl acrylate solutions were examined: the reasonable Houwink-Mark-Sakurada relations and the theta temperature (θ) were determined to be 5 °C in toluene. Further, the measurements of intrinsic viscosity for polymethyl acrylate solutions as a function of temperature yielded a thermal transition due to a conformation change at 56 ± 1 °C, irrespective of molecular weight and solvent. An application of the two-parameter theory to such a transition gave a stepwise change of the short-range interaction: K×10²=9.5 below 50 °C and 10.3 above 60 °C. This conformation transition is explained on the basis of the steric hindrance of the planar substituent to the main chain above 60 °C.     

Statistical analysis of two-parameter generalized Birnbaum-Saunders Cauchy distribution

The image features of density function and failure rate function are studied in detail for two-parameter generalized Birnbaum-Saunders Cauchy fatigue life distribution. The logarithmic moment estimation and other two point estimations of parameters are proposed under full sample, and the precisions of point estimations are investigated by Monte-Carlo simulations. The approximate interval estimations of parameters are given by using Taylor expansion, and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations. Finally, several examples show the feasibility of the methods.     

Quadratic variation of functionals of two-parameter Wiener process

The quadratic variation of functionals of the two-parameter Wiener process of the form f(W(s, t)) is investigated, where W(s, t) is the standard two-parameter Wiener process and f is a function on the reals. The existence of the quadratic variation is obtained under the condition that f′ is locally absolutely continuous and f^N is locally square integrable.     

Derivations and Automorphisms of the Positive Part of the Two-parameter Quantum Group Ur,s(B3)

We compute the derivations of the positive part of the two-parameter quantum group U_(r,s)(B_3) and show that the Hochschild cohomology group of degree 1 of this algebra is a threedimensional vector space over the base field C. We also compute the groups of(Hopf) algebra automorphisms of the augmented two-parameter quantized enveloping algebra ?_(r,s)~(≥0)(B_3).     

基于超声射频信号的支持向量机双参量B线识别方法*

肺超声中的特殊征象B线对于临床诊断肺水肿等肺部疾病有重要意义,但诊断结果依赖于医生的主观判断,为了客观、自动地识别B线,提高诊断准确率,本文提出了一种基于超声回波射频信号的肺脏超声特殊征象B线识别方法。本文首先选取了射频信号的排列熵、信息熵、峰度、偏度、能量作为特征参数,利用独立样本t检验和单参数贝叶斯分类的方法检验超声射频数据中B线以及非B线所对应射频数据的各个参量的差异性以及各参数与B线识别的相关性。然后将不同的双参量组合输入非线性支持向量机（SVM）中进行分类,比较各个组合的分类效果。结果显示信息熵与排列熵参数组合基于射频信号的分类效果最好,分类灵敏度为90.521%,特异性为98.106%,准确率为96.328%,AUC等于0.95。在引入后处理算法后,B线识别效果有进一步提升,得到分类平均灵敏度为95.23%,平均特异性为97.22%,平均准确率为96.88%。研究结果表明基于射频数据的SVM双参量B线识别方法对辅助临床诊断具有重要价值,信息熵和排列熵的组合可以有效的对特殊征象B线进行高精度识别。     

Extensivity and nonextensivity of two-parameter entropies

In this paper, we investigate two-parameter entropies and obtain some conditions for their extensivity. By using a generalized (k,r)$(k,r)$-product, correlations for subsystems are related to the joint probabilities, so that the entropy remains extensive.     

Spectral-Parameter Dependent Yang–Baxter Operators and Yang–Baxter Systems From Algebra Structures

For any algebra, two families of colored Yang–Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang–Baxter equation. An open problem about a system of functional equations is stated. The matrix forms of these operators for two and three dimensional algebras are computed. A FRT bialgebra for one of these families is presented. Solutions for the one-parameter quantum Yang–Baxter equation are derived and a Yang–Baxter system constructed.     

Functional inequalities for the two-parameter extension of the infinitely-many-neutral-alleles diffusion

By explicitly identifying the transition density function, we derived the super-Poincaré and super-log-Sobolev inequalities for the two-parameter extension of the infinitely-many-neutral-alleles diffusion, which in particular implies the Gross log-Sobolev inequality.