Weak solutions to a stationary heat equation with nonlocal radiation boundary condition and right‐hand side in Lp (p⩾1)

Accurate modelling of heat transfer in high‐temperature situations requires accounting for the effect of heat radiation. In complex industrial applications involving dissipative heating, we hardly can expect from the mathematical theory that the heat sources will be in a better space than L¹. In this paper, we focus on a stationary heat equation with nonlocal boundary conditions and L^p right‐hand side, with p?1 being arbitrary. Thanks to new coercivity results, we are able to produce energy estimates that involve only the L^p norm of the heat sources and to prove the existence of weak solutions. Copyright © 2008 John Wiley & Sons, Ltd.     

Feynman-Kac Formula for Left Continuous Additive Functionals and Extended Kato Class Measures

The perturbation of the generator of a Borel right process by a signed measure is investigated, using probabilistic and analytic potential theoretical methods. We establish a Feynman-Kac formula associated with measures charging no polar set and belonging to an extended Kato class. A main tool of this approach is the validity of a Khas’minskii Lemma for Stieltjes exponentials of positive left continuous additive functionals.      

随机右截尾情形下两个指数分布总体的比较

研究了随机右截尾情形下两个指数分布的参数估计.在两个指数分布的刻度参数都未知时,得到了两个指数分布的刻度参数的最大似然估计与参数比的区间估计.     

右(左)拟α-可逆环

给出了右(左)拟α-可逆环的定义,讨论了右(左)拟α-可逆环与线性McCoy环、可逆环、α-刚性环、约化环、阿贝尔环以及弱α-Skew Armendariz环之间的关系.研究了右(左)拟α-可逆环的相关性质和基本扩张.推广了α-可逆环和α-刚性环的相关结论.     

Poisson brackets,Novikov-Leibniz structures and integrable Riemann hydrodynamic systems

A general differential-algebraic approach is devised for constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz algebraic structures are presented and a new non-associative “Riemann” algebra is constructed, which is closely related to the infinite multi-component Riemann integrable hierarchies. A close relationship to the standard symplectic analysis techniques is also discussed.     

Group inverses for some 2 × 2 block matrices over rings

We first consider the group inverses of the block matrices (A0BC) over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices (ACBD) over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B^# and (B^πA) ^# both exist; (ii) B is invertible and m = n; (iii) A^# and (D - CA^#B)^# both exist, C = CAA^# , where A and D are m × m and n × n matrices, respectively.     

Recent development of Faith conjecture

Is a semiprimary right self-injective ring a quasi-Frobenius ring? Almost half century has passed since Faith raised this problem. He first conjectured “No” in his book Algebra II. Ring Theory in 1976, but changing his mind, he conjectured “Yes” in his article “When self-injective rings are QF: a report on a problem” in 1990. In this paper, we describe recent studies of this problem based on authors works and raise related problems.     

Cardiac magnetic resonance imaging in arrhythmogenic right ventricular cardiomyopathy: correlation to the QRS dispersion

The aim of the study was to evaluate the relationship between the presence of right ventricular abnormalities detected by cardiac magnetic resonance (CMR) and QRS dispersion, the strongest independent predictor of sudden death in ARVC. A consecutive series of 40 patients from a single institution were recruited with a clinical diagnosis of ARVC based on the diagnostic criteria. All patients underwent systematic clinical evaluation, including history and examination, electrocardiography, 24-h Holter monitor, chest radiography, echocardiography and CMR examination and were divided into two groups according to the QRS dispersion: group I, QRS dispersion ≥ 40 ms; group II, QRS dispersion < 40 ms. The relationship between the characteristic parameters of CMR image and QRS dispersion were analyzed in two groups. There were significant differences in QRS dispersion (57±14 ms vs. 26±11 ms), right ventricular end-diastolic diameter (57±10 mm vs. 48±11 mm, P=.012), right ventricular end-systolic diameter (52±10 mm vs. 44±11 mm, P=.010), right ventricular end-diastolic volume (260±105 ml vs. 180±66 ml, P=.006), right ventricular end-systolic volume (222±98 ml vs. 148±61 ml, P=.006) and myocardial fibrosis detection rate (74% vs. 38%, P=.024) between two groups. For all patients with ARVC, QRS dispersion and right ventricular end-diastolic volume (r= 0.66, P<.001), right ventricular end-systolic volume (r= 0.67, P<.001), right ventricular outflow tract area (r= 0.68, P<.001) showed a moderate positive correlation. Right ventricular outflow tract area, right ventricular end-diastolic volume and end-systolic volume detected by CMR in patients with ARVC were positively correlated to the extent of QRS dispersion (≥ 40 ms), the strongest independent predictor of sudden cardiac death.     

随机右删失非参数回归模型的影响分析

将随机删失非参数固定设计回归模型转化为非参数回归模型进行研究;然后对此模型作了局部影响分析,得到计算影响矩阵及最大影响曲率方向的简洁公式;最后通过实例分析,验证了分析方法的有效性.     

由两个右特征对构造三对角四元数矩阵

讨论由两个右特征对构造三对角四元数矩阵的数值求解问题,给出了该问题有解的充要条件,以及解的具体表达式.在已知两个特征对的条件下,进一步给出了三对角自共轭、三对角正定四元数矩阵的存在条件及计算方法.