Joint measurability and the one-way Fubini property for a continuum of independent random variables

As is well known, a continuous parameter process with mutually independent random variables is not jointly measurable in the usual sense. This paper proposes an extension of the usual product measure-theoretic framework, using a natural ``one-way Fubini' property. When the random variables are independent even in a very weak sense, this property guarantees joint measurability and defines a unique measure on a suitable minimal -algebra. However, a further extension to satisfy the usual (two-way) Fubini property, as in the case of Loeb product measures, may not be possible in general. Some applications are also given.

     

New properties of convex functions in the Heisenberg group

We prove some new properties of the weakly -convex functions recently introduced by Danielli, Garofalo and Nhieu. As an interesting application of our results we prove a theorem of Busemann-Feller-Alexandrov type in the Heisenberg groups , .

     

Carleson embeddings and some classes of operators on weighted Bergman spaces

We prove Carleson-type embedding theorems for weighted Bergman spaces with Békollé weights. We use this to study properties of Toeplitz-type operators, integration operators and composition operators acting on such spaces. In particular, we investigate the membership of these operators to Schatten class ideals.     

Factorizing operators on Banach function spaces through spaces of multiplication operators

In order to extend the theory of optimal domains for continuous operators on a Banach function space X(μ) over a finite measure μ, we consider operators T satisfying other type of inequalities than the one given by the continuity which occur in several well-known factorization theorems (for instance, Pisier Factorization Theorem through Lorentz spaces, pth-power factorable operators …). We prove that such a T factorizes through a space of multiplication operators which can be understood in a certain sense as the optimal domain for T. Our extended optimal domain technique does not need necessarily the equivalence between μ and the measure defined by the operator T and, by using δ-rings, μ is allowed to be infinite. Classical and new examples and applications of our results are also given, including some new results on the Hardy operator and a factorization theorem through Hilbert spaces.     

专职修理工多重休假且修理设备可更换的k/n(G)表决系统研究

讨论专职修理工多重休假,修理设备可发生失效且可更换的k/n（G）表决可修系统.当系统中没有故障部件时,专职修理工开始一次休假,在此期间,若有工作部件发生故障,则立即指派普通修理工修理故障部件,一直持续到系统中无故障部件或专职修理工休假回来.利用马尔可夫过程理论和矩阵解法,给出了系统瞬态和稳态下的可用度和故障频度、可靠度、系统首次故障前的平均时间、修理设备处于更换状态的概率等指标的表达式.在此基础上,基于不同的初始条件研究了相关指标随时间的变化情况.最后,特殊情形的讨论验证了所得结果的正确性.     

Minimum classification error training in example based speech and pattern recognition using sparse weight matrices

The Minimum Classification Error (MCE) criterion is a well-known criterion in pattern classification systems. The aim of MCE training is to minimize the resulting classification error when trying to classify a new data set. Usually, these classification systems use some form of statistical model to describe the data. These systems usually do not work very well when this underlying model is incorrect. Speech recognition systems traditionally use Hidden Markov Models (HMM) with Gaussian (or Gaussian mixture) probability density functions as their basic model. It is well known that these models make some assumptions that are not correct. In example based approaches, these statistical models are absent and are replaced by the pure data. The absence of statistical models has created the need for parameters to model the data space accurately. For this work, we use the MCE criterion to create a system that is able to work together with this example based approach. Moreover, we extend the locally scaled distance measure with sparse, block diagonal weight matrices resulting in a better model for the data space and avoiding the computational load caused by using full matrices. We illustrate the approach with some example experiments on databases from pattern recognition and with speech recognition.     

Perturbation theory for convolution semigroups

We deal with convolution semigroups (not necessarily symmetric) in Lp(RN) and provide a general perturbation theory of their generators by indefinite singular potentials. Such semigroups arise in the theory of Lévy processes and cover many examples such as Gaussian semigroups, α-stable semigroups, relativistic Schrödinger semigroups, etc. We give new generation theorems and Feynman-Kac formulas. In particular, by using weak compactness methods in L¹, we enlarge the extended Kato class potentials used in the theory of Markov processes. In L² setting, Dirichlet form-perturbation theory is finely related to L¹-theory and the extended Kato class measures is also enlarged. Finally, various perturbation problems for subordinate semigroups are considered.     

HEMODYNAMIC CHANGES OF THE LEFT CORONARY ARTERY DURING PERCUTANEOUS CORONARY WEI Chijun*, QIU Yue*, FAN Yubo†, PENG Liqing**, ZHENG Tinghui*,2)*

经皮冠状动脉介入治疗(percutaneous coronary intervention, PCI)是检查和治疗冠心病的常用手段,冠状动脉支架植入过程中可能引发急性血栓的发生。本文通过血流动力学计算探究PCI支架植入手术过程对急性血栓形成的影响。根据真实的冠状动脉计算机断层扫描影像进行建模,在脉动生理血流条件下模拟该手术过程中导丝介入的5个阶段,获得各项血流动力学参数。计算结果表明,导丝介入过程会导致冠状动脉内各项血流动力学参数发生改变,即冠状动脉内血流出现偏心现象,时均壁面剪切力升高,振荡剪切指数下降,粒子相对停留时间降低,横向壁面剪切应力小幅上升,使得血管的内皮细胞暴露在高壁面剪切力的环境下。虽然较短的相对粒子 停留时间、 较小的振荡剪切指数对急性血栓的形成具有阻碍作用,但高时均壁面剪切力与血流偏心对急性血栓形成的诱导作用可能更加明显。     

Benefits of intervention in spatial public goods games

The anarchy driven by private punishment is inopportune and inappropriate in modern human societies. It is necessary for a person to appeal to a higher authority such as the police so that a society can maintain more stable. We introduce strategy intervention instead of punishment in spatial public goods game. Some defectors are forced to contribute to the common pool. We show how strategy intervention affects cooperation of a population. Interestingly, weak intervention restrains the impact of spatial reciprocity leading to a lower level of cooperation or even a full defection state. Such phenomena are in contrast to ordinary intuitions. Intervention is enforced by a higher authority which avoids the second-order problems. Furthermore, high synergy factor and proper intervention has a mutual impact on increasing group incomes. We highlight the importance of institutional intervention in a stable society.     

Pilot Study: Understanding the Effects of Voicing Intervention on HFCC Therapy in People with Cystic Fibrosis

The efficacy of High-Frequency Chest Compression (HFCC) airway clearance therapy is linked to the induced-peak expiratory airflow pulse (IPEF) at the patient's mouth. The authors' goal was to determine the conditions that yield the highest IPEF using HFCC running at 6 Hz in conjunction with voicing intervention. A pilot experimental study was conducted in a laboratory setting. Six adults with moderate to mild cystic fibrosis (CF) and 10 healthy adults participated. When the component characteristics of voicing were disregarded in data analysis of four conditions, voicing only intervention (V₁I₀), HFCC only intervention (V₀I₁), voicing intervention and HFCC intervention combinations (V₁I₁) and nonintervention (V₀I₀), V₀I₁ had significantly higher (P < 0.0001) IPEF. Data analyses of 64 separate voicing component characteristics, frequency (×4), amplitude (×4), and rhythm (×2) of voicing intervention, in addition to absence and presence of HFCC intervention (V₁I₀ and V₁I₁), were examined. One condition in V₁I₀ had significantly higher (P < 0.000001) IPEF than other conditions in V₁I₀ and V₁I₁ in both experimental and control groups. Based on these findings, V₁I₁ may yield higher IPEF than V₀I₁. One condition of amplitude component of voicing and one condition of rhythm component of voicing had significantly higher (P < 0.0001) IPEF than other conditions of amplitude and rhythm components in both CF and control subjects. Analysis of this combined condition of V₁I₁ showed that this specific condition of V₁I₁ had significantly higher (P < 0.000001) IPEF than any other conditions in V₁I₁ and V₀I₁.