The boundedness of the Riesz transform on a metric cone

In this thesis we study the boundedness, on L-p spaces, of the Riesz transform associated to a Schroedinger operator with an inverse square potential on a metric cone of dimension greater or equal to 3. The definition of the Riesz transform involves the Laplacian on the cone. However, the cone is not a manifold at the cone tip, so we initially define the Laplacian away from the cone tip, and then consider its self-adjoint extensions. The Friedrichs extension is adopted as the definition of the Laplacian. Using functional calculus, we can express the Riesz transform in terms of the resolvent kernel of the Schroedinger operator. Therefore we construct and at the same time collect information about this resolvent kernel, and then use the information to study the boundedness of the Riesz transform. The two most interesting parts in the construction of the resolvent kernel are the behaviours of the kernel as both the left and right variables approach the cone tip, and as both the left and right variables approach infinity. To study them, a process called the blow-up is performed on the domain of the kernel. We use the b-calculus to study the kernel near the cone tip, while the scattering calculus is used near infinity. The main result of this thesis provides a necessary and sufficient condition on p for the boundedness of the Riesz transform on the space of L-p functions on the metric cone. When the potential function is positive, we have shown that the lower threshold is 1, and the upper threshold is strictly greater than the dimension d; when the potential function is negative, we have shown that the lower threshold is strictly greater than 1, and the upper threshold is strictly between 2 and d. Our results for p less or equal to 2 are contained in the work of J. Assaad, but we use different methods in this thesis. Our boundedness results for p greater or equal to d over 2 for positive inverse square potentials, and for p greater than 2 for negative inverse square potentials, are new

Valuing Compromise for the Common Good

Pursuing the common good in a pluralist democracy is not possible without making compromises. Yet the spirit of compromise is in short supply in contemporary American politics. The permanent campaign has made compromise more difficult to achieve, as the uncompromising mindset suitable for campaigning has come to dominate the task of governing. To begin to make compromise more feasible and the common good more attainable, we need to appreciate the distinctive value of compromise and recognize the misconceptions that stand in its way. A common mistake is to assume that compromise requires finding the common ground on which all can agree. That undermines more realistic efforts to seek classic compromises, in which each party gains by sacrificing something valuable to the other, and together they serve the common good by improving upon the status quo. Institutional reforms are desirable, but they, too, cannot get off the ground without the support of leaders and citizens who learn how and when to adopt a compromising mindset

A Density Peak-Based Clustering Approach for Fault Diagnosis of Photovoltaic Arrays

Fault diagnosis of photovoltaic (PV) arrays plays a significant role in safe and reliable operation of PV systems. In this paper, the distribution of the PV systems’ daily operating data under different operating conditions is analyzed. The results show that the data distribution features significant nonspherical clustering, the cluster center has a relatively large distance from any points with a higher local density, and the cluster number cannot be predetermined. Based on these features, a density peak-based clustering approach is then proposed to automatically cluster the PV data. And then, a set of labeled data with various conditions are employed to compute the minimum distance vector between each cluster and the reference data. According to the distance vector, the clusters can be identified and categorized into various conditions and/or faults. Simulation results demonstrate the feasibility of the proposed method in the diagnosis of certain faults occurring in a PV array. Moreover, a 1.8 kW grid-connected PV system with 6×3 PV array is established and experimentally tested to investigate the performance of the developed method

Parameter extraction of PV models using an enhanced shuffled complex evolution algorithm improved by opposition-based learning

Accurate and efficient parameter extraction of PV models from I-V characteristic curves is significant for modeling, evaluation and fault diagnosis of PV modules/arrays. Recently, a large number of algorithms are proposed for this problem, but there are still some issues like premature convergence, low accurate and instability. In this paper, a new improved shuffled complex evolution algorithm enhanced by the opposition-based learning strategy (ESCE-OBL) is proposed. The proposed algorithm improves the quality of the candidate solution by the opposition-based learning strategy. Moreover, the basic SCE algorithm evolves with the traditional competition complex evolution (CCE) strategy, but it converges slowly and is prone to be trapped in local optima. In order to improve the exploration capability, the complex in the basic SCE is evolved by a new enhanced CCE. The ESCE-OBL algorithm is compared with some state-of-the-art algorithms on the single diode model (SDM) and double diode model (DDM) using benchmark I-V curves data. The comparison results demonstrate that the proposed ESCE-OBL algorithm can achieve faster convergence, stronger robustness and higher efficiency

An intelligent fault diagnosis method for PV arrays based on an improved rotation forest algorithm

With the exponential growth of global photovoltaic (PV) power capacity, it is essential to monitor, detect and diagnose the faults in PV arrays for optimal operation. This paper presents an improved rotation forest (RoF) algorithm classifiers ensemble hybridized with extreme learning machine (ELM) for fault diagnosis of PV arrays, which mainly consists of feature selection and classification. In the feature selection step, all the attributes are ranked by the ReliefF algorithm and the top-ranked attributes are chosen to create the new training data subset. In the classification step, the base classifier decision tree of the RoF is replaced by the extreme learning machine to form a new hybrid RoF-ELM ensemble classifier. In the RoF-ELM algorithm, the feature space is first split into several subspaces and the best number of feature subsets is found through the traversal search method. Then, the bootstrap algorithm is employed to carry out bootstrap resampling for each feature subspace, and the principal component analysis (PCA) is then used to transform the resampled samples. Finally, the ELM base classifier is exploited to build each classification model and the final decision is determined by the simple voting approach. By combining the RoF ensemble method with the ELM classifier, the proposed RoF-ELM algorithm not only overcomes the overfitting problem of the basic RoF algorithm, but also improves the generalization ability of the basic ELM. In order to experimentally verify the proposed approach, different types and levels of faults have been created in a laboratory small scale grid-connected PV power system to obtain the fault data samples. Experimental results demonstrate that the RoF-ELM can achieve higher diagnosis accuracy and reliability compared to the basic RoF and ELM algorithms

22. 栃木県上都賀地区における無菌性髄膜炎,特にその不全型といわれる「夏カゼ」について(第65回日本小児科学会千葉地方会総会 第446回千葉医学会例会)

RNA-seq data overview. (XLS 7 kb

学会抄録

Tissue Composition. (XLS 6 kb