Some harmonic functions for killed Markov branching processes with immigration and culling

For a continuous-time Bienaym\'e-Galton-Watson process, $X$, with immigration and culling, $0$ as an absorbing state, call $X^q$ the process that results from killing $X$ at rate $q\in (0,\infty)$, followed by stopping it on extinction or explosion. Then an explicit identification of the relevant harmonic functions of $X^q$ allows to determine the Laplace transforms (at argument $q$) of the first passage times downwards and of the explosion time for $X$. Strictly speaking, this is accomplished only when the killing rate $q$ is sufficiently large (but always when the branching mechanism is not supercritical or if there is no culling). In particular, taking the limit $q\downarrow 0$ (whenever possible) yields the passage downwards and explosion probabilities for $X$. A number of other consequences of these results are presented

The North Carolina Racial Justice Act: An Essay on Substantive and Procedural Fairness in Death Penalty Litigation

Long term supporting schemes for photovoltaic (PV) system installation have led to accommodating large numbers of PV systems within load pockets in distribution grids. High penetrations of PV systems can cause new technical challenges, such as voltage rise due to reverse power flow during light load and high PV generation conditions. Therefore, new strategies are required to address the associated challenges. Moreover, due to these changes in distribution grids, a different response behavior of the distribution grid on the transmission side can be expected. Hence, a new equivalent model of distribution grids with high penetration of PV systems is needed to be addressed for future power system studies. The thesis contributions lie in three parts. The first part of the thesis copes with the PV modelling. A non-proprietary PV model of a three-phase, single stage PV system is developed in PSCAD/EMTDC and PowerFactory. Three different reactive power regulation strategies are incorporated into the models and their behavior are investigated in both simulation platforms using a distribution system with PV systems. In the second part of the thesis, the voltage rise problem is remedied by use of reactive power. On the other hand, considering large numbers of PV systems in grids, unnecessary reactive power consumption by PV systems first increases total line losses, and second it may also jeopardize the stability of the network in the case of contingencies in conventional power plants, which supply reactive power. Thus, this thesis investigates and develops the novel schemes to reduce reactive power flows while still keeping voltage within designated limits via three different approaches: 1. decentralized voltage control to the pre-defined set-points 2. developing a coordinated active power dependent (APD) voltage regulation Q(P) using local signals 3. developing a multi-objective coordinated droop-based voltage (DBV) regulation Q(V) using local signals In the third part of the thesis, furthermore, a gray-box load modeling is used to develop a new static equivalent model of a complex distribution grid with large numbers of PV systems embedded with voltage support schemes. In the proposed model, variations of voltage at the connection point simulate variations of the model’s active and reactive power. This model can simply be integrated into load-flow programs and replace the complex distribution grid, while still keeping the overall accuracy high. The thesis results, in conclusion, demonstrate: i) using rms-based simulations in PowerFactory can provide us with quite similar results using the time domain instantaneous values in PSCAD platform; ii) decentralized voltage control to specific setpoints through the PV systems in the distribution grid is fundamentally impossible due to the high level voltage control interaction and directionality among the PV systems; iii) the proposed APD method can regulate the voltage under the steady-state voltage limit and consume less total reactive power in contrast to the standard characteristic Cosf (P) proposed by German Grid Codes; iv) the proposed optimized DBV method can directly address voltage and successfully regulate it to the upper steady-state voltage limit by causing minimum reactive power consumption as well as line losses; v) it is beneficial to address PV systems as a separate entity in the equivalencing of distribution grids with high density of PV systems.Engineering, Systems and ServicesTechnology, Policy and Managemen

Trial By Jury Involving Persons Accused of Terrorism or Supporting Terrorism

This chapter explores issues in jury trials involving persons accused of committing acts of international terrorism or financially or otherwise supporting those who do or may commit such acts. The jury is a unique institution that draws upon laypersons to decide whether a person charged with a crime is guilty or innocent. Although the jury is instructed and guided by a trial judge and procedural rules shape what the jury is allowed to hear, ultimately the laypersons deliberate alone and render their verdict. A basic principle of the jury system is that at the start of trial the jurors should have open minds and regard the accused innocent until proven guilty. The chapter raises issues about jurors\u27 assumptions of innocence in the aftermath of terrorist bombings in the United States, England, Bali, Spain and elsewhere when persons are persons accused of committing acts of terrorism or indirectly supporting terrorists through financing organizations associated with terrorism. A study of a United States trial involving charges of supporting terrorism is used to illustrate the problem, but the thesis of this chapter is that the basic issues apply to trials that might be held in England, Australia, Canada or other countries with jury systems

Experimental Simulations and Tort Reform: Avoidance, Error and Overreaching in Sunstein Et Al.’s ‘Punitive Damages’

This article addresses tort reform claims made in Cass R. Sunstein, et al.\u27s Punitive Damages: How Juries Decide (2002)and related articles, research that was largely underwritten by the Exxon Corporation. Based upon a series of simulation experiments, those authors have made a general claim that juries are incapable of making coherent judgments about punitive damages. In this article I raise serious methodological problems bearing on the validity of the research, and, therefore, its ability to provide judges and legislators with useful information about juries and punitive damages