We consider geometric random graphs where n points are distributed independently on the unit interval [0,1] according to some probability distribution function F with density function f. Two nodes communicate with each other if their distance is less than some transmission range. For this class of random graphs, we survey results concerning the existence of zero-one laws for graph connectivity, the type of the zero-one law obtained under specific assumptions on the density function f, the form of its critical scaling and its dependence on f, and the width of the corresponding phase transitions. This is motivated by the desire to understand how node distribution affects the critical transmission range as specified by the disk model. Engineering implications are discussed for power allocation.

The purpose of this study was to discover the major elements of effective distance instruction. The participants in the study were 525 students enrolled in North Taiwanese colleges and universities who had experience in asynchronous distance instruction. A student questionnaire of affecting factors in asynchronous distance instruction was the instrument for the study. The questionnaire identified five major elements in asynchronous distance instruction, namely abundant material design, the strategies of the course activities, learners' management style, the technological knowledge of the learner, the quality of the system and the Internet. Results indicated that the quality of the system and the Internet were the most important elements of this type of instruction. Demographic variables also affected the results. The findings specifically indicated that learners' management style had a significant relationship with gender. Additionally, age differences affected the responses received in the categories of learners' management style, material design, and technological knowledge.

Knowledge of in-situ stresses is essential for designing underground structures, exploiting oil and gas fields, developing geothermal resources, and studying mechanisms of earthquake occurrences. However, the magnitude of in-situ stresses, especially, the magnitude of maximum horizontal stress, compared with other properties of rock, is difficult to measure directly. Therefore, it is only possible to deduce the in-situ stresses from measurements results of some indirect methods including fracturing test, leak off test (LOT), strain relief approach, or empirical correlations. For each of these methods, there are factors such as borehole location, borehole orientation, and pore fluid conditions that will interference their effective applications. Even the most widely used minimum principle stress determination technique, the LOT, still has disadvantages under certain circumstances: it is commonly performed in low permeable formations but not applicable for high porous rock; most of the LOT will fracture the formation and possibly contaminate underground water due to the intrusion of untreated fracturing fluid; the technique is not cost-effective and is applied to only limited wells in an oilfield. This research mainly focuses on developing a new direct inversion approach to estimate in-situ stresses. Two mathematical models were constructed and investigated in this inversion method: circular borehole model and elliptical borehole model. The advantage of this methodology is that, the inputs are relatively easier and economical to obtain compared other methods. Data required for the inversion modeling includes mud pressure, pore pressure, overburden stress, well azimuth, well inclination, and borehole axis ratio, which are either available or are able to be conveniently calculated from logging data in most of the wells. The methodology has been applied to a field case in Appalachian Basin in the USA. It is feasible to estimate in-situ horizontal stresses from the elliptical borehole of arbitrary well trajectory from drilling data using the inversion method. The stress direction calculated by circular borehole model is consistent with field observation; however, the magnitudes of in-situ stresses vary from circular model to elliptical borehole model. The research shows that even a small amount of 2% axis difference in elliptical borehole in the case study, will cause difference of 5% to 10% in the estimation of horizontal stresses; elliptical borehole based inversion can provide relatively more consistent results with the reported in-situ stresses in the area and the stresses estimated from hydraulic fracturing treatment. The error of the calculation model mainly comes from caliper reading and the values estimated from log data such as pore pressure and overburden stress. The measurement accuracy of four-arm caliper log contributes a large portion of the total error since the caliper log cannot precisely reveal the deformation of borehole due to formation caving, sloughing, and mud cake. There are limitations of this inversion method that future research should be focused on. The assumption of isotropic rock formation in current inversion model is not able to calculate anisotropic in-situ stresses; moreover, the model is not suitable for relatively thicker formations.