Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities

We study a mathematical model describing the dynamics of dislocation densities in crystals. This model is expressed as a one-dimensional system of a parabolic equation and a first order Hamilton-Jacobi equation that are coupled together. We show the existence and uniqueness of a viscosity solution among those assuming a lower-bound on their gradient for all time including the initial data. Moreover, we show the existence of a viscosity solution when we have no such restriction on the initial data. We also state a result of existence and uniqueness of an entropy solution of the system obtained by spatial derivation. The uniqueness of this entropy solution holds in the class of ``bounded from below'' solutions. In order to prove these results, we use a relation between scalar conservation laws and Hamilton-Jacobi equations, mainly to get some gradient estimates. This study takes place on $\R$, and on a bounded domain with suitable boundary conditions

An integrated MEWMA-ANN scheme towards balanced monitoring and accurate diagnosis of bivariate process mean shifts

Various artificial neural networks (ANN)-based pattern recognition schemes have been developed for monitoring and diagnosis of bivariate process variation in mean shifts. In comparison with the traditional multivariate statistical process control (MSPC) charts, these advanced schemes generally perform better in identifying process mean shifts and provide more effective information towards diagnosing the root causes. However, it seemly less effective for multivariate quality control (MQC) application due to disadvantages in reference bivariate patterns and imbalanced monitoring performance. To achieve ‘balanced monitoring and accurate diagnosis’, this study proposes an integrated multivariate exponentially weighted moving average (MEWMA)-ANN scheme for two-stages monitoring and diagnosis of some reference bivariate patterns. Raw data and statistical features input representations were applied into training of the Synergistic-ANN recognizer for improving patterns discrimination capability. The proposed scheme has resulted in better monitoring – diagnosis performances with smaller false alarm, quick mean shift detection and higher diagnosis accuracy compared to the basic scheme

The Peierls-Nabarro model as a limit of a Frenkel-Kontorova model

We study a generalization of the fully overdamped Frenkel-Kontorova model in dimension $n\geq 1.$ This model describes the evolution of the position of each atom in a crystal, and is mathematically given by an infinite system of coupled first order ODEs. We prove that for a suitable rescaling of this model, the solution converges to the solution of a Peierls-Nabarro model, which is a coupled system of two PDEs (typically an elliptic PDE in a domain with an evolution PDE on the boundary of the domain). This passage from the discrete model to a continuous model is done in the framework of viscosity solutions

Some Aspects of Shi'ite Propaganda Under the Fatimids in Egypt.

Stress is particularly laid upon two aspects of Fatimid propaganda in Egypt, viz. Education and Literature. (1) Chapter I. An account of the Shi'ite propaganda up to the rise and establishment of the Fatimid Khilafah in N. Africa. The beginning of the Shi'ite propaganda in the reign of 'Uthman, the third Khalifah, its continuation during the Umayyad dynasty, and the passing of the right to the imamah from the 'Alids to the 'Abbasids, and their mutual hostilities after the establishment of the 'Abbasid Khilafah. The failure of subsequent Shi'ite propaganda to establish an independent 'Alid empire in the East, and the transference of this propaganda to the West (N. Africa) and the causes which favoured its success there. An account of Abu 'Abdi-llah's career of conquest in N. Africa up to the establishment of the Fatimid Khilafah. Chapter II. A discussion of the genealogy of the Fatimids. The importance of Egypt for the Fatimids in the efforts to spread their Shi'ite doctrines under the following headings: (a) the geographical situation of Egypt, between the East where Shi'ite propaganda had failed and the West where it succeeded in establishing an independent empire. (b) the wealth and tranquility of Egypt as compared with Muslim dominions in the East. (c) these circumstances as favouring the establishment the Fatimid authority in Egypt and in the East soon after their conquest of Egypt. (d) Egypt, rather than the Maghrib made by the Fatimid centre of Shi'ite propaganda. Chapter III. Educational propaganda: The organisation by the Fatimids of their propaganda in the mosques and libraries; the royal palace becomes the centre of Shi'ite propaganda, which is carried on by the Chief Da'i and his assistants and supported by the Fatimid Khalifahs themselves. Chapter IV. Literary Propaganda : The part played by the poets, scribes and learned men in the spread of the Fatimid propaganda and the influence upon these learned men, and the poets in particular, were of the lavish grants made by the Fatimid Khalifahs and their wazirs and other men of high status. Each separate reign of the Fatimid Khalifahs is considered in detail

Assessment of Productivity Status Using Carlson’s TSI and Fish Diversity of Goronyo Dam, Sokoto State, Nigeria

Goronyo Dam is the largest lentic waterbody in Sokoto, it was constructed to serve as flood control and used for irrigation activities. The study was conducted to evaluate productivity status and fish diversity of Goronyo Dam in 2016. Water samples were collected monthly from the Dam at two sampling sites (Upstream and Downstream). Water samples were collected using sterilized sampling bottles and analyzed in the Laboratory for physicochemical variables and the diversity of fish was evaluated through the use of a structured questionnaire. Depth and transparency were the only variables that did not show any statistically significant difference between the months. Productivity status of the dam was evaluated using Carlson’s Trophic State Index. The downstream has high TSI value of 16.54 compared to upstream with 13.00. A diversity of fishes from the shows that 3 species were more abundant in the dam, these were; Mormyrops species, Alestes species and Clupeid species. Factors contributed to the survival of fish species were an abundance of water and plankton in the dam. While factors affecting the distribution of fish species were pollution and predation

Transfer of Training Among Teachers Attending Short Courses

The transfer of training (the application of training in the workplace) is a critical issue faced by all organizations. This issue is concerned with the impact of training on employees and the organization. Trainee's characteristics, training design and organizational support are identified in many studies as the three major factors affecting the transfer of training. This study is aimed at investigating the transfer of training on the Art of Learning courses organized by the Education Department of Pahang. The objectives of the study were: (1) to identify the outcomes of the Art of Learning course; (2) determine the level of learning and transfer of training among course participants; (3) to determine the relationship between the transfer of training and trainee's characteristic, training design and organizational support. Ninety-four teachers out of 120 participants who attended three separate training programs were interviewed. They were asked to rate ten questions regarding trainee's characteristics, twenty questions each regarding training transfer, training design and organizational support. Data were gathered through personal interviews using questionnaires specifically designed for these studies. Three relationships were tested by using Pearson Product - Moment Correlation. Frequenc:ies, mean, median, percentages and t-test were also used in the analysis. The findings from the study showed that there were changes in the level of knowledge, level of skills and level of ability to solve problems among participants after attending training program. However the levels of training transfer among the participants were low . The study also found that the score on trainee's characteristic and training design were high. The score on organizational support was less than the median. The findings indicated a positive and significant correlation between: (1) transter of training and trainee' characteristics, (2) transfer of training and training design. However the finding did not show any relationship between transfer of training and organizational support