In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

A numerical investigation is adopted for two dimensional thermal analysis of rocket thrust chamber wall (RL10), employing finite difference model with iterative scheme (implemented under relaxation factor of 0.9 for convergence) to compute temperature distribution within thrust chamber  wall (which is composed of Nickel and Copper layers). The analysis is conducted for different boundary conditions: only convection boundary conditions then combined radiation, convection boundary conditions also for  different aspect ratio (AR) of cooling channel. The results show that Utilizing cooling channels of high aspect ratio leads to decrease in temperature variation across thrust chamber wall, while no effects on heat transferred to the

Maximum likelihood estimation method, uniformly minimum variance unbiased estimation method and minimum mean square error estimation, as classical estimation procedures, are frequently used for parameter estimation in statistics, which assuming the parameter is constant , while Bayes method assuming the parameter is random variable and hence the Bayes estimator is an estimator which minimize the Bayes risk for each value the random observable and for square error lose function the Bayes estimator is the posterior mean. It is well known that the Bayesian estimation is hardly used as a parameter estimation technique due to some difficulties to finding a prior distribution.

The interest of this paper is that

Lorraine Hansberry’s A Raisin in the Sun (1959) appeared at the beginning of renewed political activity on the part of the blacks; it is a pamphlet about the dream of recognition of black people and the confusion of purposes and means to reach such recognition. It embodies ideas that have been uncommon on the Broadway stage in any period. Situations such as a black family moving into an all-white neighborhood were not familiar before this time; they were just beginning to emerge. In depicting this so realistically, Hansberry depends more on her personal experience as an African American embittered by social prejudices and discrimination. 

This study analyzes the features of historical and modern mosques in Jordan compared to that of Amman. The architecture of the Jordanian mosques reflects the images of great ancient empires and kingdoms of Europe and the Middle East. This has happened due to the geographical position of the country. From the studies of historians and archaeologists, comparative analysis of planning solutions, the use of plastics and decor of the facades of mosques, and the literature on the construction methods of the mosques allow us to conclude that age-old traditions have been preserved through the establishment of mosques in both the countries. Besides, the emergence of new features in constructing mosques has been observed. We find the influence of

It was Aristotle who first drew attention to the superior quality of literature to the other factual fields of knowledge. Contradicting his predecessor Plato on the issue of „truth,‟ Aristotle believed that „poetry is more philosophical and deserves more serious attention than history: for while poetry concerns itself with universal truths, history considers only particular facts.‟ (1) The critical attention to the disparity between the literary truth and the historical truth grew up throughout ages to flourish in the Renaissance and after with a bunch of distinctive views on this subject. Sir Philip Sidney (1554-1586), for example, found that literature does not offer a literal description of reality but rather a heightened vers

A novel robust finite time disturbance observer (RFTDO) based on an independent output-finite time composite control (FTCC) scheme is proposed for an air conditioning-system temperature and humidity regulation. The variable air volume (VAV) of the system is represented by two first-order mathematical models for the temperature and humidity dynamics. In the temperature loop dynamics, a RFTDO temperature (RFTDO-T) and an FTCC temperature (FTCC-T) are designed to estimate and reject the lumped disturbances of the temperature subsystem. In the humidity loop, a robust output of the FTCC humidity (FTCC-H) and RFTDO humidity (RFTDO-H) are also designed to estimate and reject the lumped disturbances of the humidity subsystem. Based on Lyapunov theo

The aim of this essay is to use a single-index model in developing and adjusting Fama-MacBeth.  Penalized smoothing spline regression technique (SIMPLS) foresaw this adjustment.  Two generalized cross-validation techniques, Generalized Cross Validation Grid (GGCV) and Generalized Cross Validation Fast (FGCV), anticipated the regular value of smoothing covered under this technique. Due to the two-steps nature of the Fama-MacBeth model, this estimation generated four estimates: SIMPLS(FGCV) - SIMPLS(FGCV), SIMPLS(FGCV) - SIM PLS(GGCV), SIMPLS(GGCV) - SIMPLS(FGCV), SIM PLS(GGCV) - SIM PLS(GGCV). Three-factor Fama-French model—market risk premium, size factor, value factor, and their implication for excess stock returns and portfolio return