Most of the farmers of irrigated areas cultivate their fields with simple cultivator which creates a hard pan in the subsoil due to tilling the soil at same depth with same implement which has adverse effect on crop growth and yield. In addition to tillage nitrogen management is a key factor for better crop growth and yield. Two field experiments were conducted to evaluate the “impact of different tillage systems, nitrogen rates and time of application on growth, yield attributes, grain yield, quality and nitrogen uptake of hybrid maize” at the Agronomic Research Area, University of Agriculture, Faisalabad during 2008 and 2009. Both the experiments were laid out on a randomized complete block design (RCBD) with split plot arrangement using three replications, in a net plot size of 4.5m x 10m. In first experiment three tillage systems (conventional tillage, tillage with mouldboard plough + 2-cultivation and tillage with chisel plough + 2-cultivation) were kept in main plots and nitrogen levels (100, 150 and 200 kg N ha-1) in sub-plots. Different tillage systems significantly influenced soil physical properties, growth and yield characteristics as well as maize yield. Increasing tillage intensity resulted to improved soil porosity and reduced soil bulk density which led to higher crop yield. Chisel ploughed plots produced higher leaf area index (LAI), crop growth rate (CGR), leaf area duration (LAD), yield and yield components in comparison with other tillage systems. Maize yield with chisel tilled plots was 18% and 9% higher than mould board ploughed and conventionally tilled plots, respectively. Generally differences between different nitrogen application rates were more pronounced, increasing nitrogen application rate had positive impact on growth, yield components, yield and kernel quality. Increased LAI, CGR, grains weight per cob, 1000-grain weight and grain yield was recorded with 200 kg ha-1 nitrogen application. Maize yield with 200 kg ha-1 nitrogen application was 17% and 8.50% higher than 100 and 150 kg ha-1 nitrogen application respectively. The N uptake at 200 kg ha-1 nitrogen application was 240.88 kg ha-1 which was higher in comparison with other nitrogen treatments. Nitrogen application showed positive association with protein contents but negative association with grain oil and starch contents. In the second experiment different systems and nitrogen application timings were allotted to main plots and subplots respectively. Physiological, agronomic and qualitative traits in maize varied with nitrogen application timings. Physiological attributes like LAI and CGR was higher with nitrogen application in three splits i.e. 1/3 at sowing + 1/3 at knee height + 1/3 at tasseling, while the lowest was recorded with nitrogen application in two splits i.e. 1⁄2 at knee height + 1⁄2 at tasseling. The yield contributing parameters such as grains weight per cob and 1000-grain weight were found higher in plots fertilized with nitrogen in three splits. Similarly the highest grain yield was recorded in plots fertilized with nitrogen in three splits in comparison with other nitrogen treatments. The higher LAI, CGR and maize yield with nitrogen application in three splits was probably due to more availability of nitrogen at critical growth stages as compared to other nitrogen application timings. In addition to physiological and agronomic traits, nitrogen application at different growth stages also significantly affected the maize quality. Nitrogen application in three splits resulted to higher grain protein contents (8.23%) and (8.16%) during 2008 and 2009, respectively while the lowest grain protein contents recorded where all the nitrogen was applied at the sowing time. The higher protein contents in 2008 were probably due to drier environments at grain development as compared to 2009. Nitrogen uptake was also higher with nitrogen application in three splits while the lowest N uptake was recorded in sole application. Nitrogen uptake was higher during 2009, while lower during 2008 which might be attributed to nitrogen losses through leaching due to high rainfall at seedling stage during 2008. On the basis of economic analysis benefit-cost ratio (BCR) was calculated for both the experiments which showed that maize grown with nitrogen application @ 200 kg ha-1 in three splits by ploughing the soil with chisel plough was economical and gave more profit compared with other treatments. However, it is concluded that for obtaining higher maize yield and net income maize hybrid pioneer 31R88 should be grown with 200 kg ha-1 nitrogen application in three splits by preparing the field with chisel plough.
Hadith and Science of Hadith are the terms used by specialists of Hadith known as Mohaditeen. A hadith is a recorded statement, action or approval of the Prophet Muhammad (S.A.W). It is considered as the second primary source of Islamic law after Quran. It is also a part of revelation. Prophet Muhammad (S.A.W) described it through his words. The science of hadith examplifies the principles with which a specialist in the field of Hadith evaluates the authenticity and accuracy of narrations. In the past there were two specific and developmental stages for the Books of Hadith terminology. In its 1st stage, the Scholars focused on the compilation of the statements of earlier scholars, quoting the expressions they had used without evaluating those terms or suggesting terms applicable to those expressions. This methodology was adopted by the earlier scholars such as Yaḥyā ibn Ma`īn, `Alī ibn al-Madīnī, Muslim ibn al-Ḥajjāj, and Al – Tirmidi. In the second period the Authors cited the quoted statements of the earlier works and began the collection and codification of relevant terms. In this period, the specific Principles were established. Examples of books authored in this manner are: Ma`rifah `Ulūm al-Ḥadīth by al-Ḥākim, Al-Kifāyah by al-Khaṭīb alBaghdādī and the Introduction of Ibn al-Ṣalāḥ. In this article the two major types of science of Hadith have been mentioned, Rewayat-ul-Hadith and Derayat-ulHadith. Its definition and historical background has been described.
The estimates of the Maximum Likelihood estimation method are the estimates of the global maximum likelihood function, by definition. However, the present study showed empirically that the likelihood function of the GARCH model is multimodal. Due to the presence of multimodality in the likelihood function leads to a difference in estimates at local and global maxima, and hence, Maximum Likelihood estimation methods can have unstable performance in such situations. Therefore, it will face the problem in inference and prediction, due to the difference in estimates at local and global maxima(s). Two estimation methods are chosen from the Frequentist and the Bayesian approach, respectively, to measure the significance of the difference in estimated parameters due to the presence of multimodality in the likelihood function. Besides, to calculate the level of difference, a standard method of Monte Carlo simulation method is used. The surface plot is constructed by changing the value of the Monte Carlo simulation method to evaluate their performance along the whole surface. these surfaces are then compared within each approach. Subsequently, the preferable algorithms are compared across the Bayesian and Frequentist approaches. For comparison, the present study has calculated bias and variance around the true data generating process. Empirically it is found that in case of Frequentist approach Differential Evolution (DE) algorithm is preferable estimation method for GARCH type models, as compared to Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Because there is multimodality in the likelihood function of the GARCH model, and BFGS uses a single starting value to search maximum point in the likelihood function, and often this single starting value traps into local maxima. Therefore, the estimated parameter at the local and global maxima vary, and hence, inferences and predictions. Conversely, DE uses multiple starting values with multiple chains, due to which it automatically avoid local maxima and converges to global maxima. In the case of the Bayesian approach, Robust Adaptive Metropolis (RAM) is a preferable estimation for GARCH type models as compared to Metropolis Hasting (MH). Because RAM is based on the strategy of adaptive mechanism, i.e., the Markov Chain of the RAM move to the next point, after taking information from the previous point, and finally converge to some particular value of the estimate. While MH use chain of independent nature, i.e., it does not take information while moving from one point to another point in the Markov Chain. After confirming the best estimator from frequentist and the Bayesian approach, this study compared these approaches with each other. Empirically, it is found that the Bayesian approach (RAM) is the preferable estimation method than the Frequentist approach (DE) because the level of bias and variance around the true parameter for RAM is lower than DE. Pakistan Stock Exchange (PSX) is used as a real-world application. Empirically it is found that the Bayesian approach is preferable estimation method than the frequentist approach. Reasons are followed; first, in the frequentist approach estimated parameters are the point estimates, while in the case of the Bayesian approach, the complete distribution of the estimated parameter is obtained at the low cost of simulation. Second, the distribution of the point estimate is hypothetically assumed to be normal, while in case of Bayesian approach it is not valid, i.e., the distribution of the estimates could be skewed in either direction. Therefore, the frequentist approach either over or underestimate the true value of the parameter. Finally, the standard error of the estimates which are obtained through the DE algorithm is more precise as compared to the estimates of BFGS. Therefore, the forecasting based on DE is more accurate about risk and return.