The union of two semigroups has been studied for its interesting\nproperties during the years. Constructing the new automatic\nsemigroups from the existing semigroups may be of interest because\nof their applicability in many branches of science, so in the case\nwhen the union of two finitely generated semigroups is a\nsemigroup, we give here a necessary and sufficient condition that\nthe union is automatic. Also, we here study the behaviour of\ndecomposable semigroups as a disjoint union of their\nsub-semigroups, indeed, we give a necessary and sufficient\ncondition for the automaticity of a semigroup which is the\ndisjoint union of its sub-semigroups.

Geometric Programming is a special type of nonlinear optimization problems. One of multi-objective programming problems encountered in the optimization problem is the multi-objective geometric programming problem. In this study, a method is developed based on Kuhn-Tucker Conditions and Taylor series expansion to solve the multi-objective posynomial geometric programming problems. The results obtained are compared to the results of the weighted mean method used to solve the multi-objective posynomial geometric programming problems.

In recent years there is tremendous growth of research focused on unmanned aerial vehicle stabilization and its control. This research article focused on control system design for the stabilization of Roll angle of Fix –wing UAV. There are several different types of UAVs available in the market, but fixed-wing UAVs is the most common one which is used for surveillance and rescue applications. Like other UAVs, Fix-wing UAVs are also non linear in nature and its stabilization during flight is most critical task. In lateral autopilot controlling of Fixing UAV the roll angle stabilization play very significant part and its proper controlling is essential for UAV stability. In this research work PID with Extended kalman Filter control algorithm is proposed for stabilization of roll angle of fixed-wing UAV under uncertainty conditions. PID parameters are tuned in such a way that the roll stabilized as fast as possible and within limited overshoot and the addition of extended kalman filter (EKF) makes UAV more stable by canceling the noises produced by the system and sensors. Simulation results proved that, the proposed control technique works well and produce effective results for fixed-wing UAV’s roll angle stabilization.

Non-Ignorable missing values are often a great challenge for data mining analysts. Imputation of such missing values requires models which vary depending on the dataset and distribution of values within the dataset. Statistical techniques should be implemented on the outcome of the model to impute the values. The paper proposes a new algorithm called Bayesian Genetic Algorithm (BAGEL) which combines both Bayesian principles and Genetic Algorithm. The model is created by the Bayesian method using the available values and it drives the Genetic Algorithm to find the most suited value to be substituted for missing value. BAGEL is implemented on real datasets and the results are reported in this paper. It is found that BAGEL imputes both discrete and continuous missing values with more accuracy than other existing methods at different missing rates ranging from 5% to 50%.

Different stock markets are interrelated due to the common fundamentals which influence the movement in the respective indices. Using daily stock returns from 2000 to 2010 for 21 countries paired with Pakistan, and using the Geweke methodology, the paper investigates the degree to which these stock markets are integrated with the Pakistani stock market. The paper also explores the factors that have an effect on the level of economic integration by applying fixed effect model. The result demonstrates statistically significant and high percentage of contemporaneous association between the 21 economies of the world and Pakistan. Greater comovement was observed between the equity markets during the period when Pakistani capital market and economy experience performance but less comovement was noted when KSE was under crises. In broad, an elevated export share by other economies to Pakistan has good impact on stock market comovement as well as a larger difference in inflation rates, has an inverse effect on stock market comovement between pairs of countries. On the other hand volatility in bilateral exchange rate also influences stock market comovement.