This research aims to solve the basic knowledge problems of undergraduate students who study Calculus 1 for Engineers in the Faculty of Engineering Rajamangala University of Technology Phra Nakhon. Basic Mathematics tutorials are conducted in order to improve their knowledge which leads to increase the efficiency of learning the Calculus 1 for Engineers. The basic mathematics lessons are designed and their efficiency is assessed in the tutored group using the 60/60 criteria. The pretest and posttest are assigned to both tutored and tutorless groups as well as the tutored student satisfactions with thedesigned lessons and the Calculus 1 for Engineers are conducted. The result shows that the efficiency of the designed lessons is 76.60/64.67 which is higher than the criteria; hence they are proper to be used. For the treatment group the posttest grades are higher than the pretest grades significantly (.05) with the effectiveness of 34.67. The comparison of the learning achievement for the Calculus 1 for Engineers shows that the grades of the tutored group are higher than the grades in the tutorless group significantly (.05) as well. The student satisfactions for both the designed lessons and the Calculus 1 for Engineers are at the levels of good and very good.

The conductor of an order is the largest ideal of the ring of integers of a field which is contained in the order. In this paper we characterize conductors in quartic number fields whose norm is a power of unramified prime.

In this research we introduce the notions of fuzzy d-subalgebra and fuzzy d-ideal of a d-algebra with respect to a triangular norm. Then we investigate some related properties

Differential evolution is one of the most efficient optimization algorithms for solving complication problems including single objective multiobjective and many-objective optimization. It is a stochastic population-based search approach for optimization over the continuous space. The main advantages of differential evolution are simplicity robustness and high speed of convergence. The Advanced Fuzzy-based Multiobjective Differential Evolution (AFMDE) that exploits three performance metrics specifically hypervolume spacing and maximum spread to measure the state of the evolution process. The fuzzy inference rules are applied to these metrics in order to adaptively adjust the associated control parameters of the chosen mutation strategy used in AFMDE. The optimization algorithm will stop the evolution process if the number of iterations reaches the stopping criteria which usually is the maximum number of iterations. Then the optimization algorithm delivers the optimal solution founded. However sometimes if the maximum number of iterations is not appropriately defined the found solutions may not be the optimal ones. In case of the optimization algorithm has found the optimal solutions but it must continue the evolution process because the stopping criteria are not met. This can cause unnecessary using of high computational resources and time-consuming. Therefore this research study proposed the stopping criteria based on performance metrics feedback for AFMDE. The efficiency of the proposed criteria combined with AFMDE is evaluated on the well-known ZDT benchmark test suites.