This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving the area under the curve concept. We found that on...

This paper addresses an integral sliding mode control approach for automatic generation control (AGC) of a single area power system. Genetic algorithm (GA) is employed to search the parameters of the sliding surface. The proposed design is investigated for AGC of a single area power system, made up of reheated thermal and gas power generations. Compared with the GA-based proportion-integral (PI...

We show that the Lusin area integral or the square function on the unit ball of C, regarded as an operator in weighted space L(w) has a linear bound in terms of the invariant A2 characteristic of the weight. We show a dimension-free estimate for the “area-integral” associated to the weighted L(w) norm of the square function. We prove the equivalence of the classical and the invariant A2 classes.

The grasping control problem for a hyperredundant arm is studied. Frist, dynamic model of the arm is analyzed. The control problems are divided in the subproblems: the position control in a desired reaching area, the control of the arm around the object-load and the force control of grasping. The difficulties determined by the complexity of the non-linear integral-differential equations are avo...

The representation of curves by integral invariant signatures is an important step inshape recognition and classification. Integral invariants are preferred over their differential counter-parts due to their robustness with respect to noise. However, in contrast to differential invariants ofcurves, it is currently unknown whether integral signatures offer unique representations of c...