where σn−1 denotes the surface measure of the unit sphere S n−1 = {z ∈ R : |z| = 1}, and |z| denotes the standard Euclidean norm of z ∈ R. This formula is given in equation (18) on p125 of [Ste1], and it is proved by using the Fundamental Theorem of Calculus to first write f(x) as the integral along any ray emanating from x of the directional derivative of f in the direction of the ray, and the...

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA), H aff Cℓ (d). Our construction includes an analogue of Zelevin-sky's segment representations, a complete combinatorial description of the simple calibrated H aff Cℓ (d)-modules, and a classification of the simple integral H aff Cℓ (d)-modules. Our main tool is an analogue of th...

Safety has being a concern as result of the high rate road accidents and led to development driver assistance system such Active braking, Cruise Control, Lane departure warning lane keeping etc. become very active research area. However, this paper presents performance robustness analysis model predictive control proportional integral derivative for maneuvers an autonomous vehicle using compute...

As the field of control engineering has evolved, its horizons have continually broadened. From regulation with simple proportional-integral-derivative (PID) loops, to model-based control and multivariable schemes, to explicit incorporation of uncertainty in robust and modern control theory, to hybrid and hierarchical architectures, and most recently, to control of and via networks, both theoret...

Considering the high consumption of the air compressors, a control system of screw compressor is designed and implemented to deal with energy saving and localization of mentioned compressor. In this paper the variable speed drive (VSD) control algorithm based on proportional-integral-derivative (PID) controller is optimized to decrease power consumption and more stable motor speed and outlet pr...

This paper addresses an approximation-based anti-windup (AW) control strategy for suppressing the windup effect caused by actuator saturation nonlinearity in proportional–integral–derivative (PID) controlled systems. The effect of actuator constraint is firstly regarded as a disturbance imported to the PID controller. The external disturbance can then be modeled by a linear differential equatio...

This paper addresses an approximation-based anti-windup (AW) control strategy for suppressing the windup effect caused by actuator saturation nonlinearity in proportional–integral–derivative (PID) controlled systems. The effect of actuator constraint is firstly regarded as a disturbance imported to the PID controller. The external disturbance can then be modeled by a linear differential equatio...

In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional matrices. As a byproduct of this we will prove that all the operations of the Cartan calculus, such as the exterior derivative, the interior contraction with a vecto...

IN THE PERPETUALLY RESOURCE-STARVED environment of public health, where each disease or risk factor has to fight for a scrap of the federal budget, it is easy to forget how fast progress can be made when appropriate policy attention and resources are marshaled to solve a problem. The natural response of public health professionals to the starvation diet is to maintain low expectations. But thos...