Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

This paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different type

In high-dimensional semiparametric regression, balancing accuracy and interpretability often requires combining dimension reduction with variable selection. This study intro- duces two novel methods for dimension reduction in additive partial linear models: (i) minimum average variance estimation (MAVE) combined with the adaptive least abso- lute shrinkage and selection operator (MAVE-ALASSO) and (ii) MAVE with smoothly clipped absolute deviation (MAVE-SCAD). These methods leverage the flexibility of MAVE for sufficient dimension reduction while incorporating adaptive penalties to en- sure sparse and interpretable models. The performance of both methods is evaluated through simulations using the mean squared error and variable selection cri

: In this study, a linear synchronous machine is compared with a linear transverse flux machine. Both machines have been designed and built with the intention of being used as the power take off in a free piston engine. As both topologies are cylindrical, it is not possible to construct either using just flat laminations and so alternative methods are described and demonstrated. Despite the difference in topology and specification, the machines are compared on a common base in terms of rated force and suitability for use as a generator. Experience gained during the manufacture of two prototypes is described.

   This study aimed to evaluate the reservoir petrophysical properties (porosity, water saturation, and permeability) for optimal flow unit assessment within the Sadi Formation. Utilizing open hole logging data from five wells, the Sadi formation was divided into two rock units. The upper unit (A) is 45-50 meters thick, mainly consisting of limestone, mainly consisting of shaly limestone at the lower part. The lower unit (B) has a thickness of approximately 75-80 meters and is primarily composed of limestone, further subdivided into three subunits (B1, B2, B3). The average water resistivity is 0.04 ohm-m, and the average mud filtrate resistivity is 0.06 ohm-m. The Pickett plot was utilized to determine Archie parameters (tortuosit

Low- and medium-carbon structural steel components face random vibration and dynamic loads (like earthquakes) in many applications. Thus a modification to improve their mechanical properties, essentially damping properties, is required. The present study focuses on improving and developing these properties, significantly dampening properties, without losing the other mechanical properties. The specimens used in the present study are structural steel ribbed bar ISO 6935 subjected to heating temperatures of (850, 950, and 1050) ˚C, and cooling schemes of annealing, normalizing, sand, and quenching was selected. The damping properties of the specimens were measured experimentally with the area under the curve for the loadi