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.

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

In this paper, a self-tuning adaptive neural controller strategy for unknown nonlinear system is presented. The system considered is described by an unknown NARMA-L2 model and a feedforward neural network is used to learn the model with two stages. The first stage is learned off-line with two configuration serial-parallel model & parallel model to ensure that model output is equal to actual output of the system & to find the jacobain of the system. Which appears to be of critical importance parameter as it is used for the feedback controller and the second stage is learned on-line to modify the weights of the model in order to control the variable parameters that will occur to the system. A back propagation neural network is appl

This study offers a new Mixed Meta Heuristics algorithm (HGSABAT) for estimating the parameter values of each of the six categories of Non-Linear regression models examined (Misrald, Meyer4, Meyer7, Militky4, Militky2, and MGH09) by combining the Gravitational Search Algorithm and Bat Algorithm. Some models have different numbers of parameters. For example, the Misrald and Militky2 models of the Non-Linear Regression model have two parameters (Bl, B2). In contrast, the MGH09 and Militky4 models have four parameters (MGHl, MGH2, MGH3, and MGH4), in which location as the Meyer4 and Meyer7 models have three attributes (Meyerl, MGH2, and MGH3). To examine the effectiveness of the suggested Hybrid Meta Heuristics algorithm (HGSABAT), a simulatio

The refractive index sensors based on tapered optical fiber are attractive for many industries due to sensing capability in a variety of application. In this paper, we proposed a refractive index sensor based on multicore fiber (MCF) sandwiched between two standard single mode fibers (SMF). The sensor consisting of three sections, SMF- MCF-SMF is structurally simple and can be easily produced by joining these parts. The MFC contains seven cores and these cores are surrounded by a single cladding. The sensing region is obtained by tapering the MCF section where the evanescent field is generated. The single mode propagating along the SMF is stimulated at the first joint and is coupled to the cladding modes. These modes interfere with the core

A simple all optical fiber sensor based on multimode interference (MMI) for chemical liquids sensing was designed and fabricated. A segment of coreless fiber (CF) was spliced between two single mode fibers to buildup single mode-coreless-single mode (SCS) structure. Broadband source and optical signal analyzer were connected to the ends of SCS structure. De-ionized water, acetone, and n-hexane were used to test the performance of the sensor. Two influence factors on the sensitivity namely the length and the diameter of the CF were investigated. The obtained maximum sensitivity was at n-hexane at 340.89 nm/RIU (at a wavelength resolution of the optical spectrum analyzer of 0.02 nm) when the diameter of the CF reduced from 125 μm to 60 μ

This research aims at building a proposed training program according to the self-regulated strategies for the mathematics teachers and to identify the effect of this program on relational Mathematics of teachers. The sample of the research was (60) Math teachers; (30) teachers as experimental group and (30) teachers as control group. The results of the current research reacheded that the proposed training program according to some self-managed learning strategies, meets the needs of trainees with remarkable effectiveness to improve the level of their teaching performance to achieve the desired goals. Training teacher according to self-managed learning strategies is effective in bringing about the transition of training to their students

Rock engineers widely use the uniaxial compressive strength (UCS) of rocks in designing
surface and underground structures. The procedure for measuring this rock strength has been
standardized by both the International Society for Rock Mechanics (ISRM) and American Society
for Testing and Materials (ASTM), Akram and Bakar(2007).
In this paper, an experimental study was performed to correlate of Point Load Index ( Is(50))
and Pulse Wave Velocity (Vp) to the Unconfined Compressive Strength (UCS) of Rocks. The effect
of several parameters was studied. Point load test, Unconfined Compressive Strength (UCS) and
Pulse Wave Velocity (Vp) were used for testing several rock samples with different diameters.
The predicted e