Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric
Abstract
Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t
... Show MoreAbstract: In this paper, a U-shaped probe with a curvature diameter of half a centimeter was implemented using plastic optical fibers. A layer of the outer shell of the fibers was removed by polishing to a D-section. The sensor was tested by immersing it in a sodium chloride solution with variable refractive index depending on solution concentrations ranging from 1.333 to 1.363. In this design, the sensor experienced a decrease in its intensity as the concentration of the solution increased. The next step The sensor was coated with a thin layer of gold with a thickness of 20 nm, and the sensor was tested with the same solutions which resulted in a shift in wavelengths where the shift in wavelength was 5.37 nm and sensiti
... Show MoreIn this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.
The present studier aims to study the kinetic of reaction at different experimental conditions depending on coliform bacteria concentration and hypochlorite ion. The effects that had been investigated were different of sodium hypochlorite doses, contact time, pH and temperature (20, 29, 37) o C. The water samples were taken from Al-Wathba water treatment plant in Risafa side of Tigris River in Baghdad. The biological tests included the most probable number (M.P.N) for indicating the concentration of coliform bacteria with different contact times and the total plate count (T.P.C) for indicating the amount of colonies for general bacteria. The iodimetry method (chemical test) was used for indicating the concentration of hypochlo
... Show MoreThe nanocrystalline porous silicon (PS) films are prepared by electrochemical etching ECE of p -type silicon wafer with current density (10mA/cm ) and etching times on the formation nano -sized pore array with a dimension of around different etching time (10 and 20) min. The films were characterized by the measurement of XRD, atomic force microscopy properties (AFM). We have estimated crystallites size from X -Ray diffraction about nanoscale for PS and AFM confirms the nanometric size Chemical fictionalization during the electrochemical etching show on the surface chemical composition of PS. The atomic force microscopy investigation shows the rough silicon surface, with increasing etching process (current density and etching time) porous st
... Show Morein this paper, we give a concept of
Thin films of microcrystalline and nanocrystalline -silicon carbide and silicon, where deposited on glass substrate with substrate temperature ranging from 350-400C, with deposition rate 0.5nm per pulse, by laser induced chemical vapor deposition. The deposition induced by TEACO2 laser. The reactant gases (SiH4 and C2H4) photo decompose throughout collision associated multiple photon dissociate. Such inhomogeneous film structure containing crystalline silicon, silicon carbide and amorphous silicon carbide matrix, give rise to a new type of material nanocrystalline silicon carbide in which the optical transmittance is governed by amorphous SiC phase while nanocrystalline grain are responsible for the conduction processes. This new m
... Show MoreGypseous soil is a collapsible soil, which causes large deformations in buildings that are constructed on it. Various methods have been used to minimise this effect, such as replacing the gypseous soil or using soil stabilisation (grouting or soil improvement). This study was carried out on four types of gypseous soils that have different properties and various gypsum contents. The testing was carried out on remoulded samples to evaluate the compressibility of gypseous soil under different conditions. The samples were grouted with acrylate liquid. The relationships between the injection pressure and the radius of flow, between time of injection and radius of flow, and between time and quantity of acrylate liquid are investigated on
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