This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela

    In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of  linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

Let R be a 2-torision free prime ring and ?, ?? Aut(R). Furthermore, G: R×R?R is a symmetric generalized (?, ?)-Biderivation associated with a nonzero (?, ?)-Biderivation D. In this paper some certain identities are presented satisfying by the traces of G and D on an ideal of R which forces R to be commutative

In this paper, preliminary test Shrinkage estimator have been considered for estimating the shape parameter α of pareto distribution when the scale parameter equal to the smallest loss and when a prior estimate α0 of α is available as initial value from the past experiences or from quaintance cases. The proposed estimator is shown to have a smaller mean squared error in a region around α0 when comparison with usual and existing estimators.

The main objective of this study is to determine the suitable excitation wavelengths for
urine components reaching to select the suitable lasers to execute the auto fluorescence due to their
high intensities. The auto fluorescence was measured at 305, 325 and 350 nm excitation wavelengths
for eleven urine samples which were also analyzed by conventional methods (chemical and
microscopic examination). Data manipulation using Matlab package programming language showed
that urine sample with normal chemical and biological components have emission peaks which are
different from the infected urine samples. Despite the complexity of the composition of urine,
fluorescence maxima can be observed. Most likely, the peaks obser

Data mining is one of the most popular analysis methods in medical research. It involves finding patterns and correlations in previously unknown datasets. Data mining encompasses various areas of biomedical research, including data collection, clinical decision support, illness or safety monitoring, public health, and inquiry research. Health analytics frequently uses computational methods for data mining, such as clustering, classification, and regression. Studies of large numbers of diverse heterogeneous documents, including biological and electronic information, provided extensive material to medical and health studies.

The density-based spatial clustering for applications with noise (DBSCAN) is one of the most popular applications of clustering in data mining, and it is used to identify useful patterns and interesting distributions in the underlying data. Aggregation methods for classifying nonlinear aggregated data. In particular, DNA methylations, gene expression. That show the differentially skewed by distance sites and grouped nonlinearly by cancer daisies and the change Situations for gene excretion on it. Under these conditions, DBSCAN is expected to have a desirable clustering feature i that can be used to show the results of the changes. This research reviews the DBSCAN and compares its performance with other algorithms, such as the tradit

The main objective of this study is to determine the suitable excitation wavelengths for
urine components reaching to select the suitable lasers to execute the auto fluorescence due to their
high intensities. The auto fluorescence was measured at 305, 325 and 350 nm excitation wavelengths
for eleven urine samples which were also analyzed by conventional methods (chemical and
microscopic examination). Data manipulation using Matlab package programming language showed
that urine sample with normal chemical and biological components have emission peaks which are
different from the infected urine samples. Despite the complexity of the composition of urine,
fluorescence maxima can be observed. Most likely, the peaks obser

The experiences in the life are considered important for many fields, such as industry, medical and others. In literature, researchers are focused on flexible lifetime distribution.

In this paper, some Bayesian estimators for the unknown scale parameter  of Inverse Rayleigh Distribution have been obtained, of different two loss functions, represented by Suggested and Generalized loss function based on Non-Informative prior using Jeffery's and informative prior represented by Exponential distribution. The performance of   estimators is compared empirically with Maximum Likelihood estimator, Using Monte Carlo Simulation depending on the Mean Square Error (MSE). Generally, the preference of Bayesian method of Suggeste