In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

    The paper starts with the main properties of the class of soft somewhere dense open functions and follows their connections with other types of soft open functions. Then preimages of soft sets with Baire property and images of soft Baire spaces under certain classes of soft functions are discussed. Some examples are presented that support the obtained results. Further properties of somewhere dense open functions related to different types of soft functions are found under some soft topological properties.

     This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for the new generalized beta function, including, Mellin transform, differential formulas, integral representations, and essential summation relations. Furthermore, crucial statistical application has been realized for the new generalized beta function.  

From a health standpoint, fluoride (F) is a vital element for humans. It had harmful effects on numerous organs when consumed in high dosages. Fluoride poisoning has been linked to liver damage. The purpose of this study was to see how sodium fluoride (Naf) affected liver function and the glycemic index in adult male albino rats. Fourteen (14) adult male Wistar albino rats were randomly and evenly divided into two groups and given the following treatments for thirty (30) days: G1 Group (Control group), were given distilled water and fed a balanced diet, G2 rats were administered water that contained 100 ppm Naf. The animals were fasted for 8-12 hours before being anesthetized and blood samples were taken by heart puncture technique

This study was performed at Nuclear Radiation Hospital in Baghdad for the period from
January 2011 to May 2011. 44 Blood samples were collected from patients suffered lung and
bladder cancer and 24 samples as healthy control individuals.
Routine liver functions tests were studied by measuring S.GPT, S.GOT and Kidney
function was evaluated by estimation of blood urea and creatinine in serum samples of
individuals studied.
It was observed that the incidence of lung and bladder cancer was higher in males than
females patients ( male 81.82 %, 72.73%, female18 .18%, 27.27% respectively).
Insignificant difference was noted among age of lung and bladder cancer patients
compared with control group. The results

In this paper, two parameters for the Exponential distribution were estimated using the
Bayesian estimation method under three different loss functions: the Squared error loss function,
the Precautionary loss function, and the Entropy loss function. The Exponential distribution prior
and Gamma distribution have been assumed as the priors of the scale γ and location δ parameters
respectively. In Bayesian estimation, Maximum likelihood estimators have been used as the initial
estimators, and the Tierney-Kadane approximation has been used effectively. Based on the MonteCarlo
simulation method, those estimators were compared depending on the mean squared errors (MSEs).The results showed that the Bayesian esti

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

The paper is concerned with posterior analysis of five exponentiated (Weibull, Exponential, Inverted Weibull, Pareto, Gumbel) distrebutions. The expressions for Bayes estimators of the shape parameters have been derived under four different prior distributions assuming four different loss functions. The posterior predictive distributions have been obtained, and the comparison between estimators made by using the mean squared errors through generated different sample sizes by using simulation technique. In general, the performance of estimators under Chi-square prior using squared error loss function is the best.

     In this paper, the class of meromorphic multivalent functions of the form by using fractional differ-integral operators is introduced. We get Coefficients estimates, radii of convexity and star likeness. Also closure theorems and distortion theorem for the class ,  is calculaed.