The objective of this paper is to show modern class of open sets which is an -open. Some functions via this concept were studied and the relationships such as continuous function strongly -continuous function -irresolute function -continuous function.

Decision making is vital and important activity in field operations research ,engineering ,administration science and economic science with any industrial or service company or organization because the core of management process as well as improve him performance . The research includes decision making process when the objective function is fraction function and solve models fraction programming by using some fraction programming methods and using goal programming method aid programming ( win QSB )and the results explain the effect use the goal programming method in decision making process when the objective function is
fraction .

    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

       In this paper we offer two new subclasses of an open unit disk of r-fold symmetric bi-univalent functions. The Taylor-Maclaurin coefficients  have their coefficient bounds calculated. Furthermore, for functions in , we have solved Fekete-  functional issues. For the applicable classes, there are also a few particular special motivator results.

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

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples