The cheif aim of the present investigation is to develop Leslie Gower type three species food chain model with prey refuge. The intra-specific competition among the predators is considered in the proposed model. Besides the logistic growth rate for the prey species, Sokol Howell functional response for predation is chosen for our model formulation. The behaviour of the model system thoroughly analyses near the biologically significant equilibria. The linear stability analysis of the equilibria is carried out in order to examine the response of the system. The present model system experiences Hopf bifurcation depending on the choice of suitable model parameters. Extensive numerical simulation reveals the validity of the proposed model.

In this paper, the fuzzy logic and the trapezoidal fuzzy intuitionistic number were presented, as well as some properties of the trapezoidal fuzzy intuitionistic number and semi- parametric logistic regression model when using the trapezoidal fuzzy intuitionistic number. The output variable represents the dependent variable sometimes cannot be determined in only two cases (response, non-response)or (success, failure) and more than two responses, especially in medical studies; therefore so, use a semi parametric logistic regression model with the output variable (dependent variable) representing a trapezoidal fuzzy intuitionistic number.

the model was estimated on simulati

             The study aims budget in grades use of smart phones to individuals (sample) according variable sex (males and females) and used researcher descriptive analytical method consisted sample of (300) students have chosen the way stratified random, and the study variables (academic achievement of students, sex and the use of Smart phones) resolution was adopted as a tool for data collection. The most important results of the study that females are more commonly used for smart phones, as well as the existence of a positive relationship between the inverse statistically significant use of smart phones and the rate of school for students and the use of smart phones h

Verbs are an important material in the construction of the sentence, as they are among the requirements of every sophisticated language, and in this regard, Ibn Al-Gothic (d. 367 AH): “Know that verbs are the origins of the buildings of most speech, and thus scholars called them buildings.” Verbs are the source of expression of the speakers’ ideas to represent the element of activity and movement, and with their knowledge We infer the meanings of Arabic words, and Ibn Al-Sarraj (d. 316 AH) defined it: “The verb denotes a meaning and a time, and that time is either past, present, or future.” Its letters are original and does not drop from its construction a letter in the conjugation of its conjugations, and it is in Arabic two type

Abstract

                 The research dealt with a studying the impact of oil price fluctuations on one of the rules of financial discipline, which is the rule of budget deficit in the Iraqi economy for the period (2003-2020) as it is one of the quarterly economies that rely mainly on volatile oil revenues that fluctuate with oil prices in global markets, and therefore the general budget suffers. from The state of instability and then the government resorts to borrowing for a long time . this deficit in the general budget and increase the debt burden in the public debt.The research aim to measure and study the impact of oil price flu

This research set to indicate the role of the opportunity cost in the overall economic development (human and social development) by selecting the most appropriate alternative for the growth of the country in exchange for sacrificing profit limits to achieve this growth and development of the country, especially in the present circumstances of the country and after studying the reality of the economic case for him, as the problem lies with don't selecting the best alternative that enhances the gross domestic product, which extends to promote overall economic development and revive the industrial and agricultural sectors, productivity is more like Impotent, versus sacrifice alternative consumption may bring more financially lucrative than

Volcaniclastic rocks of Al Muqdadiya Formation (Pliocene) in Injana area, southern Hemrin anticline, NE of Iraq, were studied ( petrographically, physically, mineralogically and geochemically , as well as the engineering properties) to assess the suitability of volcaniclastic rocks to use them in industry as refractories. The results show that the physical and engineering properties change with the temperature change. The bulk density and the specific gravity increase by increasing temperature while the apparent porosity, water sorption and the linear shrinkage decrease. On the other hand the compressive strength increase by increasing temperature. The volcaniclastics have very low thermal conductivi

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the <