The main theme of this thesis could be divided into three objectives : The first is to define and classify integral equations with one and multiple delay, including Fredholm, Volterra and integro-differential equations (Retarded, Neutral and Mixed types). While the second and popular objective of this work is to study the inverse problems related to delay integral equations by using non-classical variational formulation method. Some examples are given for each of the discussed type of delay integral equations. Also, a study to the direct and inverse problems related to integral equations with multiple delay, also considered as a third objective. Several examples are given for each type of these equations. Finally, the suggested approach

The purpose of this paper is applying the robustness in Linear programming(LP) to get rid of uncertainty problem in constraint parameters, and find the robust optimal solution, to maximize the profits of the general productive company of vegetable oils for the year 2019, through the modify on a mathematical model of linear programming when some parameters of the model have uncertain values, and being processed it using robust counterpart of linear programming to get robust results from the random changes that happen in uncertain values ​​of the problem, assuming these values belong to the uncertainty set and selecting the values that cause the worst results and to depend buil

In this paper, the delay integral equations in population growth will be described,discussed , studied and transfered this model to integro-differential equation. At last,we will solve this problem by using variational approach.

Background: Periodontium mainly exposed to injury by trauma or pathologic diseases, Aloe vera is a plant has many basic ingredients in its extracted gel that acts as wound healing accelerator in addition to that it's safe, and economical and without recordable of side effect. This study aimed is to evaluate the effect of topical application of Aloe vera on expression of syndecan -1 by periodontium tissue. Materials and methods: Thirty six male Albino rats were subjected for periodontium defect by electric scaler on the distal sides of both lower anterior teeth. The animals divided into two groups; control group (without treatment) and the experimental group treated with 1µLAloe vera gel/normal saline. Periodontal healing was examined at

Placental calcification is an aging process that is increasingly linked to adverse pregnancy outcomes when it occurs prematurely. Vitamin D has immunomodulatory properties and may play a role in placental calcification. This study explored the association between maternal vitamin D, inflammatory cytokines, and placental calcification. A total of 46 pregnant women aged 16–40 years were included in this study. They were divided into four groups: Group 1 (control group; n = 10, without placental calcification), Group 2 (n = 12, Grade 1 placental calcification), Group 3 (n = 12, Grade 2 placental calcification), and Group 4 (n = 12, Grade 3 placental calcification). Serum vitamin D (25(OH)D) and cytokine (TNF-α,

This research introduce a study with application on Principal Component Regression obtained from some of the explainatory variables to limitate Multicollinearity problem among these variables and gain staibilty in their estimations more than those which yield from Ordinary Least Squares. But the cost that we pay in the other hand losing a little power of the estimation of the predictive regression function in explaining the essential variations. A suggested numerical formula has been proposed and applied by the researchers as optimal solution, and vererifing the its efficiency by a program written by the researchers themselves for this porpuse through some creterions: Cumulative Percentage Variance, Coefficient of Determination, Variance

Nitrogen (N) is a key growth and yield-limiting factor in cultivated rice areas. This study has been conducted to evaluate the effects of different conditions of N application on rice yield and yield components (Shiroudi cultivar) in Babol (Mazandaran, Iran) during the 2015- 2016 season. A factorial experiment executed of a Randomized Complete Block Design (RCBD) used in three iterations. In the first factor, treatments were four N amounts (including 50, 90, 130, and 170 kg N ha^-1), while in the second factor, the treatments consisted of four different fertilizer splitting methods, including T₁:70 % at the basal stage + 30 % at the maximum tillering stage, T₂:1/3 at the basal stage + 1/3 at the maximum ti

Employing phase-change materials (PCM) is considered a very efficient and cost-effective option for addressing the mismatch between the energy supply and the demand. The high storage density, little temperature degradation, and ease of material processing register the PCM as a key candidate for the thermal energy storage system. However, the sluggish response rates during their melting and solidification processes limit their applications and consequently require the inclusion of heat transfer enhancers. This research aims to investigate the potential enhancement of circular fins on intensifying the PCM thermal response in a vertical triple-tube casing. Fin arrays of non-uniform dimensions and distinct distribution patterns were des