In the present work, first of all, a new numerical fractional differentiation formula (called the CF2 formula) to approximate the Caputo-Fabrizio fractional derivative of order a,(0

In this work, using the determination function, some new kinds of interpolation formulas are presented.These novel formulas are extensions of Lagrange interpolation. Error formula for these new kind of interpolation formulas are obtained. Finally, using these formulas, some new numerical integration formulas in closed-type and open-type are presented. Absolute Error of quadrature formulas show the efficiency of the proposed formulas.

In this work, a new type of interpolation formula is introduced. These formulas can be an extension of the Lagrange interpolation formula. The Error of this new type of interpolation is calculated. In order to display efficiency of the proposed formulas, three numerical examples are presented.

This article is an application of mathematics in finance, whose approach is different from the usual methods of writing articles in humanities. In other words، this research article can be considered as a fundamental study based on mathematics for clearer and safer disclosure of information in capital markets. In this paper, we will challenge the informational inefficiencies existing in total return indexes currently being used, while suggesting a substituting formula. In the end, we study the relationships between the returns of the currently being used formulas on one hand، and the return of the suggested total return index on the other hand.

Introduction: Enteral nutrition (EN) is crucial for patients that cannot feed orally. Different mixtures have been used for EN and several advantages and limitations have been mentioned for each. Home-made, hospital blenderized liquids have long been used in clinical setting. Hospital prepared formulas (HPF) are still preferred in Iran. There is no standard method for preparing these feedings. The purpose of this study was to analyze the nutritional quality and viscosity of standard hospital prepared formula in Kamyab hospital.Methods: This was a descriptive study which analyzed macronutrients, osmolality and viscosity of standard hospital prepared formula samples based on exchange list. To compare mean values and standard deviation one sample t test was used.Result: Caloric density of samples ranged from 77-96 kcal/100 g and the percentages of total weight for carbohydrate were 10.7, 11.3, and 6.5; for Protein and fat were 4.1 and 3.8 g/100 ml. The average variability of the viscosity was 35-110 centipoise, and osmolality ranged from 145-345 mosm/kg.Conclusion: The results showed that exchange list was reliable. This standard formula had an acceptable level of macronutrient and if it prepared like the recipe, it would supply energy requirement of patients.