A Little Aspect of Real Analysis, Topology and Probability

The body of the paper is divided into three parts: Part one: include definitions and examples of the metric, norm and topology along with some important terms such as metrics l1,l2,l∞ and vector norm |x|p which also known as the Lp space. In case of the topology space this concept adjusted to be a unit ball that is distance one from a point unit circle. Part two: demonstrate the measure and probability which is one of the main topics in this work. This section serves as an introduction for the remaining part. It explains the construction of the σ-algebra and the Borel set, and the usefulness of the Borel set in the probability theory. Part Three: to understand the measure, one has to understand finitely additive measure and countable additivity of subsets, besides knowing the definition of ring, σ-ring and their measure extension. One also has to differentiate between the terms premeasure, outer measure and measure from their domains and additivity conditions, which is clarified in the form of table. The advantage of measurable function and the induced measure is explained, as both share to define the probability as a measure, the probability that has values in the Borel set. As a summary of this section, a Borel σ-algebra shows a special role in real-life probability because numerical data, real numbers, is gathered whenever a random experiment is performed. In this work a simple technique that is supported by pictorial presentation mostly is used, and for easiness most proofs are replaced by examples. I have freely borrowed a lot of material from various sources, and collected them in the manner that makes this thesis equipped with a little aspect of the real analysis, topology and probability theory

Approximate Solution of Delay Differential Equations Using the Collocation Method Based on Bernstien Polynomials???? ???????? ????????? ????????? ????????? ???????? ?????????? ???????? ??? ??????? ???? ?????????

In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials

"Enhancement of solubility of a poorly soluble antiplatelet aggregation drug by cogrinding technique"

Objective: The goal of this study was to formulate ticagrelor tablets with enhanced dissolution rate using cogrinding technique. However, it belongs to the biopharmaceutical classification system Class IV molecule, poorly soluble, and permeable.Methods: Various ratios (0.2:1–1.67:1) of povidone (PVP)/drug were used in the formulations. Ticagrelor was coground with different percentage of PVP K 25 (carrier) in a mortar with a pestle for 30 min, then mixed with the rest excipients. A high-performance liquid chromatography stability indicating assay was developed to test the stability of ticagrelor in the selected formulae.Results: The results showed that the presence of PVP in relatively high ratios compared to the drug is desirable for enhancing the dissolution rate of ticagrelor. The best-optimized formulae found were that F8 and F9 which showed good disintegration and dissolution rate of ticagrelor more than 92% after 30 min while the dissolution rate for ticagrelor standard was only 22% after 30 min. Stability studies were performed on the selected formulae F8 and F9. Conclusion: The optimized formulae were evaluated for thickness, weight variation, hardness, friability, dissolution, and accelerated stability study for a period of 6 months. Cogrinding using PVP K 25 proved to enhance the dissolution of ticagrelor which may be due to the formation of a soluble complex between ticagrelor and PVP. The selected formulae F8 and F9 showed good stability

FORMULATION, OPTIMIZATION, AND EVALUATION OF SITAGLIPTIN AND SIMVASTATIN RAPIDLY DISSOLVING TABLETS

Objective: The scope of this work was to formulate sitagliptin and simvastatin rapidly dissolving tablets. However, simvastatin is practically insoluble in water. For improving its poor oral bioavailability and with the aim of facilitating administration to patients facing problems with swallowing rapidly dissolving tablets were preparedMethods: Tablets were prepared using superdisintegrant addition technique using croscarmellose sodium (Ac-di-sol), sodium starch glycolate (explotab) and crospovidone in different percentages. Evaluation tests such as weight variation, thickness, and content variation, and friability, disintegration, wetting time, in vitro dispersion and in vitro dissolution were carried out.Results: The results showed that the presence of crospovidone could enhance the dissolution rate of simvastatin greatly. The best-optimized formulae found were that F8, F9, and F10 which showed good disintegration and the dissolution rate of simvastatin and sitagliptin was more than 90% after 10 min while the dissolution rate for simvastatin and sitagliptin pure standards was 12% and 30%, respectively after 10 min.Conclusion: Some tablet formulae showed acceptable pharmacotechnical properties and complied with compendium requirements. Results of dissolution studies revealed that F8-F10 showed an increase in the dissolved sitagliptin and simvastatin to be more than 90% after 10 min.Â

The development and validation of a national continuing professional development model and framework for the pharmacy workforce in Kuwait

Background: Regional reports and international organisations have called for immediate actions for healthcare workforce development, including the pharmacy workforce. Scaling-up pharmacy workforce education and providing professional training systems support the provision of high-quality healthcare services. This research aims to evaluate pharmacy workforce development needs and priorities to develop a Continuing Professional Development (CPD) model and framework that would guide action, change and improvement of pharmacy practice in Kuwait. Methods: A sequential mixed methods design was used in which a literature review was conducted, followed by a series of studies. In the first study, focus groups and semi-structured interviews were employed to determine pharmacists’ and CPD providers’ perceptions, attitudes and behaviours towards CPD. The second study employed a national online questionnaire to assess pharmacists’ perceptions regarding the relevance of a set of behavioural statements to their current practice in order to develop the Kuwait Foundation Competency Framework (KFCF). The third study aimed to validate the KFCF and to assess its acceptability as a developmental tool from the pharmacists’ perspective and to create an action plan targeting the areas for improvement from educators’ and decision-makers’ perspectives. This was achieved by conducting focus groups with pharmacists, educators and decision-makers. Results: Findings showed that pharmacy CPD in Kuwait is multi-dimensional. Three main components were identified and considered as the main building blocks of a CPD model: needs-based education, system for support, and policies. Pharmacists and CPD providers agreed that needs-based education is the core of the developed CPD model. Developing competency frameworks was found to be a priority for pharmacy workforce development in Kuwait. An action plan to advance pharmacy workforce was created based on recommendations from education providers and decision-makers. Conclusions: This research provided an in-depth understanding of the multi-dimensional nature of pharmacy CPD in Kuwait. Findings from this research guided the transformation of pharmacy education and training in the context of workforce development

An Algorithm for nth Order Intgro-Differential Equations by Using Hermite Wavelets Functions

In this paper, the construction of Hermite wavelets functions and their operational matrix of integration is presented. The Hermite wavelets method is applied to solve nth order Volterra integro diferential equations (VIDE) by expanding the unknown functions, as series in terms of Hermite wavelets with unknown coefficients. Finally, two examples are give

Creation of Two Charginos and Neutralino Via Different Propagators

We investigated the creation of two Charginos.......... Keywords: Chargino, neutralino and Higgs boson DOI: 10.7176/APTA/84-02 Publication date:August 31st 202