Fundamental Mathematical Methods and Concepts | Chapter 1 | The Paradigm of Complex Probability and Markov Chains, Edition 1

 

In the current manuscript, we will apply to the well-known and established theory of Markov Chains my groundbreaking and novel Complex Probability Paradigm (or CPP) which will lead to a completely and perfectly deterministic expression of these stochastic processes in the universe of probabilities C = R + M. Consequently, it is important before “probing the depths” of Markov Chains, that we define in this chapter some essential mathematical concepts and fundamental tools and theorems that will be extensively used in the whole manuscript algorithms and C++ programs.

 

Author(s) Details

Abdo Abou Jaoudé
Department of Mathematics and Statistics, Faculty of Natural and Applied Sciences, Notre Dame University-Louaizé, Lebanon.

 

Please see the book here:- https://doi.org/10.9734/bpi/mono/978-93-48006-18-9/CH1

Investigating the Influence of pH on Drug Release from Zidovudine Matrices Containing Different Grades of Hydroxypropyl Methyl Cellulose | Chapter 02 | Challenges and Advances in Chemical Science Vol. 6

 Using a variety of hydroxypropyl methylcellulose grades, the current study analyses the effect of a multimodal dissolving profile on the drug release of zidovudine-containing sustained-release hydrophilic matrices. Zidovudine is commonly used to treat AIDS, either alone or in combination with other antiviral medications. It was the first anti-HIV treatment to earn FDA approval for clinical usage. Matrixes were constructed using a combination of multiple grades of HPMC, including HPMCK4M and HPMCK15M, to maintain the medication's release. In order to imitate the in-vivo condition, in-vitro multimodal dissolution investigations were conducted. The drug's exposure from the stomach to the intestine/colon determines the pH/buffer. pH fluctuations have an effect on drug breakdown and release for absorption, according to the study. Matrices also allow for a very controlled delivery of the medication zidovudine over a long period of time.

Author(S) Details

Masheer Ahmed Khan
School of Pharmacy, Devi Ahilya Vishwavidyalaya, Takshshila Campus, Khandwa Road, Indore, 452001, India.

View Book:- https://stm.bookpi.org/CACS-V6/article/view/4347

Study on Vector Operations Transform into Matrix Operations | Chapter 11 | Current Topics on Mathematics and Computer Science Vol. 6

 In this study, a valuable approach called "Vector operation Transforms into Matrix operation" (VTM) is devised to make vector algebraic and differential operations easier to manipulate. In the subject of vector analysis, an efficient technique is created to simplify computations. By converting vector algebraic and differential operations into matrix operations, the evaluation of these operations becomes more easy and straightforward. When vector operations involve multiple coordinate bases, the matrix operations are extremely beneficial.

Author (S) Details

Feng Cheng Chang
Allwave Corporation 3860 Del Amo Blvd, Torrance, California 90503, USA.

View Book :- https://stm.bookpi.org/CTMCS-V6/article/view/2591

Classical Algebra: Matrix Multiplication (The Rule of Vacancies) | Chapter 9 | Theory and Practice of Mathematics and Computer Science Vol. 11

In this paper, I describe a new and simpler method for matrix multiplication that I developed as a result of my extensive teaching experience. For beginners, the “Rule of Vacancies” method is very effective. This enthusiastic research work, I hope, will pique the students' interest.

Author (s) Details

Prof. Surajit Bhattacharyya
Seth Anandram Jaipuria College, The University of Calcutta, India.

View Book :  https://stm.bookpi.org/TPMCS-V11/article/view/1314

Swelling and Drug Release Studies from Hydrophilic Matrices Containing Combination of Different Grades of Hydroxyl Propyl Methylcellulose | Chapter 6 | Trends in Pharmaceutical Research and Development Vol. 5

 In formulating sustained release tablets, polymers are very common and commonly used because they are excellent drug carriers. The current research explores the release of drugs from hydrophilic matrices prepared using a mixture of hydroxyl propyl methylcellulose (HPMC), HPMCK4 M, HPMCK15 M and HPMCK100 M grades. The findings suggest that the concentration and viscosity grades of the polymer were influenced by the swelling and release profiles. The rate of water absorption into the matrices regulates this swelling action of HPMC of different grades in turn. The drug release rate and the matrix-swelling rate have an inverse relationship. This means that the rational combination of the various grades appears to provide a reasonably controlled drug release. Therefore, in predicting drug release, the swelling behaviour is useful.

Author(s) Details

Dr. Masheer Ahmed Khan
School of Pharmacy, Devi Ahilya Vishwavidyalaya, Takshshila Campus, Khandwa Road, Indore, 452001, India.

Prof. S. C. Chaturvedi
School of Pharmacy, Devi Ahilya Vishwavidyalaya, Takshshila Campus, Khandwa Road, Indore, 452001, India.

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/303