الصفحة 129
الصفحة 129
A Geometric Approach to Differential Forms
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember.
A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
This book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization.
A comparison between ovate pontic and modified ridge-lap pontic
Aims to explore the differences in aesthetic, hygienic, and functional aspects of replacing missing anterior teeth using various pontic designs, with a particular focus on the ovate pontic design with a focus on the different stages needed for a pontic design placement on a ridge missing either a single or multiple teeth and the procedures needed to condition the soft tissues surrounding the prothesis.
3D Segmentation for medical images (OsteoVision) = التقطيع ثلاثي الأبعاد للصور الطبية
With the increasing integration of AI across various sectors, artificial intelligence (AI) is already playing a significant role in the healthcare industry, and its use is expected to grow further. AI systems used in image processing and computer vision algorithms have shown a significant ability to perform many operations such as segmentation, classification, and detection. This project presents the application of computer vision algorithms in the field of medical imaging for diagnostic, therapeutic, and interventional purposes. This thesis explores the use of several computer vision algorithms to address different pathologies, specifically brain tumors (glioma) (see Appendix A) and knee osteoarthritis (OA), as well as tracking the progression of knee osteoarthritis using the Kellgren and Lawrence (KL) grading system, a common method for classifying the severity of OA into five grades. To achieve the desired impact, the project employs various techniques, including 3D segmentation for brain tumors, 2D segmentation for knee joints, and multinomial classification for determining the severity of knee OA injuries. The primary aims of the project are to enhance diagnostic accuracy, assist in creating treatment plans, provide an assistive tool for healthcare providers to make more informed decisions, leverage AI's capabilities to detect abnormalities that might escape the human eye, and streamline workflow. To facilitate these goals, the project incorporates a user-friendly UI, a website, and a Flutter-based mobile application, enabling healthcare providers to efficiently integrate these tools into their practice and improve patient care.
3D printing in oral & maxillofacial surgery
A comprehensive guide to 3D printing and 3D bioprinting methods and their application in oral and maxillofacial surgeries. Among the 3D printing methods considered are fused deposition modeling, selective laser sintering, photopolymer jetting, powder binder printing, and stereolithography, while the coverage of 3D bioprinting encompasses inkjet, microextrusion, and laser techniques. In each case, the relevance of the technique to oral and maxillofacial surgery is explained. In addition, the available inks and bioinks for 3D printing are reviewed. The roles of soft and hard tissue printing in oral and maxillofacial tissue engineering and the use of 3D printing in multi- and interfacial tissue engineering are then examined in depth. The particular value of 3D printing in the treatment of critically sized defects is discussed separately. Finally, up-to-date information is provided on guided tissue/bone regeneration using 3D printing. The book will be of interest to both oral and maxillofacial surgeons and biomedical engineers.
104 Number Theory Problems : From the Training of the USA IMO Team
This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
