Mathematical evaluation of post-radiotherapy salivary gland function using salivary gland scintigraphy

Objective: Xerostomia is the most common treatment-related toxicity after radiotherapy (RT) for head and neck carcinoma, reducing the quality of life of patients due to a decrease in salivary gland function. Methods: Salivary gland scintigraphy was performed to quantitatively evaluate the salivary gland functions in patients undergoing RT. It was done chronologically for 62 salivary glands of 31 patients before RT and retested 12 months later. Results: The salivary gland functions of most patients deteriorated post-RT and recovered when the radiation dose to the salivary gland was not high. The mean dose to the salivary gland was found to be the most reliable factor in deteriorating salivary gland function, and the tolerance dose was determined to be 46 Gy. The recovery rate of salivary gland function after 1 year of RT was 72% in the RT alone group (n = 10), 56% in the conformal radiotherapy group (n = 15), and 44% in the bioradiotherapy group (n = 6). Conclusion: Scintigraphy revealed that the salivary glands recovered from post-RT hypofunction when decreased doses were administered. The determined tolerance dose of 46 Gy may guide the approach to minimizing associated xerostomia in RT. Advances in knowledge: In this study, the average tolerated dose to the salivary glands was 46 Gy.

Taqī al-Dīn al-Rasid and His Treatise on Algebra Mathematical Evaluation, Translation, and Editio Princeps

Taqī al-Dīn al-Rāṣid is one of the most important representatives of the Ottoman tradition on mathematical sciences. His research focus being on astronomy, astronomical instruments, mathematics, optics, mechanics, and physics is understood from his surviving works. Taqī al-Dīn’s establishment and management of the Istanbul Observatory, which was the first observatory in the Ottoman Empire, made him an important figure in many ways. However, despite the aforementioned importance, the mathematics he learned, taught, produced and used has been a subject for very few studies. The primary way of determining the quality and the level of a work is to look at the kind of tools used for its creation. Therefore, this article will present the edition princeps, the translation and the evaluation of Taqī al-Dīn al-Rāṣid’s treatise on algebra, al-Nisab al-mutashākila fī ʻilm al-jabr wa-l-muqābala. It will be presented in the context of the idea that revealing a scientific character and the career of scholars who stand out in mathematical sciences can be possible by analyzing their mathematical works. The nature of the science of algebra, which can be applied to any problem encountered on any subject regardless of geometry or arithmetic, makes this idea more meaningful. For the correct examination of classical mathematical works, first the original text is verified and transformed into a format that provides an easy reading, then it is to be translated into the desired language. Finally a mathematical analysis and historical evaluation are needed to explain the main structure and justification of the content of the article.

Design of a Model for Risk Reduction in Project Management in Small and Medium-Sized Enterprises

In general, it can be said that a project is a means of change so that the organization or individual obtain something they do not currently have, and which, in some respects, can ensure its functioning within the system in society, in the market, etc. Organizations often use different tools and techniques in project implementation to help manage projects. The selection of the optimal method requires a thorough systematic analysis. The chosen method must cover the requirements of project management with regard to its size and nature. One such tool is the ISO 21500 Guidance on project management standard, which defines the basic processes and documents needed for project management. The aim of this article is to propose a model through which it would be possible to effectively manage projects in small and medium enterprises (SMEs), i.e., where generally available international methodologies for project management are not introduced. The proposed model (referred to as Model B) was verified on projects in different SMEs in Slovakia. Mathematical evaluation presented in the paper as well as the knowledge and experience from this verification were summarized and the proposed Model B was modified (referred to as SMEPM: small and medium enterprises project management) so that it can be used in the implementation of other projects in the conditions of SMEs.

Standards of Classical Architecture Criticism: Between Mathematics and Philosophy

Criticism is an intellectual process that primarily searches for beauty aspects in the works of art, including architecture. This article explores the mathematical and philosophical principles of classical architectural criticism. It is hypothesized that design criteria during the Classic period were clear and specific. The research presents theories of classical art that focus on the process of beauty interpretation. It also assesses the mathematical evaluation of architectural art and beauty through “The Golden Ratio” and “The “Fibonacci Sequence.” Classical philosophy, and its perception of beauty, is discussed as an essential basis in any artistic critical activity. The research asserts that the science of aesthetics is both objective and subjective, which explains the difference in aesthetic evaluation across eras. Objectivity stems from conditions of proportionality that must be met for an architectural art to be aesthetically judged as beautiful. Subjectivity lies in the time and place of the architectural work, whereby tendencies, tastes, and needs related to the human and geographical environment can affect the standards of beauty. This makes the evaluation of beauty in classical architecture a delicate and complex process in which many aspects must be considered to have an objective, fair, and correct judgment.

Invariant stress state parameters for forging upsetting of magnesium in the shell

Introduction. For pressure treatment of low-plastic metals, it is necessary to develop special techniques for increasing plasticity. In the cold state, an increase in plastic properties is possible due to an increase in the level of compressive stresses during deformation. In the processes of forging precipitation, this is achieved by using shells or clips of various types. At the same time, the configuration of the precipitation tool also matters. To create additional compressive stresses and increase the ductility of the metal, the working surface of the tool can be configured differently than with a normal free draft, where it is obviously larger than the contact surface area of the workpiece, so that metal broadening can occur. The stress state has a great influence on the plasticity of the processed material. This state is described by methods of tensor representation, but to assess the situation, it is customary to use invariants of tensors in one form or another, which eliminates the influence of coordinates on the results of the analysis. In the sections of deformable body mechanics dealing with the influence of the stress state on plasticity, the first, but sometimes other invariants of the stress tensor are used, the invariants themselves are transformed into the stress state indicator and the lode coefficient. The aim of the work: mathematical evaluation of invariant parameters of the stress state of the magnesium precipitation process at room temperature, according to the results of which it is possible to obtain a positive result in real experiments. Research methods: finite element simulation using the DEFORM software module. Results and discussion. The theoretical justification of increasing the plasticity of the magnesium billet in the process of precipitation in the cage without its compression is carried out. An increase in the stress state index modulo 2...5 times is revealed, which contributes to an increase in the plasticity of the metal. At the same time, a zone with a lode coefficient close to zero is identified. It is adjacent to the middle of the height of the workpiece at the point of contact with the cage and can be a dangerous cross-section from the position of crack formation.

Application of information entropy and TOPSIS coupling model in impervious design of hydraulic engineering

The establishment of a scientific and reasonable mathematical evaluation model plays a vital role in the optimization of impervious design scheme of water conservancy projects. The steps of constructing the coupling model of information entropy and TOPSIS are analyzed. The seepage prevention design scheme of an urban artificial lake is comprehensively evaluated by using this model, so as to obtain the optimal scheme.