Current Issue : July-September Volume : 2024 Issue Number : 3 Articles : 5 Articles
Radiotherapy can differentially affect the phases of the cell cycle, possibly enhancing suppression of tumor growth, if cells are synchronized in a specific phase. A model is designed to replicate experiments that synchronize cells in the S phase using gemcitabine before radiation at various doses, with the goal of quantifying this effect. The model is used to simulate a clinical trial with a cohort of 100 individuals receiving only radiation and another cohort of 100 individuals receiving radiation after cell synchronization. The simulations offered in this study support the statement that, at suitably high levels of radiation, synchronizing melanoma cells with gemcitabine before treatment substantially reduces the final tumor size. The improvement is statistically significant, and the effect size is noticeable, with the near suppression of growth at 8 Gray and 92% synchronization....
In this paper, it is noted that three apparently disparate areas of mathematics—singularity analysis, complex symmetry analysis and the distributional representation of special functions— have a basic commonality in the underlying methods used. The insights obtained from the first of these provides a much-needed explanation for the effectiveness of the latter two. The consequent explanations are provided in the form of two theorems and their corollaries....
Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form ∫u ( f ,dμ ) , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector- valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach....
In order to achieve the change rule of the induced residual stress (RS) 3eld after multipass ultrasonic surface rolling (USR), a mathematical model of the induced residual stress (RS) 3eld after multipass ultrasonic surface rolling is 3rst established. +en, the coupling mechanisms of the RS 3eld after dual-pass USR and multipass USR are analyzed, respectively. Subsequently, a 3nite element (FE) model is established, and the in8uence of the interval between two adjacent rolling paths LS is investigated. Finally, both the mathematical model and the FE model are experimentally veri3ed. +e results show that both the mathematical model and the FE model can predict the RS 3eld after multipass USR. Two adjacent RS 3elds will couple with each other in their overlapping regions. For a relatively small interval LS, the RS 3eld after multipass USR can be fully coupled, so as to form a uniform compressive RS layer. In this study, when LS � 0.05 mm, the values of the surface compressive RS, the maximum compressive RS, the depth of the maximum compressive RS, and the depth of the compressive RS layer reach 426.71 MPa, 676.54 MPa, 0.05 mm, and 0.54 mm, respectively....
A presence of tumor zones within biological tissues can be defined during the analysis of the skin surface temperature. This research is devoted to mathematical simulation of the time-dependent bio-heat transfer in tissues under a tumor influence. The one-dimensional partial differential equation of the Pennes model has been used for description of bio-heat transfer within the biological tissue with five layers, namely, epidermis, papillary dermis, reticular dermis, subcutaneous adipose tissue, and a muscle layer. The formulated boundary-value problem has been solved using the developed in-house computational code based on the finite difference schemes. The developed numerical algorithm has been verified using analytical and numerical solutions of other authors for the simpler test problem. As a result of this study, the temperature distributions have been obtained for the tissue in the presence of tumor zones in different layers of the skin. The influence of five layers of skin on the temperature distribution has been investigated, and the dependence for the skin surface temperature on the tumor zone location has been obtained. The obtained outcomes illustrate the effectiveness of this technique of cancer diagnosis and identify the optimal parameters for its application. Thus, this work represents an important step in the development of cancer diagnosis methods using thermography. The results obtained can be used to improve the accuracy of diagnosis and develop new treatment methods....
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