Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
Some Types of Generalized Closed and Generalized Star Closed Sets in Topological Ordered Spaces
Optimizing Capsule Endoscopy Detection: A Deep Learning Approach with L-Softmax and Laplacian-SGD
Kernel Ideals in Semigroups
Modeling the Dynamics of Covid-19 with the Inclusion of Treatment, Vaccination and Natural Cure
Calculation of Combined Vibrational Frequencies in Cl₂O using Lie Algebraic Method
An Introduction to Various Types of Mathematics Teaching Aids
A Simple Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems
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A Homotopy Based Method for Nonlinear Fredholm Integral Equations
Proof of Beal's Conjecture and Fermat Last Theorem using Contra Positive Method
Trichotomy–Squared – A Novel Mixed Methods Test and Research Procedure Designed to Analyze, Transform, and Compare Qualitative and Quantitative Data for Education Scientists who are Administrators, Practitioners, Teachers, and Technologists
Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test
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Surfaces in R3 with density
This study presents the calculation of stretching vibrational frequencies for the triatomic molecule dichlorine monoxide (Cl₂ O), explicitly focusing on the fourth, fifth, and sixth overtones. Using a Lie algebraic framework, a detailed mathematical modeling approach is provided to predict these higher overtone frequencies accurately. The results demonstrate the effectiveness of the Lie algebraic method in capturing the complex vibrational behavior of Cl₂ O, offering valuable insights into its vibrational spectra.
In the present work, the intention is to establish a relationship between new types of closed sets, namely g*b-closed sets (resp.gb-closed) and g*i-closed sets(resp.gi-closed) and g*b-closed sets(resp.gb-closed) and g*d-closed sets(resp.gd-closed). Additionally, the independence between the notions of g*i-closedness (resp.gi-closedness) and g*dclosedness (resp.gd-closedness) is established.
Capsule endoscopy has emerged as a non-invasive diagnostic tool for gastrointestinal diseases; however, efficient disease classification remains a challenge due to the inherent complexities of image analysis. Furthermore, the extensive time required for manual examination of capsule endoscopy images has led researchers and clinicians to seek timeefficient automated detection methods. This is where the profound advantages of deep learning (DL) become crucial. This research proposes a novel approach that combines L-Softmax with Laplacian Smoothing Stochastic Gradient Descent (LSSGD) within a ResNet architecture to enhance disease classification accuracy in capsule endoscopy images from the Kvasir dataset. The L-Softmax function is integrated into the DL framework, facilitating better class separation and feature representation. Additionally, LSSGD is employed to mitigate overfitting and enhance model generalization. Experimental results demonstrate that our methodology is stable and easy to utilize in capsule endoscopy.
The concepts of *-ideals, strong ideals, *-congruences and kernel ideals are introduced in a pseudo-complemented semigroup and discussed certain properties of these. Some equivalent conditions for an ideal of a pseudocomplemented semigroup to become a kernel ideal are obtained. The lattice structure of strong ideals is discussed.
In this paper, a Covid-19 pandemic model with five compartments is presented. Model assumptions, flowchart and the system of model equations are included. It is found that the solutions for the model equations exist and they are unique, positive and bounded. Hence, the present model is termed as mathematically well-posed and biologically meaningful. Mathematical analysis, sensitivity analysis are conducted in order to draw meaningful conclusions. Sensitivity analysis on the model equations reveal that the immunity loss has a positive impact while vaccination and treatment have negative impact on the effective reproduction number. The research results assert that the pandemic can be kept under control by enhancing vaccination and treatment facilities and similarly by implementing suitable methods to reduce loss of immunity. Outcomes of both qualitative and quantitative analyses are included and described elaborately. Disease free equilibrium point is identified and it's local and global stability analyses are conducted using powerful techniques like Routh-Hurwitz criteria and Lyapunov function method. Detailed description of the model is presented in the text of the paper lucidly.
The present study demonstrates a thorough study of dichlorine monoxide's combined stretching vibrational frequencies (Cl₂ O) with particular reference to its fourth, fifth and sixth overtone transitions. The research proposes a systematic method for modelling vibrational dynamics and frequency predictions utilizing a Lie algebraic framework. The methodology accounts for anharmonicity and higher inter-level coupling modulation, which provides a basis for overtone theoretical interpretation. These results are helpful within the framework of molecular spectroscopy for interpreting the results of experiments with this compound. Such an approach can be generalized to other polyatomic molecules possessing similar vibrational modes.
