Journal of AppliedMath

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Article ID: 532

Fundamental properties of the gyroscope oscillation
by Ryspek Usubamatov

Journal of AppliedMath, Vol.2, No.3, 2024; 31 Views, 15 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.532

Despite partial solutions by famous scientists during the early Industrial Revolution, gyroscope problems remained unsolvable until the beginning of the twentieth century, when several fundamental physical laws were finally formulated to describe them. Today, the principles of classical mechanics enable the formulation and description of the physical processes involved in the rotation of any object. Gyroscopic devices are objects that rotate and exhibit oscillation, which has been a challenging problem in engineering mechanics. The oscillation of a gyroscope is caused by the interaction between external and inertial torques. This is different from other examples of oscillation, such as pendulums and springs, which have been well documented. The main difference in the physics of gyroscopic oscillation is that the spinning rotors of the gyroscopic devices are supported on one side, with their axes perpendicular to the axis of oscillation. The oscillation of gyroscopic devices is interrelated with the potential and kinetic energy of their components. However, the physics of the oscillation of such objects has not been fully described in publications until recently. The theory of gyroscopic effects for rotating objects has now been published and provides a solution to this problem. According to this theory, gyroscopic inertial torques represent the potential energy of the external torque and the kinetic energy of the spinning rotor. This paper demonstrates the distribution of inertial torques about the axes of Cartesian coordinates, which enables the computation of gyroscope motion and oscillation.

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Article

Article ID: 179

Modelling the dynamics of syphilis infection with personal protection and treatment as optimal control strategies
by Elvis Kobina Donkor, Bismark Ansu, Shaibu Osman, Dominic Otoo, Winnie Mokeira Onsongo, Ernest Yeboah Boateng

Journal of AppliedMath, Vol.2, No.3, 2024; 12 Views, 8 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.179

Syphilis is a sexually transmitted infection which when left untreated would lead to major health problems. Syphilis can easily be contracted by direct contact with Syphilis sore during vaginal, anal, or oral sex. Syphilis can also be passed on from an infected mother to her unborn child. In this paper, a nonlinear deterministic model of Syphilis disease was constructed to determine the dynamics of Syphilis infections. The study deduced model’s equilibria and analyzed the local and global stability of these equilibria. The model was extended to optimal control problem by adding timedependent controls that helped characterize a range of possible controls that minimized the disease. The control system was solved qualitatively and numerically to evaluate the effectiveness of the considered controls using Pontryagin’s Maximum Principle. The analysis indicated that strategies B and C are considered most effective as they substantially minimized the exposed, asymptomatic and symptomatic infectious. We recommend that stakeholders should consider strategy B and C in their effort to mitigate the disease from the population as they all have the same effect of substantially minimizing the exposed, symptomatic and asymptomatic populations.

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Article ID: 563

Computation of topological indices of linear chains of perylene and coronene using M-polynomial
by Ashwini Shivappa Yalnaik, Mookanahallipatna Shivanna Ranganath, Veerabhadraiah Lokesha, Raju Basavaraju Jummannaver

Journal of AppliedMath, Vol.2, No.3, 2024; 4 Views, 0 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.563

The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M- polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.

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Editor-in-Chief

Assoc. Prof. Ahmad Zeeshan

International Islamic University, Pakistan

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2972-4805

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Bi-monthly

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

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Volume Arrangement

2024

2023

Featured Articles

H∞ hybrid control and MRD in a steel frame building subjected to excessivevibrations caused by the dynamic action of wind and earthquake

The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural designs must be developed to decrease the damage induced by these actions. The objective of this work is to design a hybrid controller based on the H∞ optimization via state feedback and the magneto-rheological damper (MRD) to mitigate the excessive vibrations of a three-story steel frame building, represented through the shear building model, subjected to the simultaneous dynamic action of wind and earthquake. All research is based on computational simulation, experimental research and results will not be addressed. In the numerical analysis, digital computer and MATLAB® software are used, and implemented codes generate the expected results based on the mathematical modeling. With the application of the H∞ control technique via state feedback, the displacements were reduced by 77%. With MRD this reduction was 79%. With the hybrid controller, this reduction was 100%. Thus, the verifications in relation to maximum displacements were met for NBR 15421:2006, NBR 8800:2008 and NBR 6118:2014. From the results, it is concluded that the hybrid controller proved to be more efficient and achieved the proposed objective. The exogenous inputs had zero influence on the behavior of the system output.

Topological analysis of multiple tables

The paper proposes a topological approach in order to explore several data tables simultaneously. These data tables of quantitative and/or qualitative variables measured on different homogeneous themes, collected from the same individuals. This approach, called topological analysis of multiple tables (TAMT), is based on the notion of neighborhood graphs in the context of a joint analysis of several data tables. It allows the simultaneous study of possible links between several thematic tables. The structure of the correlations or associations of the variables in each thematic table is analyzed according to quantitative, qualitative or mixed variables considered. Like the multiple factorial analysis (MFA), the TAMT allows several tables of variables to be analyzed simultaneously, and to obtain results, in particular graphical representations, which make it possible to study the relationship between individuals, variables and tables of data. These can also be tables of temporal data, collected at different times on the same individuals. The proposed TAMT approach is illustrated using real data associated with several and different homogeneous themes. Its results are compared to those from the MFA method.

Development of a stacked hybrid Decision Tree model leveraging the NSL-KDD dataset

Intrusion detection in information technology as well as operational technology networks is highly required in modern day systems due to the increased spate of cyber-attacks in both number and complexity. Anomaly-based intrusion detection systems which have the capacity to detect novel or zero-day attacks are highly employed in this regard. One important component of anomaly-based intrusion detection systems which ensures their behaviour is artificial intelligence in general and machine learning in particular. The burden in modern day cybersecurity research is to investigate and develop models that can outperform existing ones. This paper is aimed at developing a hybrid decision tree model using the stacking ensemble approach. Performances were measured on the basis of recall, precision, accuracy, F1-score, receiver operating characteristics and confusion matrices. The hybrid model presented a precision of 97%, accuracy of 81%, F1-score of 80% and AUC score of 0.96, respectively.

The synergistic effect of the multiple parameters of vibro-impact nonlinear energy sink

This article studies the dynamics and efficiency of a vibro-impact damper (single-sided vibro-impact nonlinear energy sink—SSVI NES) depending on the exciting force parameters. The damper is coupled with a linear oscillator—the primary structure. It is shown that the damper is quite effective in a wide range of the exciting force amplitude and in the range of its frequency, which are higher than the resonant frequency; damper efficiency in these regions is fairly stable. The dynamics of the vibro-impact system “primary structure—SSVI NES” is rich and complex, which, however, does not impair the damper efficiency. In complex oscillatory regimes, the damper makes bilateral impacts: it hits both an obstacle and directly against the primary structure, which actually turns a single-sided NES into a double‐sided one. The optimization procedure and the choice of optimal damper parameters play a very important role in damper design. Optimizing multiple damper parameters instead of three shows a synergistic effect and provides better results.

Optimization imposition upon drone gimbal control electronics

The goal of the manuscript is to design a relatively good control structure for the noise suppression of a drone’s camera gimbal action. The gimbal’s movement can be simplified as a rest-to-rest reorientation system that can achieve the boundary result of a dynamic system. Six different control architectures are proposed and evaluated based on their ability to control the trajectory of the dynamic-system position and speed, their running time, and their quadratic cost. The robustness of the control architecture to uncertainties in inertia and sensor noise is also analyzed. Monte Carlo figures are used to assess the performance of the six control systems. The conditions for applying different architectures are identified through this analysis. The analysis and experimental tests reveal the most suitable control of the drone’s camera gimbal rotation.

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