Vol. 1 No. 1 (2023)

Applied mathematics plays a crucial role in solving real-world problems by providing quantitative and analytical tools to address complex challenges across various fields. In the first issue of our journal, we aim to explore how applied mathematics contributes to problem-solving and the discovery of underlying principles in diverse areas, including aerospace engineering, music analysis, safety management, stress management, mathematical physics, mining, and finance. Through this exploration, we aim to provide our readers with novel insights into how the application of mathematics offers a systematic and rigorous approach to tackling practical issues and driving progress.

Full Issue

  • Open Access

    Article

    Article ID: 42

    Novel learning for control of nonlinear spacecraft dynamics

    by Bo-Ruei Huang, Timothy Sands

    Journal of AppliedMath, Vol.1, No.1, 2023; 160 Views, 148 PDF Downloads

    With accurate dynamic system parameters (embodied in self-awareness statements), a controller can provide precise signals for tracking desired state trajectories. If dynamic system parameters are initially guessed inaccurately, a learning method may be used to find the accurate parameters. In the deterministic artificial intelligence method, self-awareness statements are formed as mathematical expressions of the governing physics. When the nonlinear, coupled expressions are precisely parameterized as the product of known matrix components and unknown vectrix (i.e., an intermediate between a dyadic and a matrix in regression form) tracking errors may be projected onto the known matrix to update the unknown vectrix in an optimal form (in a two-norm sense). In this work, a modified learning method is proposed and proved to have global convergence of both state error and parameter estimation error. The modified learning method is compared with those in the prequels using simulation experiments of three-dimensional rigid body dynamic rotation motion. The achieved state error convergence using the modified approach is two magnitudes better than using the methods in the prequels.

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  • Open Access

    Article

    Article ID: 85

    Statistical analysis of a Tagore song based on Raga Kafi

    by Soubhik Chakraborty, Prerna Singh

    Journal of AppliedMath, Vol.1, No.1, 2023; 107 Views, 59 PDF Downloads

    Rabindra Sangeet  or Tagore songs encompass a wide variety of human emotions. Most of these songs are based on Hindustani ragas. Kafi is a joyful raga and therefore could be helpful to combat stress. We are motivated to analyse a popular Tagore song, namely, Momo Chitte , which is based on this raga. Statistical analysis compares two phases of 30 s each of a vocal recording of this song. Several statistical features are considered including note duration, inter onset interval, rate of change of pitch, statistical parameterization of melody and rhythm in addition to analysis of spectrogram and pitch profile. The experimental results are encouraging.

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  • Open Access

    Article

    Article ID: 68

    Towards a solution to the problem of safety management of structurally complex systems

    by Alexander V. Bochkov

    Journal of AppliedMath, Vol.1, No.1, 2023; 358 Views, 40 PDF Downloads

    The non-isolation of modern, structurally complex, multi-purpose systems implies not only their interaction with the external environment, but also the impact of this environment on the systems themselves. The ability to predict and assess the consequences of these impacts, which are characterised by great uncertainty about the time, place and method of implementation, as well as the choice of a particular object of influence, is a task of extreme urgency in today’s globalised world. If the stability of functioning of any structurally complex system is understood as the achievement by it of the purpose of its functioning with acceptable deviations on the volumes and times of implementation of private tasks, the safety management in this system is reduced, in fact, to minimisation of unplanned losses at the occurrence of abnormal situations of various kinds and to carrying out of measures for their prevention. The success of such tactics depends largely on the effectiveness of the risk management system, on the ability of decision-makers to foresee the possibility of poorly formalised threats turning into significant risks, i.e., on having methods and tools for ranking threats and significant risk factors. Inevitably, there is the task of setting protection priorities, ranking objectives (usually of different types), problems and threats, and reallocating available (usually limited) resources. The article considers the issues involved in building an integral security model that takes into account the risks to the assets being protected.

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  • Open Access

    Article

    Article ID: 143

    Impact of Hindustani ragas in stress management: A statistical study

    by Soubhik Chakraborty, Avinav Prasad, Apoorva Chakraborty, Prerna Singh

    Journal of AppliedMath, Vol.1, No.1, 2023; 133 Views, 59 PDF Downloads

    This work is a part of our ongoing research project entitled Hindustani Raga Analysis Using Statistical Musicology with Therapeutic Applications for Stress Management . Using the perceived stress scale (PSS), baseline data were collected on 28 participants, 14 for the control group (non-music intervention group) and the remaining 14 for the case group (music intervention group), the allotment of a participant to one of the groups being done using randomized control trial (RCT) to prevent bias in allocation. After 5 music therapy sessions, the follow-up data were collected and the scores (0, 1, 2, 3, 4) were filled for the 10 questions in the questionnaire of the PSS scale. The rating is 0–13 implying low stress, 14–26 implying moderate stress and 27–40 implying high stress. As per the PSS rule, those having stress levels below 13 were dropped from the study. Thus, the actual number of participants in both groups would be less than those interviewed (sample size n = 7 for each group). Using paired t test, it is found that the case group participants have shown considerable improvement in comparison to the control group. Thus, the efficacy of music intervention in combatting stress is established.

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  • Open Access

    Article

    Article ID: 95

    Conservation laws, exact solutions and nonlinear dispersion: A lie symmetry approach

    by Adnan Shamaoon, Zartab Ali, Qaisar Maqbool

    Journal of AppliedMath, Vol.1, No.1, 2023; 159 Views, 79 PDF Downloads

    In this study, we investigated a set of equations that exhibit compact solutions and nonlinear dispersion. We used the classical lie symmetry approach to derive ordinary differential equations (ODEs) that are well suited for qualitative study. By examining the dynamic behavior of these ODEs, we gained insights into the intricate nature of the underlying system. We also used a powerful multiplier approach to establish nontrivial conservation laws and exact solutions for these equations. These conservation laws provide essential information regarding the underlying symmetries and invariants of the system, and shed light on its fundamental properties.

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  • Open Access

    Perspective

    Article ID: 74

    Machine learning in coal and gas outburst prediction

    by Peng Ji, Shiliang Shi

    Journal of AppliedMath, Vol.1, No.1, 2023; 123 Views, 55 PDF Downloads

    Artificial intelligence is flourishing, and its research achievements are being extensively applied across various industries. In the field of predicting coal and gas outbursts, methods such as machine learning and deep learning have been widely explored, resulting in accurate prediction accuracy and excellent predictive effects. This has significantly improved the safety of coal mine underground operations.

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  • Open Access

    Perspective

    Article ID: 125

    Sustainable information into portfolio optimization models

    by Gabriele Sbaiz

    Journal of AppliedMath, Vol.1, No.1, 2023; 192 Views, 112 PDF Downloads

    In the last fifteen years, extreme events such as the global financial and economic crisis of 2007–2008 and the Covid-19 pandemic have highlighted the importance of corporate social responsibility and sustainability in different aspects of our society. The environmental, social, and governance (ESG) disclosures have also gained increasing significance for investors due to initiatives undertaken by international bodies. In particular, with the Action Plan in 2018, the European Commission has assigned specific responsibilities to financial intermediaries to drive flows toward sustainable investments, explicitly requiring portfolio managers to integrate these non-financial factors into their decision-making processes. More and more, asset management firms and insurance companies offer tailored products to meet their customers’ sustainable needs and desires. This trend implies a growing recognition of sustainable practices in the financial sector, emphasized by the need to integrate ESG considerations in investment strategies.

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