Mathematical Calculations Research Articles

An Approach to Near-Optimal Continuous-Thrust Solution for Plane Constellation Deployment

Paving the way in satellite constellation deployment, this article presents the Comprehensive Program (GCP) for planning constellation deployment missions by introducing a near-optimal solution for continuous-thrust maneuvers. The GCP establishes time constraints, enabling appropriate time scheduling and eliminating reconfiguration phases. It considers various cases of satellite departure and arrival sequences, collision avoidance constraints, and time limitations. A near-optimal solution for the continuous-thrust trajectory of each satellite is introduced, relying on the Fourier series approximation of the thrust pointing angle. The Fourier series with constant coefficients replaces the thrust angle in the satellite’s orbital motion equations in polar coordinates. The primary advantage of this near-optimal approach lies in its simplicity in accommodating space perturbations, posing no challenges in problem-solving. Additionally, the approach is beneficial due to its straightforward implementation and simple mathematical computations. This approach does not require pre-determining the revolution number of the transfer trajectory, unlike shape-based methods. The proposed method’s flexibility allows it to adapt and optimize the trajectory without prior assumptions about the number of revolutions required for the mission. Analyses demonstrate the proposed algorithm’s versatility and precision across various scenarios involving different orbital eccentricities, thrust forces, and thrust pointing angles. The constant coefficients of the Fourier series are determined by defining a set of objective functions and minimizing them using the Multi-Objective Particle Swarm Optimization algorithm (MOPSO). The first and second objective functions ensure that the transfer orbit reaches the desired deployment point, while the third and fourth ones guarantee the tangential conditions between the transfer orbit and the final orbit. An additional objective function minimizes the trajectory time. As a perturbation of interest, the effect of Earth’s oblateness is considered.

Improving the Usability of Graphical Authentication Systems Using Subject-Based Images

Recognition based graphical authentication systems rely on a system user’s ability to recognize previously chosen images and use those images to gain access into a computing systems, devices or application. Recognition based systems that utilise several types of images have been developed and studied. The déjà vu scheme depends on the use of abstract (meaningless) images. Images in the déjà vu scheme have no exact meaning. This scheme has also been actively studied. This article presents a between user study conducted on two recognition-based schemes using system prototypes. The Abstract Based Graphical Authentication (ABGA) was designed to simulate the déjà vu scheme. The performance of this system was compared with the performance of a novel system developed for this research. The novel system, called Subject Based Graphical Authentication (SBGA), in which the system used images from the various disciplines of the research participants. The researcher conducted a lab-based study with 100 participants, 50 participants for each of the prototypes. The study investigated the impact of using subject based images to enhance the usability and security of recognition-based graphical passwords. Two graphical models were thus developed and presented to the 100 participants, which comprised of staff and students from the departments of Computer Science, Mathematics, and Engineering. In the experiments, participants selected their graphical passwords from sets of images representing their various disciplines. The researcher observed that the memorability rate for graphical passwords consisting of subject based images aligned with participants' disciplines surpassed the rate for passwords with purely abstract images. The results indicated 81.7% successful login rate and 18.3% failure rate for Subject Based Graphical Authentication (SBGA). In contrast, Abstract Based Graphical Authentication (ABGP) exhibited a 51.5% successful login rate and a 48.7% failure rate. The findings provide significant insights for graphical password designers and developers seeking to enhance system memorability. Balancing image familiarity with security considerations can lead to more user-friendly and effective recognition-based authentication systems. This study provides valuable insights into the benefits of incorporating familiar images in recognition-based graphical passwords, showcasing a significant improvement in memorability and user authentication success. The findings underscore the importance of considering the user’s familiarity with portfolio images in the design of graphical authentication systems.

Mathematical modeling of Ebola using delay differential equations

Nonlinear delay differential equations (NDDEs) are essential in mathematical epidemiology, computational mathematics, sciences, etc. In this research paper, we have presented a delayed mathematical model of the Ebola virus to analyze its transmission dynamics in the human population. The delayed Ebola model is based on the four human compartments susceptible, exposed, infected, and recovered (SEIR). A time-delayed technique is used to slow down the dynamics of the host population. Two significant stages are analyzed in the said model: Ebola-free equilibrium (EFE) and Ebola-existing equilibrium (EEE). Also, the reproduction number of a model with the sensitivity of parameters is studied. Furthermore, the local asymptotical stability (LAS) and global asymptotical stability (GAS) around the two stages are studied rigorously using the Jacobian matrix Routh–Hurwitz criterion strategies for stability and Lyapunov function stability. The delay effect has been observed in the model in inverse relation of susceptible and infected humans (it means the increase of delay tactics that the susceptibility of humans increases and the infectivity of humans decreases eventually approaches zero which means that Ebola has been controlled into the population). For the numerical results, the Euler method is designed for the system of delay differential equations (DDEs) to verify the results with an analytical model analysis.

Formation of a heterogeneous group of UAVS with a reasonable number of false and real drones

The subject of scientific research is the joint use of false and real unmanned aerial vehicles (UAVs) as part of a heterogeneous group of UAVs to perform military tasks. This article aimsto determine the appropriate number of false and real drones (UAVs) as part of a heterogeneous group of UAVs to ensure that a certain number of real UAVs can fly to targets with the aim of further reliable target destruction. The scientific task is to develop a methodology for determining the appropriate number of false drones in a heterogeneous group of UAVs, considering the diversity of UAVs included in the UAV group. To achieve the goals of scientificresearch, partial scientific tasks were solved. The joint use of false drones as part of a UAV group to defeat targets with a given degree of damage was formalized. The formalization was carried out taking into account two possible cases of use: a) when the enemy has a sufficient number of means to destroy the entire group of UAVs; b) when the enemy has an insufficient number of means to destroy the entire UAV group. A mathematical model for determining the optimal composition of false and real drones (UAVs) as parts of a heterogeneous group of UAVs has been developed, which will allow to fulfill the task of defeating enemy targets with the desired degree of reliability. A program code has been developed that simplifies the mathematical calculations in the presented mathematical model and allows it to be used in the process of making an appropriate military decision. An algorithm to find the numbers of real and false UAVs in a heterogeneous group of UAVs is proposed. The obtained formulas and algorithms were verified by computer simulation using the Monte Carlo method. Methods. The mathematical model is based on combinatorial methods of probability theory. Programming for calculating analytical formulas and computer modeling of the Monte Carlo method was carried out based on the R computer language. The following results were obtained. A multifunctional algorithm is presented: on one hand, its application makes it possible to determine the optimal number of false UAVs in a heterogeneous group of UAVs to ensure that the required number of real UAVs reach the target, and on the other hand, to determine the predicted loss level of real UAVs in a heterogeneous group of UAVs when using a certain number of false drones.Conclusions. The availability of the developed mathematical model, algorithm, and program code makes it possible to predict the possible results of the combat use of heterogeneous groups of UAVs based on the initial parameters and to substantiate recommendations for a possible composition of such groups.

Efficient Model Updating of a Prefabricated Tall Building by a DNN Method.

The significance of model updating methods is becoming increasingly evident as the demand for greater precision in numerical models rises. In recent years, with the advancement of deep learning technology, model updating methods based on various deep learning algorithms have begun to emerge. These methods tend to be complicated in terms of methodological architectures and mathematical processes. This paper introduces an innovative model updating approach using a deep learning model: the deep neural network (DNN). This approach diverges from conventional methods by streamlining the process, directly utilizing the results of modal analysis and numerical model simulations as deep learning input, bypassing any additional complex mathematical calculations. Moreover, with a minimalist neural network architecture, a model updating method has been developed that achieves both accuracy and efficiency. This distinctive application of DNN has seldom been applied previously to model updating. Furthermore, this research investigates the impact of prefabricated partition walls on the overall stiffness of buildings, a field that has received limited attention in the previous studies. The main finding was that the deep neural network method achieved a Modal Assurance Criterion (MAC) value exceeding 0.99 for model updating in the minimally disturbed 1st and 2nd order modes when compared to actual measurements. Additionally, it was discovered that prefabricated partitions exhibited a stiffness ratio of about 0.2-0.3 compared to shear walls of the same material and thickness, emphasizing their role in structural behavior.

The Potential of Talisay-Dagat (Terminalia catappa L.) for Phytoremediation in Langihan Lagoon, Butuan City, Agusan del Norte, Philippines

The study aims to determine the potential of Talisay-dagat (Terminalia catappa L.) for phytoremediation and to examine its influence on reducing concentrations of heavy metals in the soil of Langihan Lagoon, Butuan City. Soil, roots, and leaves were collected and brought to the Regional Soils Laboratory using microwave-assisted aqua-regia digestion and determination through Inductively Coupled Plasma Optical Emission Spectrometer. The study made use of mathematical computations such as translocation factor (TF), bioconcentration factor (BCF), and enrichment factor (EF) to determine whether the tree is a hyperaccumulator, excluder, or indicator. In the TF results, T. catappa was a hyperaccumulator for Ni and Cu, considering that the concentration exceeds one (1) while demonstrating as a possible excluder for Cr. There was also an emphasis on limited absorption of heavy metals, as evidenced by the BCF and EF value of less than 1. The results show that based on TF, BCF, and EF values, only TF shows the effectivity of restricting the root-shoot ratio translocation of Ni and Cu (TF > 1). Regression analysis found that the absorption of T. catappa was not influenced by the amount of heavy metal in the soil within the studied condition. This insight was crucial in understanding the plant’s absorption and could guide further research or practical applications in environmental management and phytoremediation. Keywords: bioconcentration factor, hyperaccumulator, phytoremediation, Terminalia catappa, translocation factor

Numerical calculation of groundwater geofiltration processes in multilayer porous media

In this The article presents the modeling of multilayer hydrogeological processes in porous media, the results of fundamental and applied research, numerical modeling of hydrogeological processes, computational mathematics and methods of finite-difference schemes for solving simple differential equations, the development and improvement of mathematical models, and considers computational algorithms and software tools for solving problems analysis and forecasting of processes.

Advancing Climate Modeling through High-Performance Computing: Towards More Accurate and Efficient Simulations

A crucial branch of science called climate modeling uses mathematical equations and computer simulations to study and forecast the Earth's climate sys- tem. The main elements of climate modeling, such as general circulation models (GCMs), data assimilation methods, and numerical formulations, are outlined in this paper. GCMs, which include grid point and spectral models, are effective instruments for examining the behavior of the climate. Four-Dimensional Data Assimilation (4D-Var) is one example of a data assimilation technique that in- corporates observational data into models to improve their correctness. Numeri cal methods, ocean dynamics, heat transport, radiative transfer, and atmospheric dynamics are all included in numerical formulations. The simulation of different climate processes is possible because to these mathematical representations. Fur thermore, the detection of precipitation patterns within climate modeling is using machine learning techniques like Random Forest more frequently. This paper highlights the importance of high-performance computing (HPC) in climate modeling, boosting efficiency and simulations, in the context of research technique. Advanced data assimilation and validation techniques are also examined, as well as the influence of high-resolution modeling on small-scale climatic processes. On HPC platforms, accessibility to climate modeling is addressed. It is shown how climate modeling crosses physics, mathematics, computer science, and engineering to be interdisciplinary. A comprehensive understanding of the Earth's intricate climate system gains from the integration of all its parts, from atmospheric dynamics to data assimilation. We explore the consequences of these research approaches, their contribution to enhancing climate prediction models, and the influence of various factors on climatic variables in the debate. Climate modeling becomes an essential tool for studying precipitation patterns and climate change, ultimately improving our comprehension of the complex cli- mate system on Earth.

Some cases of explicit expression of the resulting field strength of magnets placed in the field of external sources

Formulas for calculating of the resulting magnetic field strength of magnets with a given magnetization distribution or given field of external sources are presented. We have collected exactly those cases where a user who does not have much experience in the field of computational mathematics and programming can perform calculations using these formulas. Namely, in these cases formulas for tension are mostly expressed in final form through elementary functions or require the use of one of the standard subroutines available in the library of any programming language. Such formulas can serve both as reference material and for solving corresponding problems with suitable real objects, as well as for determining optimal strategies and the optimal set of input parameters when using universal software packages and assessing the error of the results obtained.

Educating Professionals to Develop Nature-Based Solutions (NBS) as Infrastructure for Water Pollution Control: A Course Proposal

The objective of this study was to design a university-level course focused on Nature-Based Solutions (NBS) for water pollution control. The work unfolded in three phases: the initial planning, course delivery, and assessment of learning outcomes. In the planning phase, a set of competencies was outlined using the Developing a Curriculum Method (DACUM), resulting in defined learning outcomes and a structured course outline. Subsequently, the course was conducted over a two-week period, employing a hybrid format including both online and in-person sessions. The assessments of the learning outcomes included one test, an assignment, a satisfaction survey, and the post-course feedback. As a result of the planning phase, four competencies, seven learning outcomes and four course units were defined. The participant cohort encompassed a diverse group of 50 individuals, including undergraduate and postgraduate students, professionals working in industry and institutions, and professors. The assessment of the learning outcomes showed good results. However, issues regarding the mathematical calculations and field-trip experience were noted, suggesting areas for course enhancement. The participants expressed high satisfaction levels across the various course components. Notably, 70% of the participants indicated the application of the acquired knowledge in their professional endeavors. These findings underscore the successful implementation of the course, establishing it as a pioneering university-level program in NBS for water pollution control.

Modelling insertion behaviour of PVP (Polyvinylpyrrolidone) and PVA (Polyvinyl Alcohol) microneedles

A comprehensive investigation into the effects of nonlinear material behaviour of polymeric (MN) and skin on the dynamics of the MN insertion in skin was undertaken in this study using experiments and numerical simulations. The nonlinearity of the material behaviour was incorporated by employing the Ramberg–Osgood and neo-Hookean equations for stress–strain relationships for the MN materials and skin, respectively. For this purpose, a characteristic type of dissolving MN array was selected. This type of MN is made by a combination of poly(vinyl alcohol) and poly(vinyl pyrrolidone). The numerical simulations were validated using experimental investigations where the MNs were fabricated using laser-engineered silicone micromould templates technology. Young’s modulus, Poisson’s ratio, and compression breaking force for the MN polymers were determined using a texture analyser. The alignment between experimental findings and simulation data underscores the accuracy of the parameters determined through mechanical testing and mathematical calculations for both MN materials (PVP/PVA) and skin behaviour during the MN insertion. This study has demonstrated a strong alignment between the experimental findings and computational simulations, confirming the accuracy of the established parameters for MNs and skin interactions for modelling MN insertion behaviour in skin, providing a solid foundation for future research in this area.

Generative artificial intelligence performs rudimentary structural biology modeling

Natural language-based generative artificial intelligence (AI) has become increasingly prevalent in scientific research. Intriguingly, capabilities of generative pre-trained transformer (GPT) language models beyond the scope of natural language tasks have recently been identified. Here we explored how GPT-4 might be able to perform rudimentary structural biology modeling. We prompted GPT-4 to model 3D structures for the 20 standard amino acids and an α-helical polypeptide chain, with the latter incorporating Wolfram mathematical computation. We also used GPT-4 to perform structural interaction analysis between the anti-viral nirmatrelvir and its target, the SARS-CoV-2 main protease. Geometric parameters of the generated structures typically approximated close to experimental references. However, modeling was sporadically error-prone and molecular complexity was not well tolerated. Interaction analysis further revealed the ability of GPT-4 to identify specific amino acid residues involved in ligand binding along with corresponding bond distances. Despite current limitations, we show the current capacity of natural language generative AI to perform basic structural biology modeling and interaction analysis with atomic-scale accuracy.

Quantifying the risk of spillover reduction programs for human health.

Reducing spillover of zoonotic pathogens is an appealing approach to preventing human disease and minimizing the risk of future epidemics and pandemics. Although the immediate human health benefit of reducing spillover is clear, over time, spillover reduction could lead to counterintuitive negative consequences for human health. Here, we use mathematical models and computer simulations to explore the conditions under which unanticipated consequences of spillover reduction can occur in systems where the severity of disease increases with age at infection. Our results demonstrate that, because the average age at infection increases as spillover is reduced, programs that reduce spillover can actually increase population-level disease burden if the clinical severity of infection increases sufficiently rapidly with age. If, however, immunity wanes over time and reinfection is possible, our results reveal that negative health impacts of spillover reduction become substantially less likely. When our model is parameterized using published data on Lassa virus in West Africa, it predicts that negative health outcomes are possible, but likely to be restricted to a small subset of populations where spillover is unusually intense. Together, our results suggest that adverse consequences of spillover reduction programs are unlikely but that the public health gains observed immediately after spillover reduction may fade over time as the age structure of immunity gradually re-equilibrates to a reduced force of infection.

An Example of Using Advanced Excel Applications Within the Scope of Financial Mathematics Calculations: Modelling of Calculations Related to Annuities in Microsoft Excel Program

Financial mathematics applications, form the mathematical basis for rational financial decisions within the scope of financial management. Carrying out financial management in line with the scientific rules is of vital importance for businesses to sustain their existence and carry out their activities effectively and efficiently. In this context, the ability to carry out financial management rationally is only based on the correct determination of the mathematical datas (etc. time value of money) that forms the basis for decisions. The use of technology in this area is very important and technology level in this area has evolved from financial calculators to computer programs and MS. Excel program is perhaps the most important application tool in this field according to its mathematical calculation capacity and capability. In this regard, the study reveals how to perform complex calculations regarding the present and future values of different annuity types in Excel. The calculation of all variables related to annuity calculations and the mathematical relationships between variables are discussed separately according to different annuity types is examined with a model which developed in Excel program within the scope of the purpose of the study. The study will provide guidance to academics related to the field and professionals working in the field of financial management by combining theoretical knowledge and practical applications.

The influence of mental calculations on brain regions and heart rates

Performing mathematical calculations is a cognitive activity that can affect biological signals. This study aims to examine the changes in electroencephalogram (EEG) and electrocardiogram (ECG) signals of 36 healthy subjects during the performance of arithmetic tasks. To process EEG signals in different frequency bands, the energy and entropy of entropy (EoE) were extracted from the power spectrum and phase spectrum, respectively. Statistical analysis was conducted to determine meaningful features. These features were sent into support vector machine (SVM) and multi-layer perception (MLP) classifiers to assess their capability in separating math and rest classes. Results indicated the highest classification accuracy of 98.4% for classifying good counters in math and rest state using the MLP method. Based on the majority of features selected for each EEG channel, discriminative brain areas were identified. Analyzing EEG signals proved that math calculation may have multiple influences on various parts of the brain. By comparing good counters’ brain activities to those in a resting state, prominent changes were observed in the F4, C4, T4, T5, P3, and O2 areas. However, O1 and O2 channels showed significant changes in the brain of bad counters compared to the resting state. Considering ECG signals also demonstrated that during math calculation the number of heart rates per minute surpasses the rest state. These alterations can occur due to cognitive abilities or emotional processes which were observed to be prominent in subjects who performed more accurate calculations.

МАТЕМАТИКАЛЫК МАСЕЛЕЛЕРДИ АР ТҮРДҮҮ ЖОЛДОР МЕНЕН ЧЫГАРУУ ОКУУЧУЛАРДЫН ЧЫГАРМАЧЫЛЫК ИШМЕРДҮҮЛҮГҮН ӨСТҮРҮҮНҮН КАРАЖАТЫ КАТАРЫНДА

The article discusses solution of mathematical tasks in different ways and teaching students to solve them applying different methods, which helps to increase the level of cognitive interest of students. The goals of solving tasks in different ways are: ✓ to expand students' knowledge of various ways of solving math tasks; ✓ to teach different methods of mathematical calculations; ✓ to provide with the advanced capacity to solve problems in different ways. The goals, role and significance of solving mathcalculations in different ways are also reflected and accompanied by examples. Problem solving using a variety of methods plays a key role in successfully achieving goals and personal and professional development. Several roles of this method can be listed.

A New Variant of the Conjugate Descent Method for Solving Unconstrained Optimization Problems and Applications

Unconstrained optimization problems have a long history in computational mathematics and have been identified as being among the crucial problems in the fields of applied sciences, engineering, and management sciences. In this paper, a new variant of the conjugate descent method for solving unconstrained optimization problems is introduced. The proposed algorithm can be seen as a modification of the popular conjugate descent (CD) algorithm of Fletcher. The algorithm of the proposed method is well-defined, and the sequence of the directions of search is shown to be sufficiently descending. The convergence result of the proposed method is discussed under the common standard conditions. The proposed algorithm together with some existing ones in the literature is implemented to solve a collection of benchmark test problems. Numerical experiments conducted show the performance of the proposed method is very encouraging. Furthermore, an additional efficiency evaluation is carried out on problems arising from signal processing and it works well.

Hydrodynamic Impact of Dusty Fluid-Suspended Solid Particles in a Single-Walled Corrugated Channel for Water-Curing Infrastructure Networks

Infrastructure engineering is impacted by solid particles in fluids, and engineering components are influenced by fluid flow methods. This work explores the effects of dusty fluids with suspended solid particles in a single-walled corrugated channel using electromagnetic hydrodynamics. Potential, continuity, and momentum equations were employed to study the periodic sinusoidal waves in the corrugations of two wavy walls using the perturbation method. We assessed the impact of corrugation on velocity for EMHD fluid flow using mathematical computation, concentrating on the analytical velocity solutions. The analysis of velocity profiles through graphs reveals that corrugation affects fluid and particle velocity behavior, with small amplitude reducing wave effects and dusty particles boosting velocity. The proposed model uses mathematical induction to solve engineering problems using corrugated wall conditions for fluid control during curing stages. It may be valuable for sanitation networks, rainwater drainage networks, and irrigation systems. In the end, a thorough examination of the obtained results and information from past papers demonstrated a high level of agreement. Additionally, its use in the curing of water will offer alternative methods of managing the flowing fluid than mechanical pressure.

PROBLEMATIC ISSUES OF MECHANICS OF DEFORMABLE SOLIDS, AFFECTING THE ACCURACY OF ITS TECHNOLOGICAL APPLICATIONS. 1. INTRODUCTION

The need for an intelligible consideration of some problems in the mechanics of a deformable solid, which strongly affect the accuracy and reliability of mathematical models and calculation formulas obtained on its basis when solving specific engineering and technological problems in the production of various metal products, is substantiated.

Approximate solutions for diatomic molecules under combined potentials in a global monopole and Aharonov–Bohm flux field

AbstractBound state energy eigensolutions of nine different diatomic molecules, specifically, , TiH, , CO, NO, ScH, CrH, HCl and LiH, placed in a point‐like global monopole, have been calculated by solving the time‐independent Schrödinger equation (SE). The molecules are confined by the Aharonov–Bohm (AB) flux field and the interaction potential among the charged particles is governed by the combined screened modified Kratzer potential (SMKP) plus Hulthén potential model. Three other special cases of the interaction potential have also been discussed here. Asymptotic iteration method has been used for the mathematical calculations. It is difficult to solve the SE exactly for any non‐zero values of the azimuthal quantum number due to the presence of the centrifugal barrier term. The well‐known Pekeris approximation technique for the terms and has taken into consideration for the purpose of performing numerical computations connected to an arbitrary state. The outcomes of this study are in reasonable agreement with the results of previous research on SMKP, Kratzer‐Fues potential, and modified Kratzer potential in the Minkowski space. It is observed that the energy spectra of the diatomic molecules suffer considerable change due to the effects of the background AB‐flux field and topological defect parameter.