Mathematical Solution Research Articles

Approximation of the Absorption Spectrum of Indium Phosphide in the Context of Simulation of the Process of Sensitivity Enhancement

Examines the fundamental rights of Phosphide of India, legitimized by Tellur and, in the last resort, compensated for. Data on the composition of four high-quality images of the InP: Cu photoelectronic spectrum are presented in the individual layers. The work is characterized by the semi-empiric approach to photoconduction of InP: Cu oxide films. It is concluded that the photoresistance Iph (α(ћω)) was analytically approximated as the function of the experimental-complete spectral distribution of the coefficiency phosphorus india. It is proposed to use five approximating functions with the aim of analyzing the coefficient of absorption of Indian phosphorus α(ћω). Completed 5 locations with different signs of median isolation. On the basis of analytical amplitudes, the complete analytical amplitude Iph(α(ћω)) is modelled. Analogously, five conclusions were drawn that indicate a sign of median isolation. Five non-stationary measures of IF photometry have been taken (as two functions: co-efficiency of exposure, as photo energy functions, and time-consuming observations) in normal situations. The answer to the question is the most mathematical and physical solution of the proximate function α(ћω). Obviously, it shows that this the degree of variance is optimal for its implementation (inclusion of this degree of variance in the structure Iph = f(α) and α = f(ћω)) of the complete analytical description of the process photoconductivity. It should be noted that subsequent research may be based on the establishment of physical bases of photoconductivity in the short wave of fundamental transfers of phosphorus from India, as well as research into the properties of air on the high InP: Cu layer, with its stability and stability.

Enhancing Supply Chain Sustainability and Reliability Through WSM and TOPSIS: A Symmetrical Real-World Case Study

Large corporations have recently demonstrated an increasing propensity to enhance the sustainability and reliability of their supply chains in order to comply with environmental regulations and improve customer satisfaction through on-time demand fulfillment. There are two phases to this study: mathematical modeling and model solution using precise techniques. In the first step, a mixed-integer linear programming model is developed. This model is an improvement of an existing supply chain model. Further, our suggested strategy is verified by using numerical data based on three criteria and four suppliers. The goals of the proposed model are to maximize supply chain reliability, economic profit, and social responsibilities by taking suppliers’ priorities into account. Modeled as a mixed-integer linear programming problem, the constraints on the problem include budget, emission, demand, allocation, facility, and shipping capacity. Power symmetry and information symmetry are incorporated in order to perform symmetric analysis. The weighted sum method (WSM) and the technique for order of preference by similarity to ideal solution (TOPSIS) are the two methods used in the second step of solving the model to identify the best supplier. In order to evaluate how well the proposed methodology was applied, a practical case was considered and implemented.

No Missing Flare in OJ 287

The quasar OJ 287 has shown large flares since 1888, following a pattern that arises in a supermassive black hole binary when the secondary hits the accretion disk of the primary, and releases a hot bubble of gas at every disk crossing. A complete mathematical solution of the flare sequence produced a list of future flares, the latest happening in the summer of 2022. Here I look into the origin of the idea that the lack of seeing the 2022 flare is a theoretical problem. During the summer OJ 287 cannot be observed by ground-based optical telescopes. In a paper published in 2021, ahead of the 2022 observing campaign, this was clearly stated. The often repeated claim that there is a “missing flare problem,” is a misunderstanding, as no detection was possible with the current instrumentation.

Medicinal Plants Approach for Diabetes Mellitus-A Computational Model

The multidimensional metabolic syndrome that includes diabetes mellitus poses a serious threat to world health. There is an increasing interest in researching herbal remedies for their possible therapeutic advantages, even as traditional allopathic treatments continue to be widely used. This work throws light on the multiple ways of metabolism and biochemical interactions of medicinal plants in the control of glucose level, highlighting their crucial role in the process. The work clarifies several herbal extracts' efficacy and safety profiles, such as Aloe vera, Garlic, Gurmar, Bitter Melon, Neem, Tulsi, and through a thorough literature review and empirical evidence. These plants, which are abundant in bioactive substances like tannins, flavonoids, and alkaloids, show promise in treating insulin resistance, improving pancreatic function, and controlling blood sugar level. A further assessment of the rising risk associated with diabetes mellitus is discussed, and a differential equation model for diabetes mellitus is developed to minimize the complications. When using medicinal plants to treat diabetes, several factors are considered, including blood sugar level, sugar intake activity, and plasma insulin concentrations. The stability criterion for the mathematical model is examined through the system of differential equations. A representation highlighting the medicinal plants that can aid individuals with diabetes mellitus is provided. The blood sugar level, insulin generalization variable and plasma insulin concentration have all been measured at different points in time. Aloe vera, Gurmar, Garlic, Tulsi, Bitter Melon and Neem are among the medicinal plants selected for their demonstrated anti-hyperglycemic properties due to their easy availability in India. Mathematical solutions were calculated for every plant and proved to be steady.

Modeling and Performance Evaluation of a Cellular Network with OMA and NOMA Users with Batch Arrivals by Means of an M[X]/M/S/0 Model

Nowadays, efficient spectrum usage is one of the most important design principles to take into account in wireless communications due to the exponential growth of mobile devices. In that sense, solutions such as Non-Orthogonal Multiple Access (NOMA) and cognitive radio (CR) have been proposed. In essence, NOMA allows some interference level by using non-orthogonal resource allocation with a tolerable increase in receiver complexity employing successive interference cancellation (SIC). In this work, a novel mathematical model of teletraffic for users performing accessment, simultaneously, by means of Orthogonal Multiple Access (OMA) and NOMA, is developed using a Markovian process that considers bursts of arrivals to model the access schemes. This novel procedure implies a closed-form solution of the proposed system compared to other works where these parameters are estimated assuming the moment generating function obtained with approximation models. The model is validated with a discrete event simulator, considering different scenarios and simulation conditions. The simulation results are in agreement with the mathematical solution proposed.

Indoor Pedestrian Positioning Method Based on Ultra-Wideband with a Graph Convolutional Network and Visual Fusion.

To address the challenges of low accuracy in indoor positioning caused by factors such as signal interference and visual distortions, this paper proposes a novel method that integrates ultra-wideband (UWB) technology with visual positioning. In the UWB positioning module, the powerful feature-extraction ability of the graph convolutional network (GCN) is used to integrate the features of adjacent positioning points and improve positioning accuracy. In the visual positioning module, the residual results learned from the bidirectional gate recurrent unit (Bi-GRU) network are compensated into the mathematical visual positioning model's solution results to improve the positioning results' continuity. Finally, the two positioning coordinates are fused based on particle filter (PF) to obtain the final positioning results and improve the accuracy. The experimental results show that the positioning accuracy of the proposed UWB positioning method based on a GCN is less than 0.72 m in a single UWB positioning, and the positioning accuracy is improved by 55% compared with the Chan-Taylor algorithm. The proposed visual positioning method based on Bi-GRU and residual fitting has a positioning accuracy of 0.42 m, 71% higher than the Zhang Zhengyou visual positioning algorithm. In the fusion experiment, 80% of the positioning accuracy is within 0.24 m, and the maximum error is 0.66 m. Compared with the single UWB and visual positioning, the positioning accuracy is improved by 56% and 52%, respectively, effectively enhancing indoor pedestrian positioning accuracy.

The analytical curvature distribution model of columns and mathematical solution for pushover analysis

AbstractThe acquisition of a flexural backbone curve for columns primarily relies on finite element analysis and experiments, of which the complexity and high cost are significant challenges. Hence, this study proposes an analytical curvature distribution model (CDM) along the full height of the column, which is the key point of formula derivation and theoretical solution of the column backbone curve. The proposed CDM is a piecewise function model composed of linear and quadratic functions, with the characteristics of continuity and differentiability at the intersection point. The deformation compatibility equations, equilibrium equations, and material constitutive equations based on the variables of CDM are constructed to form an equation system, the solution of which can be theoretically determined by an iterative algorithm. Furthermore, 155 test specimen columns of different materials, for example, reinforced concrete, high‐strength reinforced concrete, and shape memory alloy are used to validate the proposed CDM and mathematical solutions of pushover analysis through three crucial indicators, that is, goodness of fit of backbone curve, ultimate displacement, and peak force, indicating strong practicability, high accuracy, and wider applicability. This theoretical method can be applied to deal with the key issues of interest during pushover analysis, that is, predicting the flexural backbone curves with different materials, determining the curvature distribution throughout the entire process of pushover analysis, and characterizing the evolution process of the plastic region.

Using mathematical models in the assessment of the circulatory system in employees working under harmful occupational conditions

Introduction. According to the results of medical examinations of metallurgists, in the structure of newly identified somatic morbidity, circulatory system diseases (CSD) are one of the leading pathologies. To assess the prevalence of CSD in workers in harmful working conditions, it is possible to use various mathematical solutions as a tool. The objective of the study was to substantiate the possibility of using variance analysis and classification tree (CT) methods to assess the prevalence of circulatory diseases in industrial workers. Materials and methods. Data of medical examinations and a questionnaire-based survey of three hundred eight workers of steel production were input into a database. The interrelationship between CSD and individual and occupational risk factors was examined using a one- and two-way ANOVA. The classification tree method was used for a multivariate analysis. Results. The one- and two-way ANOVA revealed a statistically significant correlation between the CSD family history (p=0.001) and age, years of occupational exposure, overweight, blood glucose level, total cholesterol (p<0.05) and the CSD prevalence in the steel workers. We applied the classification tree method to make decisions on referring the subjects to potentially “healthy” and “sick” workers by determining the CSD prevalence in relation to various combinations of risk factors. Limitations. This study is limited to the results of medical examinations of the workers collected over a one-year period. Conclusions. Our experience in using the analysis of variance and classification tree to evaluate the CSD prevalence in ferrous industry employees allows recommending them for use in assessing the prevalence of various diseases in workers exposed to occupational hazards.

Impact of induced electric field on the motion of a charged particle in a uniform time-dependent magnetic field that is linearly increasing with time

The classical and quantum motion of a charged particle in a uniform constant magnetic field is widely studied in the scientific literature since it is a problem that allows an exact mathematical analytical solution. On the other hand the cases of a non-uniform, time-dependent or both non-uniform and time-dependent magnetic field lead to mathematical problems that do not have general exact analytical solutions except for a few very specific cases. We present in this work, the results for the two-dimensional motion of a charged particle in a uniform time-dependent magnetic field that is linearly increasing with time for a certain finite interval and then stabilizes to a constant value afterwards. The work draws attention to certain interesting features observed for the two-dimensional motion of the charged particle as a result of the interplay between the effects of an induced electric field and the time varying magnetic field.

Systematic integration of a rubric in first-year engineering calculus courses

ABSTRACT For many first-year engineering students, their first calculus or pre-calculus courses can be a substantial barrier for initial success and persistence to subsequent engineering courses. One approach that may mitigate this challenge for some students is to support their development as stronger metacognitive learners – learning how to self-evaluate and improve based on informed feedback. A structured mathematical problem-solving rubric designed to offer feedback on how to develop and communicate mathematical solutions to engineering problems can be a helpful tool to support metacognitive development. After a semester of careful and systematic instruction, practice, and use of such a rubric in engineering calculus courses, we found significant improvement in pre-calculus students' metacognitive awareness. A median split analysis showed that for both calculus and pre-calculus courses, the lower metacognitive half of each class improved significantly in their metacognitive abilities, as was the intent for the rubric. Students reported an overwhelmingly positive perception of the value of the rubric for their own learning, and the subset of calculus I students who improved in their sophistication of rubric use had significantly higher (12.5%) final exam scores compared to those who did not improve.

Interpretation of TSH results can be improved by reference values fluctuating in time.

The secretion of thyroid stimulating hormone (thyrotropin, TSH), is characterized by a marked circadian rhythm. Plasma or serum TSH values are significantly lower in the afternoon and in the evening as compared to the early morning. As in clinical practice, blood sampling time shows an important variation, a reliable assessment of thyroid status is often not an easy task for the clinician. The biological variation of TSH plays a major role in the intra-individual variability of TSH results in serum or plasma. The observed intra-day variation largely exceeds the reported inter-vendor variation and the coefficient of variation of clinical TSH assays. Therefore, a mathematical solution was sought for correcting interpretation of TSH results for sampling time. We have developed a cosinor model which allows to compensate TSH decision values for the fluctuating serum or plasma TSH concentrations throughout the day. The following mathematical function could be derived: corrected TSH cutoff_value (mIU/L)=0.40+0.24*cos(((π/12) *T)+6) in which T represents the time (hours). This mathematical function can be easily implemented into a laboratory's informatics system and furthermore allows a better tailored diagnosis of (subclinical) hyperthyroidism, regardless the blood sampling time. Implementing the corrected cut-off values result in a marked reduction of apparent (false positive) hyperthyroidism diagnosis, in particular in the afternoon.

Assessing the energy system's greenhouse emissions via the health of Smart Territories and Cities

The aim of this paper is to understand how the main drivers of air pollution and greenhouse emissions impact public health in a Smart Territory — meaning a technologically integrated city or neighborhood — as well as how to design an optimized energy system model beyond only data by including the holistic experience of its people through phenomenology and ethics. We understand that a Territory and a City is a complex system where mathematical tool modeling known as Design of Experiment (DOE) and its optimization solutions are required to establish causality and identify the variables that have a broader impact on public health so that mortality rates due to air pollution are reduced. DOE's statistical branch is a novel methodology when applied to energy systems and the design of Smart Territories and Cities. Because of it, we have been able to demonstrate how energy emissions, capacity and Levelized Cost of Energy (LCOE) affect the mortality rate and create the foundations for building fully decarbonised energy systems enhanced by mathematical solutions. However, the Cartesian approach of extrapolating from models which align themselves with economic growth alone will not solve the energy dilemma. In fact, the current energy transition project is based on outdated archetypes that lead to scary futures. To course-correct the problematic energy model of a Smart Territory, phenomenologists and creative imagination need to be cultivated and put into action together with mathematical modeling, leading to vectors of positive change and adaptation. Only then might the energy models designed to be reproducible could became ethically virtuous and therefore accepted by the Territory's co-dwellers within the chain of causalities.

Mathematical theory and CFD solutions for internal convective cooling of gas turbine blades highlighting the effects of rotation

A quasi-one-dimensional mathematical theory is developed for determining the effects of rotation on the fluid flow and heat transfer in a cooling channel within a rotating gas turbine blade. The three-dimensional intricacies in the solutions of the same problem are captured through accurate computational fluid dynamic simulations. The derived analytical closed-form solutions predict the amount by which the relative total temperature of the coolant changes as a result of rotation. It is shown that such changes due to rotation are significant proportion of the change of coolant temperature due to heat transfer. The computed spatial evolutions of the primary velocity field, secondary velocity field and the force fields are presented as the coolant progresses from the inlet to the outlet so that the complexities and subtleties are exposed to a high degree of visualizability. Detailed considerations to various components of the centrifugal, Coriolis and pressure forces are given. The flow field is shown to depend strongly on whether the coolant moves in the spanwise outward or inward direction. The three-dimensionality of the flow field is reflected in complex circumferential variations of the blade temperature and the internal heat transfer coefficient. When the effects of the x–component of the Coriolis force interacts non-linearly with the effects of the z–component of the centrifugal force and a drastic x-gradient in fluid density due to a thin thermal boundary layer, then the primary velocity profile may exhibit great complexity, including flow separation. The present paper thus captures the strong, non-linear, two-way coupling between the fluid dynamics and heat transfer in the internal convective cooling occurring in a channel within a rotating gas turbine blade. Based on about 100 three-dimensional computational fluid dynamics simulations, new heat transfer correlations are developed for average Nusselt number for a rotating channel that will be of practical use.

Sinusoidal heating on convective heat transfer of nanofluid under differential technique

AbstractSinusoidal convection describes a smooth and repetitive heat transfer oscillation that reasonably calculates the optimal heat transfer for nanoparticle's intermolecular interactions. This study aims to investigate the heat transfer effects of Stokes second problem on the performance of novel fractional differential operators based on rheological characteristics of nanofluid. For the sake of augmentation in thermal characteristics of the nanofluid, the fractionalized governing equations based on the suspension of nanoparticles namely copper and silver in ethylene‐glycol have been developed. The fractional Stokes second problem is simulated with the help of transformation techniques and statistical data analysis. The analytic optimization of mathematical solutions of velocity and temperature have been established in terms of newly defined different Mittag‐Leffler functions. The statistical data for velocity field is generated by varying Hartman number, Prandtl number and Eckert number. The comparative analysis for two types of fractional differential operators of temperature distribution is perceived through bar column label, three‐dimensional color pie chart, three‐dimensional color map surface with projection, three‐dimensional bars and linear fitting of data. The comparative results revealed that temperature distribution has a significant effect and great influence on the stability of nanofluid by the embedded parameters.

Study of Systems of Active Vibration Protection of Navigation Instrument Equipment

Assessment of the influence of vibration isolator parameters on the distribution of the system’s natural frequencies is a significant task in the design of vibration isolation systems. The root method was used to determine the natural frequencies of the controlled vibration isolator. For a certain feedback structure of a controlled electrodynamic type vibration isolator, the need for a consistent selection of parameters has been justified. A mathematical solution has been proposed for the approximate determination of the roots of the characteristic equation of the controlled vibration isolator, which enables the analytical assessment of the influence of the vibration isolator parameters on the distribution of its natural frequencies. The research has been conducted in relative parameters, which makes it possible to generalize the results. The specificity of the inertial dynamic vibration isolator, which in some cases is associated with the implementation of anti-resonance conditions, can lead to the fact that resonant frequencies can occur on both sides of the tuning frequency of the vibration isolator. The use of an elastic suspension on flat springs to protect navigation equipment from vibration allows reduction in the intensity of translational vibration, while not changing the orientation of the device relative to the Earth. The implementation of an elastic suspension according to the scheme of the inverted pendulum allows an increase in the effectiveness of vibration isolation, under the conditions of a controlled change of the vibration isolator parameters and due to the use of feedback. The results of this research can be used in precision systems, such as vibration isolators, laser processing equipment, ultraprecision measurements or medical devices.

Channel flow dynamics of fractional viscoelastic nanofluids in molybdenum disulphide grease: A case study

Nanoscopic fluids especially viscoelastic Nanofluids are very useful in engineering and industrial problems. This research is to determine the open channel flow of a viscoelastic nanofluid (namely Oldroyd-B (OBNF)). Oldroyd-B fluid (OBF) was used as the base fluid and molybdenum disulphide nanopatrials were added in the fluid to form desired OBNF. To convert the mathematical model to a fractional model from a classical order partial differential equation PDE, fractional type derivative named Caputo-Fabrizio (CF) was used. The main objective of this study is to find the exact mathematical solution for the temperature, concentration and velocity distributions by using integral transformation technique. Final results are discussed graphically for the influence of different parameters on calculated temperature, concentration and velocity. Skin friction of the said fluid and engineering related dimensionless numbers including Reynolds number (Re), Prandtl number (Pr), Grashof number (Gr) and Schmidt number (Sc) are also discussed. At the end a comparison is illustrated in graphical form between current studied fluid (i.e. OBNF), another non-Newtonian fluid (i.e. Maxwell Nanofluid (MWNF)) and Newtonian fluid. As we know speed of Newtonian fluid is greater than non-Newtonian fluid, the same statement is validated by our solution. It is also noted that adding molybdenum disulphide nanoparticles to grease, heat transmission increased to 19.11% and mass transmission decreased to 2.51%.

Multiquadric Collocations for Nonlinear Vibration of Functionally Graded Plates of Ti–6Al–4V Metal

While Finite Element Method (FEM) has proven reliable for analyzing linear or nonlinear stresses in materials, structures, and fluid flows, its reliance on mesh generation can escalate project simulation costs. In contrast, mesh- free techniques offer an alternative by directly generating system algebraic equations for the entire issue domain, bypassing the need for a preset mesh. This study focuses on investigating the nonlinear free vibration response of shear-deformable Functionally Graded Material (FGM) plates. These plates are expected to exhibit varying material properties, following a power-law distribution linked to the volume fractions of constituent materials as plate thickness increases. Utilizing shear deformation theories and von Karman nonlinear kinematics, the study seeks a mathematical solution for the real physical issues encountered in these plates. To address these challenges, a meshless method employing the Multi Quadric Radial Basis Function (MQRBF) is employed for evaluation. The computed results reveal insights into how different material properties and amplitudes influence the nonlinear free vibration response of composite plates. Comparing these outcomes to prior research demonstrates promising progress in this area.

Comparative study of optimization methods for building energy consumption and daylighting performance

When striving for sustainable development, designers encounter the formidable task of integrating the advantages of daylighting into energy-efficient designs. The process of investigating a multitude of design variables can be arduous and time-intensive. However, computational simulations provide indispensable insights into forecasting performance. A considerable number of these design challenges do not have explicit mathematical solutions; thus, black-box optimization techniques are favored for the purpose of determining the most effective design solutions. Popular meta-heuristic optimization algorithms, including the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Sine Cosine Algorithm (SCA), Grey Wolf Optimizer (GWO), Ant Lion Optimizer (ALO), and Multi-Verse Optimizer (MVO), are described and thoroughly analyzed in this article. In addition, the present study run empirical studies to compare these optimization algorithms by applying them to tackle five distinct daylighting and energy optimization problems associated with enhancing building performance. In the test cases, the present study results demonstrate that the PSO and MVO algorithms exhibit better performance compared to the GA and WOA algorithms. The selection of the most suitable algorithm is contingent upon the distinctive attributes of the problem, and the intricacy of the optimization landscape.

Revisiting Weak Energy Condition and wormholes in Brans-Dicke gravity

It is known that the formation of a wormhole typically involves a violation of the Weak Energy Condition (WEC), but the reverse is not necessarily true. In the context of Brans-Dicke gravity, the generalized Campanelli-Lousto solution, which we shall unveil in this paper, demonstrates a WEC violation that coincides with the appearance of unbounded sheets of spacetime within the region where 0<r<rs. The emergence of a wormhole in the region where r>rs is thus only an indirect consequence of the WEC violation. Whereas the two regions, 0<r<rs and r>rs, in general are disconnected by physical singularities at r=rs, they are both part of the same mathematical solution, and their behavior can provide insights into the WEC, which is a mathematical property of the solution. Furthermore, we utilize the generalized Campanelli-Lousto solution to construct a Kruskal-Szekeres diagram, which exhibits a “gulf” sandwiched between the four quadrants in the diagram, a novel feature in Brans-Dicke gravity. Overall, our findings shed new light onto a complex interplay between the WEC and wormholes in the Brans-Dicke theory.

A Mathematical and Analytical Solution for MHD Boundary Layer Flow and Heat Transfer of a Nanofluid Over a Stretching Sheet Using the Homotopy Analysis Method

A Mathematical and Analytical Solution for MHD Boundary Layer Flow and Heat Transfer of a Nanofluid Over a Stretching Sheet Using the Homotopy Analysis Method