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This research focuses on elucidating a system of partial differential equations designed to model the process of water uptake by a single root within an unsaturated soil. This model extends a unidimensional root scenario by incorporating radial and axial hydraulic conductance in the root structure. The flow dynamics in the rhizosphere are represented by the Richards equation, while a diffusion equation is employed to characterize water movement within the root. The resulting system forms a strongly coupled, nonlinear parabolic-elliptic system. To establish the existence and uniqueness of a solution, we utilize the technique of semi-discretization and the Schauder-Tychonoff fixed point theorem. Additionally, we approximate the system using a mixed finite element method, and the subsequent numerical tests presented align well with the model predictions. This comprehensive approach contributes to our understanding of the intricate dynamics involved in root water uptake and provides a robust framework for further exploration in this field. [ABSTRACT FROM AUTHOR]

In recent years, the demand for computing resources in daily life has risen due to the rapid development of smart terminal devices. Cloud computing facilities may not be able to handle the massive amounts of data that will be generated in the future. Edge computing, a new paradigm after cloud computing, places edge servers closer to the terminals, improving the efficiency of processing the massive data generated by the terminals. However, during actual use, the edge computing system is limited by factors such as population density and service demand, resulting in suboptimal data processing efficiency and operator profits. This paper studies the deployment of edge servers in a fixed area, focusing on operator profitability. We propose the Advanced K-Means method, an improvement of K-means for users with different needs in a fixed area, to maximize system profitability at various times. Experimental results based on subscriber and base station datasets from Melbourne’s Central Business District (CBD) demonstrate that this deployment strategy improves profitability by at least 22 % , outperforming several other representative approaches. [ABSTRACT FROM AUTHOR]

Some nonlinear real-valued equations have no solution in the real number field, and only roots of this nature are of practical interest. However, complex roots associated with the solution may introduce an interpretation of the physical problem analysis. This paper investigates the solution of nonlinear equations exploiting fractional order derivative (FOD) calculus resources. The theory addresses a solver that considers the FOD and Newton-Raphson method. The problem is extended to a multivariate fractional order derivative (MFOD) method so that a set of nonlinear equations can be resolved iteratively. Applications to the computation of the power flow problem in energy systems are used to illustrate some types of equations and solutions. The MFOD uses a numerical limits technique to determine a Jacobian required for the fractional application. This work demonstrates how real-valued nonlinear equations with complex roots can be solved by the MFOD Newton-Raphson approach. The results indicate the potentiality of the method reaches complex-valued solutions despite the iterative process starting with a real-valued guess. The complex-valued results are interpreted considering the connection between the imaginary part of a root and the divergence of the classical Newton-Raphson (CNR) method. [ABSTRACT FROM AUTHOR]

Malaria, a lethal protozoan disease transmitted through the bites of female Anopheles mosquitoes infected with Plasmodium parasites, remains a significant global health concern. This study introduces a compartmental mathematical model to explore the impact of insecticide use and malaria treatment based on awareness initiatives. The model incorporates the influence of media-based awareness on the effectiveness of insecticide utilization for malaria control. Key mathematical properties, such as positivity, boundedness of solutions, feasibility, and stability of equilibria, are systematically investigated. Our analysis demonstrates that all solutions to the system are positive and bounded within a specified set of initial conditions, establishing the mathematical soundness and epidemiological relevance of the model. The basic reproduction number R 0 is determined through the next-generation matrix method. Stability analysis reveals that the disease-free equilibrium is globally asymptotically stable when R 0 is less than one, while it becomes unstable if R 0 exceeds one. Global stability of the endemic equilibrium is established using an appropriate quadratic Lyapunov function in cases where R 0 surpasses one. We identify the most sensitive parameters of the model through normalized forward sensitivity indices. In addition, numerical simulations employing the Runge–Kutta method in Python software further validate our findings. Both analytical and numerical results collectively suggest that the integration of awareness-based insecticide usage with malaria treatment holds the potential for malaria elimination. This comprehensive approach not only contributes to the mathematical rigor of the model but also underscores its practical implications for effective malaria control strategies. [ABSTRACT FROM AUTHOR]

We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem, grounded in a purely algebraic theory of quantity spaces, allows the classical π theorem to be restated in an explicit and precise form and its prerequisites to be clarified and relaxed. Augmented dimensional analysis, in contrast to classical dimensional analysis, is guaranteed to take into account all relations among the quantities involved. Several examples are given to show that the information thus gained, together with symmetry assumptions, can lead to new or stronger results. We also explore the connection between dimensional analysis and matroid theory, elucidating combinatorial aspects of dimensional analysis. It is emphasized that dimensional analysis rests on a principle of covariance. [ABSTRACT FROM AUTHOR]

This paper develops a novel set of displacement temperature potential functions to solve the thermoelastodynamic problems in functionally graded transversely isotropic media subjected to thermal source. For this purpose, three-dimensional heat and wave equations are considered to obtain the displacement temperature equations of motion for functionally graded materials. In the present study, a systematic method is used to decouple the elasticity and heat equations. Hence one sixth-order differential equation and two second-order differential equations are obtained. Completeness of the solution is proved using a retarded logarithmic Newtonian potential function for functionally graded transversely isotropic domain. To verify the obtained solution, in a simpler case, potential functions are generated for homogeneous transversely isotropic media that coincide with respective equations. Presented potential functions can be used to solve the problems in various media like infinite and semi-infinite space, beams and columns, plates, shells, etc., with arbitrary boundary conditions and subjected to arbitrary mechanical and thermal loads. [ABSTRACT FROM AUTHOR]

Functionally graded materials (FGMs) are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties. This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method. Under the assumptions of the Euler-Bernoulli beam theory, the governing differential equations of an individual FGM beam are derived with Hamilton's principle and decoupled via the separation-of-variable approach. Then, the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method (TMM). Two models, i.e., a three-level FGM stepped beam and a five-level FGM stepped beam, are considered, and their natural frequencies and mode shapes are presented. To demonstrate the validity of the method in this paper, the simulation results by ABAQUS are also given. On this basis, the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out. The results show the accuracy and efficiency of the TMM. [ABSTRACT FROM AUTHOR]

A novel phase-field model for the propagation of mixed-mode hydraulic fractures, characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids, is proposed. In this model, the driving force for the phase field consists of both tensile and shear components, with the fluid contribution primarily manifesting in the tension driving force. The displacement and pressure are solved simultaneously by an implicit method. The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson (NR) iterative methods. The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks, and the limitations of the hydraulic fracture expansion phase-field model, which only considers mode I fractures, are revealed. In addition, the influence of matrix mode II fracture toughness value, natural fracture mode II toughness value, and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied. [ABSTRACT FROM AUTHOR]

More than half of the coronavirus disease 19 (COVID-19) related mortality rates in the United States and Europe are associated with long-term-care facilities (LTCFs) such as old-age organizations, nursing homes, and disability centers. These facilities are considered most vulnerable to spread of an pandemic like COVID-19 because of multiple reasons including high density of elderly population with a diverse range of medical requirements, limited resources, nursing activities/medications, and the role of external visitors. In this study, we aim to understand the role of visitor’s family members and specific interventions (such as use of face masks and restriction of visiting hours) on the dynamics of infection in a community using a mathematical model. The model considers two types of social contexts (community and LTCFs) with three different groups of interacting populations (non-mobile community individuals, mobile community individuals, and long-term facility residents). The goal of this work is to compare the outbreak burden between different centre of disease control (CDC) planning scenarios, which capture distinct types of intensity of diseases spread in LTCF observed during COVID-19 outbreak. The movement of community mobile members is captured via their average relative times in and out of the long-term facilities to understand the strategies that would work well in these facilities the CDC planning scenarios. Our results suggest that heterogeneous mixing worsens epidemic scenario as compared to homogeneous mixing and the epidemic burden is hundreds times greater for community spread than within the facility population.

The globalization in business and tourism becomes crucial more and more for the economical sustainability of local communities. In the presence of an epidemic outbreak, there must be such a decision on the policy by the host community as whether to accept visitors or not, the number of acceptable visitors, or the condition for acceptable visitors. Making use of an SIRI type of mathematical model, we consider the influence of visitors on the spread of a reinfectious disease in a community, especially assuming that a certain proportion of accepted visitors are immune. The reinfectivity of disease here means that the immunity gained by either vaccination or recovery is imperfect. With the mathematical results obtained by our analysis on the model for such an epidemic dynamics of resident and visitor populations, we find that the acceptance of visitors could have a significant influence on the disease’s endemicity in the community, either suppressive or supportive. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild- $ N.\,lugens $ N. l u g e n s -eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild $ N.\,lugens $ N. l u g e n s are also given. In addition, the sufficient conditions for the extinction and persistence of the wild $ N.\,lugens $ N. l u g e n s in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild $ N.\,lugens $ N. l u g e n s , and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions. [ABSTRACT FROM AUTHOR]

The choice of an adequate mathematical model is a key step in solving problems in many different fields. When more than one model is available to represent a given phenomenon, a poor choice might result in loss of precision and efficiency. Well-known strategies for comparing mathematical models can be found in many previous works, but seldom regarding several models with uncertain parameters at once. In this work, we present a novel approach for measuring the similarity among any given number of mathematical models, so as to support decision making regarding model selection. The strategy consists in defining a new general model composed of all candidate models and a uniformly distributed random variable, whose sampling selects the candidate model employed to evaluate the response. Global Sensitivity Analysis (GSA) is then performed to measure the sensitivity of the response with respect to this random variable. The result indicates the level of discrepancy among the mathematical models in the stochastic context. We also demonstrate that the proposed approach is related to the Root Mean Square (RMS) error when only two models are compared. The main advantages of the proposed approach are: (i) the problem is cast in the sound framework of GSA, (ii) the approach also quantifies if the discrepancy among the mathematical models is significant in comparison to uncertainties/randomness of the parameters, an analysis that is not possible with RMS error alone. Numerical examples of different disciplines and degrees of complexity are presented, showing the kind of insight we can get from the proposed approach. [ABSTRACT FROM AUTHOR]

The harmonic balance method (HBM) is one of the most widely used methods in solving nonlinear vibration problems, and its accuracy and computational efficiency largely depend on the number of the harmonics selected. The adaptive harmonic balance (AHB) method is an improved HBM method. This paper presents a modified AHB method with the asymptotic harmonic selection (AHS) procedure. This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response, by which the additional calculation is avoided. A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters, and then all solution branches of the amplitude-frequency response are obtained. Numerical experiments are carried out to verify the performance of the AHB-AHS method. Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples. Compared with the classical HBM and Runge-Kutta methods, the proposed AHB-AHS method is of higher accuracy and better convergence. The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems. [ABSTRACT FROM AUTHOR]

We consider a modified SIR model with a four-dimensional system of ordinary differential equations to consider the influence of a limited isolation capacity on the final epidemic size defined as the total number of individuals who experienced the disease at the end of an epidemic season. We derive the necessary and sufficient condition that the isolation reaches the capacity in a finite time on the way of the epidemic process, and show that the final epidemic size is monotonically decreasing in terms of the isolation capacity. We find further that the final epidemic size could have a discontinuous change at the critical value of isolation capacity below which the isolation reaches the capacity in a finite time. Our results imply that the breakdown of isolation with a limited capacity would cause a drastic increase of the epidemic size. Insufficient capacity of the isolation could lead to an unexpectedly severe epidemic situation, while such a severity would be avoidable with the sufficient isolation capacity. [ABSTRACT FROM AUTHOR]

This paper proposes a quasi-zero stiffness (QZS) isolator composed of a curved beam (as spider foot) and a linear spring (as spider muscle) inspired by the precise capturing ability of spiders in vibrating environments. The curved beam is simplified as an inclined horizontal spring, and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator. The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region. The harmonic balance method (HBM) is used to explore the effects of the excitation amplitude, damping ratio, and stiffness coefficient on the system's amplitude-frequency response and transmissibility performance, and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method (RK-4). The experimental data of the QZS isolator prototype are fitted to a nine-degree polynomial, and the RK-4 can theoretically predict the experimental results. The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator. The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz, and it can isolate 90% of the excitation signal at 7 Hz. The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators. [ABSTRACT FROM AUTHOR]

We prove that it is possible to obtain the exact closure of SIR pairwise epidemic equations on a configuration model network if and only if the degree distribution follows a Poisson, binomial, or negative binomial distribution. The proof relies on establishing the equivalence, for these specific degree distributions, between the closed pairwise model and a dynamical survival analysis (DSA) model that was previously shown to be exact. Specifically, we demonstrate that the DSA model is equivalent to the well-known edge-based Volz model. Using this result, we also provide reductions of the closed pairwise and Volz models to a single equation that involves only susceptibles. This equation has a useful statistical interpretation in terms of times to infection. We provide some numerical examples to illustrate our results. [ABSTRACT FROM AUTHOR]

Broadly speaking, models are representations of something concrete or not. In science, models have always a purpose related to understanding and explaining phenomena. This requires focus and selecting what to represent and what not to represent and how to represent, among other things. Thus, a side effect of developing the scientific method is the development of a well-structured modelling paradigm. Starting from phenomena and objects, I discuss many decision-abstraction steps in the modelling process that leads to models of phenomena expressed mathematically or computationally, highlighting underlining contexts and procedures. This discourse is undertaken centred on a cross- and trans-disciplinary system science perspective. It grounds on a personal perspective and may be considered as a model of the modelling process. [ABSTRACT FROM AUTHOR]

This paper considers a mathematical model that accounts for the hematological disorders of blood in its flow in human arteries. Blood is described as a Newtonian fluid but with its viscosity as a function of the hematocrit, plasma viscosity, and shape factor of the red blood cells. The artery is modeled as a flexible circular pipe with the blood flow as oscillatory. This model is solved using HAM (Homotopy Analysis Method), an approximate analytical method, and we computed expressions for wall shear stress (WSS) and volumetric flow rate. With the help of publicly available data, blood flow in the human femoral artery for male and female populations aged 19 to 60 and above years is simulated for healthy, anemia, and polycythemia cases. The model projected a significant difference in the mean volumetric flow rates in the conditions mentioned above. Results also indicated that the mean WSS of healthy and anemic populations are not significantly different. However, a significant difference in the mean has been observed in healthy and polycythemic conditions. Furthermore, a 33.3% decrease in hematocrit value from that in the normal range (taken as 0.45) of a healthy population has increased the flow rate by 33.5%. For a value 33.3% above 0.45, there is a decrease of 42.7% in the flow rate.

The motion of a test particle within the context of the restricted four-body problem (R4BP) driven by a new kind of potential, called the generalized Manev potential, with perturbations in the Coriolis and centrifugal forces is considered in this study. The system possesses eight libration points which were distributed on its plane of motion in different manner from those of the usual Newtonian potential. Unlike the case of the perturbed R4BP under Newtonian potential, where two of these librations are stable, all of them are unstable in linear sense under Manev potential. We found that a gradual perturbation in the centrifugal force causes the trajectories of motion to drift inward but the Coriolis force was proven to have no effect on the location of the libration points of the system. Using first order Lyapunov characteristic exponents, the dynamical behavior of the system is found irregular. We experimented with a high velocity stellar system (82 G. Eridani) to establish the applicability of the model in astrophysics. [ABSTRACT FROM AUTHOR]

The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion, vicious, and Darcy dissipation is studied. The first region consists of a clear fluid, and the second one is filled with a nanofluid saturated with a porous medium. The behaviors of Cu-H2O, In-H2O, and Au-H2O nanofluids are analyzed. The transport properties are assumed to be constant. The coupled non-linear equations of the flow model are transformed into the dimensionless form, and the solutions for the velocity, temperature, and concentration are obtained by the regular perturbation technique. Investigations are carried out on the flow characteristics for various values of the material parameters. The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number, solutal Grashof number, and Brinkman number while decrease with the porosity parameter and solid volume fraction. [ABSTRACT FROM AUTHOR]

Multi-access edge computing (MEC) offers cloud computing capabilities and IT services situated at the Radio Access Network (RAN) in the mobile users' proximity. Applications could offload their computation-intensive tasks to the MEC servers. Consequently, MEC significantly diminishes the mean response time and job rejection probability compared to conventional Mobile Cloud Computing (MCC). Cost-performance trade-off is one of the major concerns of the system designers. Low performance leads to the Service Level Agreement (SLA) violation and disappoints the service consumers. On the other hand, reaching high performance by augmenting the number of servers in the MEC and Cloud sides incur more infrastructure and other operational costs. In this paper, we formulate the mentioned cost-performance trade-off into an optimization problem. We demonstrate that the optimization problem is integer and non-linear. Moreover, we propose a capacity planning framework to determine the optimal number of servers in the MEC and Cloud sides, minimizing the Total Cost of Ownership (TCO) with SLA satisfaction. The proposed capacity planning framework gains from the simulated annealing algorithm to obtain a globally optimum solution. Furthermore, we deploy the stochastic performance model to measure mean response time and job rejection probability at each iteration. Numerical results reveal that the proposed framework determines the optimal solution within a reasonable time. [ABSTRACT FROM AUTHOR]

This paper presents the current state of mathematical modelling of the electrochemical behaviour of lithium-ion batteries (LIBs) as they are charged and discharged. It reviews the models developed by Newman and co-workers, both in the cases of dilute and moderately concentrated electrolytes and indicates the modelling assumptions required for their development. Particular attention is paid to the interface conditions imposed between the electrolyte and the active electrode material; necessary conditions are derived for one of these, the Butler–Volmer relation, in order to ensure physically realistic solutions. Insight into the origin of the differences between various models found in the literature is revealed by considering formulations obtained by using different measures of the electric potential. Materials commonly used for electrodes in LIBs are considered and the various mathematical models used to describe lithium transport in them discussed. The problem of upscaling from models of behaviour at the single electrode particle scale to the cell scale is addressed using homogenisation techniques resulting in the pseudo-2D model commonly used to describe charge transport and discharge behaviour in lithium-ion cells. Numerical solution to this model is discussed and illustrative results for a common device are computed. [ABSTRACT FROM AUTHOR]

The mathematical study of the growth and treatment of cancer has been of great interest to researchers in the recent past as that can help clinical practitioners in adopting new treatment strategies to fight effectively against cancer. Although chemotherapy is the most common method of cancer treatment, the drug-resistant nature of tumor cells and the toxic effect of chemotherapeutic drugs on normal cells are major threats to the success of chemotherapy. In this paper, we propose a multi-drug chemotherapy model combined with an optimal control approach in which the amount of drugs is taken as control functions. The underlying mathematical model discusses the evolution of a heterogeneous tumor population and the dynamics of normal cells under chemotherapy. The model incorporates the pharmacokinetics of the anticancer agents as well. The proposed optimal control approach ensures maximum decay of the tumor cells while preserving a sufficient level of normal cells that would help faster recovery. [ABSTRACT FROM AUTHOR]

One of the critical measures to control infectious diseases is a lockdown. Once past the lockdown stage in many parts of the world, the crucial question now concerns the effects of relaxing the lockdown and finding the best ways to implement further lockdown(s), if required, to control the spread. With the relaxation of lockdown, people migrate to different cities and enhance the spread of the disease. This work presents the population migration model for n-cities and applies the model for migration between two and three cities. The reproduction number is calculated, and the effect of the migration rate is analyzed. A punctuated lockdown is implemented to simulate a protocol of repeated lockdowns that limits the resurgence of infections. A damped oscillatory behavior is observed with multiple peaks over a period.

In literature, various mathematical models have been developed to have a better insight into the transmission dynamics and control the spread of infectious diseases. Aiming to explore more about various aspects of infectious diseases, in this work, we propose conceptual mathematical model through a SEIQR (Susceptible-Exposed-Infected-Quarantined-Recovered) mathematical model and its control measurement. We establish the positivity and boundedness of the solutions. We also compute the basic reproduction number and investigate the stability of equilibria for its epidemiological relevance. To validate the model and estimate the parameters to predict the disease spread, we consider the special case for COVID-19 to study the real cases of infected cases from [2] for Russia and India. For better insight, in addition to mathematical model, a history based LSTM model is trained to learn temporal patterns in COVID-19 time series and predict future trends. In the end, the future predictions from mathematical model and the LSTM based model are compared to generate reliable results.

COVID-19 global outbreak has been significantly damaging the human well-being, life style of people and the global economy. It is clear that the entire world is moving into a dangerous phase of this epidemic at the moment. With absence of a preventive vaccine, the governments across world implement, monitor and manage various public health and social distancing measures to control the spread of this extremely contagious disease and it is found that most of these responses have been critical results of numerous mathematical and decision support models. In this study, SEIR compartment structure is used to model the COVID-19 transmission in Sri Lanka. Reported cases data during the first 80 days of the outbreak is used to model the time dependent transmission rate of the disease. Optimal transmission rates and initial size of the exposed and infected sizes of the populations are then estimated matching between clinically identified cases to model based simulated outcomes.

Human motion induced vibration has very low frequency, ranging from 2 Hz to 5 Hz. Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity. In this paper, inspired by the human spine, we propose a novel bionic human spine inspired quasi-zero stiffness (QZS) vibration isolator which consists of a cascaded multi-stage negative stiffness structure. The force and stiffness characteristics are investigated first, the dynamic model is established by Newton's second law, and the isolation performance is analyzed by the harmonic balance method (HBM). Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages, and reducing the damping values and external force values can obtain better low-frequency isolation performance. In comparison with the linear structure and existing traditional QZS isolator, the bionic spine isolator has better vibration isolation performance in low-frequency regions. It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications. [ABSTRACT FROM AUTHOR]

House building is a desire for many individuals these days. If we create our own structure via our own efforts, we may save money to a certain amount, but this is not feasible for everyone, particularly for families with two employees. Because the employee's family cannot devote their entire attention to all areas of the building as and when necessary, they naturally present material contracts and negotiate with the builders. The length and cost of a prefabricated construction project are converted into quantifiable cost data during the early stages of the project using an earned value analysis technique, which is then used to determine the project's implementation cost. A mathematical model of the pre-cost budget for prefabricated buildings is built based on the project parameters. By comparing the improved neural network algorithm's cost budget performance in the early stages of an assembly construction project to that of the original mathematical model, it was determined that the improved neural network algorithm's cost budget performance was superior, and the cost budget performance was improved. Methodology: first plan the preparation of the house construction, then determine whether the location is urban or rural, then calculate the square footage and floor division for their convenience, as well as check quantity take off, evaluate the primary materials for house construction, and paint the entire house, as well as fix rooms doors, windows, and window grilles. Following the selection of floor laying stones, the budget will be computed. Result and conclusion: I concluded that home building estimation is beneficial for newly constructed individuals, and then this project thoroughly taught how to calculate the house construction budget and how to implement it within our budget. [ABSTRACT FROM AUTHOR]

There are several soft computing methods in use to predict rainfall. Mainly two features were included to increase rainfall prediction: (1) using data pre-processing procedure and (2) using a modular approach. The projected pre-processing approach incorporated Moving Average (MA) and Singular Spectrum Analysis (SSA). The method of modular was poised of Support Vectors Regression l (SVR) models or the Rough Set Technique (RST). In the development for forecasting of rainfall, the RST was initially applied for the data- preprocessing. Modular models used to pre-process the preparation data into three distinct subsets (level-1, level-2, and level-3) from the scales of the trained data, and lastly, two SVRs were used in the level-2 and level-3 subsets. In contrast, Artificial Neural Network (ANN) or SVR was concerned with predicting and was useful in training the data. Each day's rate of downpour proof, the level-1 subset tended to be modelled by the ANN because it was overwhelming in the training data. ANN is beneficial for huge-scale samples training because of its corresponding information processing configuration. This work explores the use of hybridization technique of RST and time series, where RST helps to find the essential attribute from the collection of raw meteorological data set then analyzing the important characteristic using time series and various classifiers. There are several prediction techniques available to predict based on meteorological data set to suitably predict a meteorological phenomenon. In this work, our objective is to find the most frequent meteorological phenomena which affects our state most. Purposefully, we consider the RST to predict the most significant meteorological phenomena by using the RST and predict the rainfall per day basis. Hybrid soft computing techniques and RST are used in the present work. We validate our claim using the Chi-square test. [ABSTRACT FROM AUTHOR]

Primeval history of India, and religious text manifest the close acceptance of "Third gender" in the society. It is only after the colonial interventionism the divide and rule policy of British, transgender were criminalized by passing the "Criminal tribe act of 1871" which created the punishment and fine for cross dressers in public sphere. Study was conducted by employing Quantitative method through which semi-structured interview schedule was used to collect the data from 77 transgender (transwomen (58), transmen (19)) residing in Chennai, Tamil Nadu. Data collected were analyzed using SPSS 21 software, where regression and correlation method has been employed to find out the relationship between the variables. Results shows that Transgender ID card forms the basic identity document to benefit the various amenities of government and Transmen were deserted to get those provisions because of Trans ID card which is not offered to them. Transwomen were fortunate to apply for the subsidy policies of State government, in case of Transmen were struggling to form their individuality within the Transgender community. Study accomplishes with the view that there should be a clarity in the classification and variance between the Transwomen and Transmen, as their transition process differs, so there ought to be strategies to address and satisfy the need of both categories of Transgenders. [ABSTRACT FROM AUTHOR]

In this research, a mathematical model consisting of non-pharmaceutical control measures is formulated. The developed model helps to examine the transmission of COVID-19 infection in Plateau State, Nigeria, using face masks c f and social distancing c d as control measures. Data used for the simulation of the developed model were obtained from Nigeria Centre for Disease Control which was fitted to the system of ordinary differential equations using nonlinear least squares method. Results at baseline values c f = 0.1 and c d = 0.2 of control measures indicate 2.3 estimation as basic reproduction number which suggests that COVID-19 in Plateau State tends towards endemic state. However, above about 40% in the use of face masks in the population and corresponding above 50% adherence to social distancing could as well bring down the basic reproduction number to a value below 1 necessary for disease eradication. The results at baseline values further indicate that the peak of the COVID-19 had been reached in less than 250 days from the first detection date after about 476,455 undetected asymptomatic individuals, 92,168 undetected symptomatic individuals and 83,801 detected quarantined individuals have been fully infectious. Therefore, the policymakers in Plateau State have the possibility of eradicating the disease with further strict non-pharmaceutical control measures provided that the present conditions of analysis remain fairly the same. [ABSTRACT FROM AUTHOR]

Numerous investigations are introduced to designate the growth dynamic of coronavirus (GDC). We aim to study the dynamic system in view of the fractional calculus in terms of the Caputo-Fabrizio derivative. The flexibility of this operator implies more information and application regarding the dynamic system. Our study will be in two directions, the first one is to suggest the fractional dynamic system without perturbation and the second part is to include a perturbation terms. [ABSTRACT FROM AUTHOR]

The software project manager must plan and conduct testing activities economically and efficiently. Due to the constraints, such as limited testing resources, delivery time, and cost, it isn't easy to conclude. The software reliability growth models (SRGMs) based on testing-effort, help the project manager in the decision process. Therefore, we reckon the testing effort function (TEF) during model formulation. This paper introduces a new model for estimating the growth of software reliability. This model incorporates generalized inflection S-shaped (GISS) distribution for TEF. Here, the TEF is involved as a time-dependent failure rate function. Besides, the developed model is in perfect debugging environment. Here, we estimate the values of the unknown parameters by the least square estimation (LSE). All the performance measures are calculated using real software failure data-set and comparisons made between the proposed model and the existing models. It is noted that the performance of the proposed model prediction for the total number of faults is more trustworthy. [ABSTRACT FROM AUTHOR]

In this article, we discuss an age-structured SIR model in which disease spread not only through direct person-to-person contacts, but also spread through indirect contacts. It is evident that age also plays a crucial role in SARS virus infection including COVID-19 infection. We formulate our model as an abstract semilinear Cauchy problem in an appropriate Banach space to show the existence of solution and also show the existence of steady states. In this study, it is assumed that the population is in a demographic stationary state and we show that there is no disease-free equilibrium point as long as there is a transmission of infection due to the indirect contacts in the environment. We also solved our model numerically to study the effect of indirect contacts on the density of infected individuals. [ABSTRACT FROM AUTHOR]

Queueing systems are modeled by equations which depend on a large number of input parameters. In practice, significant uncertainty is associated with estimates of these parameters, and this uncertainty must be considered in the analysis of the model. The objective of this paper is to propose a sensitivity analysis approach for a queueing model, presenting parameters that follow a Gaussian distribution. The approach consists in decomposing the output of the model (stationary distribution of the model) into a polynomial chaos. The sensitivity indices, allowing to quantify the contribution of each parameter to the variance of the output, are obtained directly from the coefficients of decomposition. The proposed approach is then applied to M/G/1/N queueing model. The most influential parameters are highlighted. Finally several numerical and data examples are sketched out to illustrate the accuracy of the proposed method and compare them with Monte Carlo simulation. The results of this work will be useful to practitioners in various fields of theoretical and applied sciences. [ABSTRACT FROM AUTHOR]