World Academy of Science, Engineering and Technology

Authors: Vishnu A., Ashesh Saha

Abstract:

The operation of high-speed rotating machinery in industries is accompanied by rotor vibrations due to many factors. One of the primary instability mechanisms in a rotor system is the centrifugal force induced due to the eccentricity of the center of mass away from the center of rotation. These unwanted vibrations may lead to catastrophic fatigue failure. So, there is a need to control these rotor vibrations. In this work, control of rotor vibrations by using a 4-pole Radial Active Magnetic Bearing (RAMB) as an actuator is analysed. A continuous rotor system model is considered for the analysis. Several important factors, like the gyroscopic effect and rotary inertia of the shaft and disc, are incorporated into this model. The large deflection of the shaft and the restriction to axial motion of the shaft at the bearings result in nonlinearities in the system governing equation. The rotor system is modeled in such a way that the system dynamics can be related to the geometric and material properties of the shaft and disc. The mathematical model of the rotor system is developed by incorporating the control forces generated by the RAMB. A simple PD controller is used for the attenuation of system vibrations. An analytical expression for the amplitude and phase equations is derived using the Method of Multiple Scales (MMS). Analytical results are verified with the numerical results obtained using an ‘ode’ solver in-built into MATLAB Software. The control force is found to be effective in attenuating the system vibrations. The multi-valued solutions leading to the jump phenomenon are also eliminated with a proper choice of control gains. Most interestingly, the shape of the backbone curves can also be altered for certain values of control parameters.

Keywords: rotor dynamics, continuous rotor system model, active magnetic bearing, PD controller, method of multiple scales, backbone curve

Procedia PDF Downloads 79

Authors: Jerry Hu

Abstract:

Let G = (V, E) with V = {1, 2, ..., k} be a graph, the k positive integers a₁, a₂, ..., ak are G-wise relatively prime if (aᵢ, aⱼ ) = 1 for {i, j} ∈ E. We use an inductive approach to give an asymptotic formula for the number of k-tuples of integers that are G-wise relatively prime. An exact formula is obtained for the probability that k positive integers are G-wise relatively prime. As a corollary, we also provide an exact formula for the probability that k positive integers have exactly r relatively prime pairs.

Keywords: graph, independent set, G-wise relatively prime, probability

Procedia PDF Downloads 91

Authors: Boris Djartov, Sanaz Mostaghim

Abstract:

This paper presents a number-based dominance method. The main idea is how to fragment the many attributes of the problem into subsets suitable for the well-established concept of Pareto dominance. Although other similar methods can be found in the literature, they focus on comparing the solutions one objective at a time, while the focus of this method is to compare entire subsets of the objective vector. Given the nature of the method, it is computationally costlier than other methods and thus, it is geared more towards selecting an option from a finite set of alternatives, where each solution is defined by multiple objectives. The need for this method was motivated by dynamic alternate airport selection (DAAS). In DAAS, pilots, while en route to their destination, can find themselves in a situation where they need to select a new landing airport. In such a predicament, they need to consider multiple alternatives with many different characteristics, such as wind conditions, available landing distance, the fuel needed to reach it, etc. Hence, this method is primarily aimed at human decision-makers. Many methods within the field of multi-objective and many-objective decision-making rely on the decision maker to initially provide the algorithm with preference points and weight vectors; however, this method aims to omit this very difficult step, especially when the number of objectives is so large. The proposed method will be compared to Favour (1 − k)-Dom and L-dominance (LD) methods. The test will be conducted using well-established test problems from the literature, such as the DTLZ problems. The proposed method is expected to outperform the currently available methods in the literature and hopefully provide future decision-makers and pilots with support when dealing with many-objective optimization problems.

Keywords: multi-objective decision-making, many-objective decision-making, multi-objective optimization, many-objective optimization

Procedia PDF Downloads 90

Authors: Wang Jiankun

Abstract:

This paper analyses how different educational backgrounds affect the mathematics performance of middle and high school students in terms of three dimensions: parental involvement, school teaching ability, and demographic variables and personal attributes of the student. Based on the analysis of Beijing High School Mathematics Competition in 2022, it was found that students from high level schools won significantly more awards than those from low level schools. In addition, a significant positive correlation (p<0.05) was identified between school level and students' mathematics performance. This study also confirms that parents' education level and family environment show a significant impact on the next generation’s mathematics learning performance. The findings suggest that interest and student’s habits, the family environment and the quality of teaching and learning at school are the main factors affecting the mathematics performance of middle and high school students.

Keywords: educational background, academic performance, middle and high school education, teenager

Procedia PDF Downloads 80

Authors: Paola Causin, Andrea Aspri, Alessandro Benfenati

Abstract:

Diffuse Optical Tomography (DOT) is an emergent medical imaging technique which employs NIR light to estimate the spatial distribution of optical coefficients in biological tissues for diagnostic purposes, in a noninvasive and non-ionizing manner. DOT reconstruction is a severely ill-conditioned problem due to prevalent scattering of light in the tissue. In this contribution, we present our research in adopting hybrid knowledgedriven/data-driven approaches which exploit the existence of well assessed physical models and build upon them neural networks integrating the availability of data. Namely, since in this context regularization procedures are mandatory to obtain a reasonable reconstruction [1], we explore the use of neural networks as tools to include prior information on the solution. 2. Materials and Methods The idea underlying our approach is to leverage neural networks to solve PDE-constrained inverse problems of the form 𝒒 ∗ = 𝒂𝒓𝒈 𝒎𝒊𝒏𝒒 𝐃(𝒚, 𝒚̃), (1) where D is a loss function which typically contains a discrepancy measure (or data fidelity) term plus other possible ad-hoc designed terms enforcing specific constraints. In the context of inverse problems like (1), one seeks the optimal set of physical parameters q, given the set of observations y. Moreover, 𝑦̃ is the computable approximation of y, which may be as well obtained from a neural network but also in a classic way via the resolution of a PDE with given input coefficients (forward problem, Fig.1 box ). Due to the severe ill conditioning of the reconstruction problem, we adopt a two-fold approach: i) we restrict the solutions (optical coefficients) to lie in a lower-dimensional subspace generated by auto-decoder type networks. This procedure forms priors of the solution (Fig.1 box ); ii) we use regularization procedures of type 𝒒̂ ∗ = 𝒂𝒓𝒈𝒎𝒊𝒏𝒒 𝐃(𝒚, 𝒚̃)+ 𝑹(𝒒), where 𝑹(𝒒) is a regularization functional depending on regularization parameters which can be fixed a-priori or learned via a neural network in a data-driven modality. To further improve the generalizability of the proposed framework, we also infuse physics knowledge via soft penalty constraints (Fig.1 box ) in the overall optimization procedure (Fig.1 box ). 3. Discussion and Conclusion DOT reconstruction is severely hindered by ill-conditioning. The combined use of data-driven and knowledgedriven elements is beneficial and allows to obtain improved results, especially with a restricted dataset and in presence of variable sources of noise.

Keywords: inverse problem in tomography, deep learning, diffuse optical tomography, regularization

Procedia PDF Downloads 74

Authors: Noora Al-Shanfari, M. Mazharul Islam

Abstract:

The cumulative incidence function (CIF) is a fundamental approach for analyzing survival data in the presence of competing risks, which estimates the marginal probability for each competing event. Parametric modeling of CIF has the advantage of fitting various shapes of CIF and estimates the impact of covariates with maximum efficiency. To calculate the total CIF's covariate influence using a parametric model., it is essential to parametrize the baseline of the CIF. As the CIF is an improper function by nature, it is necessary to utilize an improper distribution when applying parametric models. The Gompertz distribution, which is an improper distribution, is limited in its applicability as it only accounts for monotone hazard shapes. The generalized Gompertz distribution, however, can adapt to a wider range of hazard shapes, including unimodal, bathtub, and monotonic increasing or decreasing hazard shapes. In this paper, the generalized Gompertz distribution is used to parametrize the baseline of the CIF, and the parameters of the proposed model are estimated using the maximum likelihood approach. The proposed model is compared with the existing Gompertz model using the Akaike information criterion. Appropriate statistical test procedures and model-fitting criteria will be used to test the adequacy of the model. Both models are applied to the ‘colon’ dataset, which is available in the “biostat3” package in R.

Keywords: competing risks, cumulative incidence function, improper distribution, parametric modeling, survival analysis

Procedia PDF Downloads 102

Authors: Serena Gomez, Raeesa Tanseen, Netra Shaligram, Nithin Francis, Sandesh B. J.

Abstract:

The human gut consists of a community of microbes which has a lot of effects on human health disease. Metabolic modeling can help to predict relative populations of stable microbes and their effect on health disease. In order to study and visualize microbes in the human gut, we developed a tool that offers the following modules: Build a tool that can be used to perform Flux Balance Analysis for microbes in the human gut using the Artificial Bee Colony optimization algorithm. Run simulations for an individual microbe in different conditions, such as aerobic and anaerobic and visualize the results of these simulations.

Keywords: microbes, metabolic modeling, flux balance analysis, artificial bee colony

Procedia PDF Downloads 100

Authors: Wajahat Ali, Shakeel Javaid

Abstract:

In this study, we have developed a mathematical programming model for a solid transportation problem with three objective functions arranged in hierarchical order. The mathematical programming models with more than one objective function to be solved in hierarchical order is termed as a multi-level programming model. Our study explores a Multi-Level Solid Transportation Problem with Uncertain Parameters (MLSTPWU). The proposed MLSTPWU model consists of three objective functions, viz. minimization of transportation cost, minimization of total transportation time, and minimization of deterioration during transportation. These three objective functions are supposed to be solved by decision-makers at three consecutive levels. Three constraint functions are added to the model, restricting the total availability, total demand, and capacity of modes of transportation. All the parameters involved in the model are assumed to be uncertain in nature. A solution method based on fuzzy logic is also discussed to obtain the compromise solution for the proposed model. Further, a simulated numerical example is discussed to establish the efficiency and applicability of the proposed model.

Keywords: solid transportation problem, multi-level programming, uncertain variable, uncertain environment

Procedia PDF Downloads 81

Authors: Tasir Khan, Yejuan Wang

Abstract:

The study of extreme rainfall events is very important for flood management in river basins and the design of water conservancy infrastructure. Evaluation of quantiles of annual maximum rainfall (AMRF) is required in different environmental fields, agriculture operations, renewable energy sources, climatology, and the design of different structures. Therefore, the annual maximum rainfall (AMRF) was performed at different stations in Pakistan. Multiple probability distributions, log normal (LN), generalized extreme value (GEV), Gumbel (max), and Pearson type3 (P3) were used to find out the most appropriate distributions in different stations. The L moments method was used to evaluate the distribution parameters. Anderson darling test, Kolmogorov- Smirnov test, and chi-square test showed that two distributions, namely GUM (max) and LN, were the best appropriate distributions. The quantile estimate of a multi-parameter PD offers extreme rainfall through a specific location and is therefore important for decision-makers and planners who design and construct different structures. This result provides an indication of these multi-parameter distribution consequences for the study of sites and peak flow prediction and the design of hydrological maps. Therefore, this discovery can support hydraulic structure and flood management.

Keywords: RAMSE, multiple frequency analysis, annual maximum rainfall, L-moments

Procedia PDF Downloads 81

Authors: Tasir Khan, Yejuan Wan, Kalim Ullah

Abstract:

Hydrological frequency analysis has been conducted to estimate the minimum flow elevation of the Indus River in Pakistan to protect the ecosystem. The Maximum likelihood estimation (MLE) technique is used to estimate the best-fitted distribution for Minimum Ecological Flows at nine stations of the Indus River in Pakistan. The four selected distributions, Generalized Extreme Value (GEV) distribution, Generalized Logistics (GLO) distribution, Generalized Pareto (GPA) distribution, and Pearson type 3 (PE3) are fitted in all sites, usually used in hydro frequency analysis. Compare the performance of these distributions by using the goodness of fit tests, such as the Kolmogorov Smirnov test, Anderson darling test, and chi-square test. The study concludes that the Maximum Likelihood Estimation (MLE) method recommended that GEV and GPA are the most suitable distributions which can be effectively applied to all the proposed sites. The quantiles are estimated for the return periods from 5 to 1000 years by using MLE, estimations methods. The MLE is the robust method for larger sample sizes. The results of these analyses can be used for water resources research, including water quality management, designing irrigation systems, determining downstream flow requirements for hydropower, and the impact of long-term drought on the country's aquatic system.

Keywords: minimum ecological flow, frequency distribution, indus river, maximum likelihood estimation

Procedia PDF Downloads 77

Authors: Mohammad Anwar, Shah Waliullah

Abstract:

This study investigated panel data regression models. This paper used Bayesian and classical methods to study the impact of institutions on economic growth from data (1990-2014), especially in developing countries. Under the classical and Bayesian methodology, the two-panel data models were estimated, which are common effects and fixed effects. For the Bayesian approach, the prior information is used in this paper, and normal gamma prior is used for the panel data models. The analysis was done through WinBUGS14 software. The estimated results of the study showed that panel data models are valid models in Bayesian methodology. In the Bayesian approach, the effects of all independent variables were positively and significantly affected by the dependent variables. Based on the standard errors of all models, we must say that the fixed effect model is the best model in the Bayesian estimation of panel data models. Also, it was proved that the fixed effect model has the lowest value of standard error, as compared to other models.

Keywords: Bayesian approach, common effect, fixed effect, random effect, Dynamic Random Effect Model

Procedia PDF Downloads 68

Authors: Jude K. Safo

Abstract:

Knowledge Graphs KG) and their relation to Graph Embeddings (GE) represent a unique data structure in the landscape of machine learning (relative to image, text and acoustic data). Unlike the latter, GEs are the only data structure sufficient for representing hierarchically dense, semantic information needed for use-cases like supply chain data and protein folding where the search space exceeds the limits traditional search methods (e.g. page-rank, Dijkstra, etc.). While GEs are effective for compressing low rank tensor data, at scale, they begin to introduce a new problem of ’data retreival’ which we observe in Large Language Models. Notable attempts by transE, TransR and other prominent industry standards have shown a peak performance just north of 57% on WN18 and FB15K benchmarks, insufficient practical industry applications. They’re also limited, in scope, to next node/link predictions. Traditional linear methods like Tucker, CP, PARAFAC and CANDECOMP quickly hit memory limits on tensors exceeding 6.4 million nodes. This paper outlines a topological framework for linear mapping between concepts in KG space and GE space that preserve cardinality. Most importantly we introduce a traceable framework for composing dense linguistic strcutures. We demonstrate performance on WN18 benchmark this model hits. This model does not rely on Large Langauge Models (LLM) though the applications are certainy relevant here as well.

Keywords: representation theory, large language models, graph embeddings, applied algebraic topology, applied knot theory, combinatorics

Procedia PDF Downloads 68

Authors: Charlene N. T. Mfangnia, Henri E. Z. Tonnang, Berge Tsanou, Jeremy Herren

Abstract:

Microsporidia MB is a recently discovered symbiont capable of blocking the transmission of Plasmodium from mosquitoes to humans. The symbiont can spread both horizontally and vertically among the mosquito population. This dual transmission gives the symbiont the ability to invade the mosquito population. The replacement of the mosquito population by the population of symbiont-infected mosquitoes then appears as a promising strategy for malaria control. In this context, the present study uses differential equations to model the transmission dynamics of Microsporidia MB in the population of female Anopheles mosquitoes. Long-term propagation scenarios of the symbiont, such as extinction, persistence or total infection, are obtained through the determination of the target and basic reproduction numbers, the equilibria, and the study of their stability. The stability is illustrated numerically, and the contribution of vertical and horizontal transmission in the spread of the symbiont is assessed. Data obtained from laboratory experiments are then used to explain the low prevalence observed in nature. The study also shows that the male death rate, the mating rate and the attractiveness of MB-positive mosquitoes are the factors that most influence the transmission of the symbiont. In addition, the introduction of temperature and the study of bifurcations show the significant influence of the environmental condition in the propagation of Microsporidia MB. This finding proves the necessity of taking into account environmental variables for the potential establishment of the symbiont in a new area.

Keywords: differential equations, stability analysis, malaria, microsporidia MB, horizontal transmission, vertical transmission, numerical illustration

Procedia PDF Downloads 113

Authors: Charlene N. T. Mfangnia, Henri Tonnang, Berge Tsanou, Jeremy Herren

Abstract:

The Microsporidia MB found in the populations of anopheles is a recently discovered symbiont responsible for the Plasmodium transmission blocking. From early studies, it was established that the symbiont can be transmitted vertically and horizontally. The present study uses compartmental mathematical modelling approach to investigate the dynamics of Microsporidia transmission in the mosquito population with the mindset of establishing a mechanism for use to control malaria. Data and information obtained from laboratory experiments are used to estimate the model parameters with and without temperature dependency of mosquito traits. We carry out the mathematical analysis focusing on the equilibria states and their stability for the autonomous model. Through the modelling experiments, we are able to assess and confirm the contribution of vertical and horizontal transmission in the proliferation of Microsporidia MB in the mosquito population. In addition, the basic and target reproductions are computed, and some long-term behaviours of the model, such as the local (and global) stability of equilibrium points, are rigorously analysed and illustrated numerically. We establish the conditions responsible for the low prevalence of the symbiont-infected mosquitoes observed in nature. Moreover, we identify the male death rate, the mating rate and the attractiveness of MB-positive mosquitoes as mosquito traits that significantly influence the spread of Microsporidia MB. Furthermore, we highlight the influence of temperature in the establishment and persistence of MB-infected mosquitoes in a given area.

Keywords: microsporidia MB, vertical transmission, horizontal transmission, compartmental modelling approach, temperature-dependent mosquito traits, malaria, plasmodium-transmission blocking

Procedia PDF Downloads 130

Authors: M. S. Wickramarachchi, L. S. Nawarathna, C. M. B. Dematawewa

Abstract:

Hatchery performance is critical for the profitability of poultry breeder operations. Some extrinsic parameters of eggs and breeders cause to increase or decrease the hatchability. This study aims to identify the affecting extrinsic parameters on the commercial hatchability of local chicken's eggs and determine the most efficient classification model with a hatchability rate greater than 90%. In this study, seven extrinsic parameters were considered: egg weight, moisture loss, breeders age, number of fertilised eggs, shell width, shell length, and shell thickness. Multiple linear regression was performed to determine the most influencing variable on hatchability. First, the correlation between each parameter and hatchability were checked. Then a multiple regression model was developed, and the accuracy of the fitted model was evaluated. Linear Discriminant Analysis (LDA), Classification and Regression Trees (CART), k-Nearest Neighbors (kNN), Support Vector Machines (SVM) with a linear kernel, and Random Forest (RF) algorithms were applied to classify the hatchability. This grouping process was conducted using binary classification techniques. Hatchability was negatively correlated with egg weight, breeders' age, shell width, shell length, and positive correlations were identified with moisture loss, number of fertilised eggs, and shell thickness. Multiple linear regression models were more accurate than single linear models regarding the highest coefficient of determination (R²) with 94% and minimum AIC and BIC values. According to the classification results, RF, CART, and kNN had performed the highest accuracy values 0.99, 0.975, and 0.972, respectively, for the commercial hatchery process. Therefore, the RF is the most appropriate machine learning algorithm for classifying the breeder outcomes, which are economically profitable or not, in a commercial hatchery.

Keywords: classification models, egg weight, fertilised eggs, multiple linear regression

Procedia PDF Downloads 87

Authors: Abraham Terán Salcedo, Didier Samayoa Ochoa

Abstract:

This work presents a numerical implementation of a method for estimating the box-counting dimension of self-avoiding curves on a planar space, fractal objects captured on digital images; this method is named fractioning estimator. Classical methods of digital image processing, such as noise filtering, contrast manipulation, and thresholding, among others, are used in order to obtain binary images that are suitable for performing the necessary computations of the fractioning estimator. A user interface is developed for performing the image processing operations and testing the fractioning estimator on different captured images of real-life fractal objects. To analyze the results, the estimations obtained through the fractioning estimator are compared to the results obtained through other methods that are already implemented on different available software for computing and estimating the box-counting dimension.

Keywords: box-counting, digital image processing, fractal dimension, numerical method

Procedia PDF Downloads 82

Authors: Mohammad Saber Rohi, Saghar Heidari

Abstract:

In this paper, we studied the pricing problem of American options under a regime-switching model with the possibility of a non-optimal exercise policy (early or late exercise time) which is called an irrational strategy. For this, we consider a Markovmodulated model for the dynamic of the underlying asset as an alternative model to the classical Balck-Scholes-Merton model (BSM) and an intensity-based model for the irrational strategy, to provide more realistic results for American option prices under the irrational behavior in real financial markets. Applying a partial differential equation (PDE) approach, the pricing problem of American options under regime-switching models can be formulated as coupled PDEs. To solve the resulting systems of PDEs in this model, we apply a finite element method as the numerical solving procedure to the resulting variational inequality. Under some appropriate assumptions, we establish the stability of the method and compare its accuracy to some recent works to illustrate the suitability of the proposed model and the accuracy of the applied numerical method for the pricing problem of American options under the regime-switching model with irrational behaviors.

Keywords: irrational exercise strategy, rationality parameter, regime-switching model, American option, finite element method, variational inequality

Procedia PDF Downloads 73

Authors: Ozgu Turgut

Abstract:

Water scarcity is a problem for many regions which requires immediate action, and solutions cannot be postponed for a long time. It is known that farming consumes a significant portion of usable water. Although in recent years, the efforts to make the transition to dripping or spring watering systems instead of using surface watering started to pay off. It is also known that this transition is not necessarily translated into an increase in the capacity dedicated to other water consumption channels such as city water or power usage. In order to control and allocate the water resource more purposefully, new watering systems have to be used with monitoring abilities that can limit the usage capacity for each farm. In this study, a decision support model which relies on a bi-objective stochastic linear optimization is proposed, which takes crop yield and price volatility into account. The model generates annual planting plans as well as water usage limits for each farmer in the region while taking the total value (i.e., profit) of the overall harvest. The mathematical model is solved using the L-shaped method optimally. The decision support model can be especially useful for regional administrations to plan next year's planting and water incomes and expenses. That is why not only a single optimum but also a set of representative solutions from the Pareto set is generated with the proposed approach.

Keywords: decision support, farming, water, tactical planning, optimization, stochastic, pareto

Procedia PDF Downloads 71

Authors: Charles Lee

Abstract:

The Principal Orthogonal Decomposition (POD) technique has been used as a model reduction tool for many applications in engineering and science. In principle, one begins with an ensemble of data, called snapshots, collected from an experiment or laboratory results. The beauty of the POD technique is that when applied, the entire data set can be represented by the smallest number of orthogonal basis elements. It is the such capability that allows us to reduce the complexity and dimensions of many physical applications. Mathematical formulations and numerical schemes for the POD method will be discussed along with applications in NASA’s Deep Space Large Antenna Arrays, Satellite Image Reconstruction, Cancer Detection with DNA Microarray Data, Maximizing Stock Return, and Medical Imaging.

Keywords: reduced-order methods, principal component analysis, cancer detection, image reconstruction, stock portfolios

Procedia PDF Downloads 82

Authors: Claudia García-García, Catalina B. García-García, Román Salmerón-Gómez

Abstract:

Much economic-environmental research includes the analysis of possible interactions by using Moderated Regression Analysis (MRA), which is a specific application of multiple linear regression analysis. This methodology allows analyzing how the effect of one of the independent variables is moderated by a second independent variable by adding a cross-product term between them as an additional explanatory variable. Due to the very specification of the methodology, the moderated factor is often highly correlated with the constitutive terms. Thus, great multicollinearity problems arise. The appearance of strong multicollinearity in a model has important consequences. Inflated variances of the estimators may appear, there is a tendency to consider non-significant regressors that they probably are together with a very high coefficient of determination, incorrect signs of our coefficients may appear and also the high sensibility of the results to small changes in the dataset. Finally, the high relationship among explanatory variables implies difficulties in fixing the individual effects of each one on the model under study. These consequences shifted to the moderated analysis may imply that it is not worth including an interaction term that may be distorting the model. Thus, it is important to manage the problem with some methodology that allows for obtaining reliable results. After a review of those works that applied the MRA among the ten top journals of the field, it is clear that multicollinearity is mostly disregarded. Less than 15% of the reviewed works take into account potential multicollinearity problems. To overcome the issue, this work studies the possible application of recent methodologies to MRA. Particularly, the raised regression is analyzed. This methodology mitigates collinearity from a geometrical point of view: the collinearity problem arises because the variables under study are very close geometrically, so by separating both variables, the problem can be mitigated. Raise regression maintains the available information and modifies the problematic variables instead of deleting variables, for example. Furthermore, the global characteristics of the initial model are also maintained (sum of squared residuals, estimated variance, coefficient of determination, global significance test and prediction). The proposal is implemented to data from countries of the European Union during the last year available regarding greenhouse gas emissions, per capita GDP and a dummy variable that represents the topography of the country. The use of a dummy variable as the moderator is a special variant of MRA, sometimes called “subgroup regression analysis.” The main conclusion of this work is that applying new techniques to the field can improve in a substantial way the results of the analysis. Particularly, the use of raised regression mitigates great multicollinearity problems, so the researcher is able to rely on the interaction term when interpreting the results of a particular study.

Keywords: multicollinearity, MRA, interaction, raise

Procedia PDF Downloads 103

Authors: Benjamin Lee Warren

Abstract:

Many problems exist in additive number theory which is essential to determine the primes that are the sum of two elements from a given single-variable polynomial sequence, and most of them are unattackable in the present day. Here, we determine solutions for this problem to a few certain sequences (certain binomial coefficients and power sums) using only elementary algebra and some algebraic factoring methods (as well as Euclid’s Lemma and Faulhaber’s Formula). In particular, we show that there are finitely many primes as sums of two of these types of elements. Several cases are fully illustrated, and bounds are presented for the cases not fully illustrated.

Keywords: binomial coefficients, power sums, primes, algebra

Procedia PDF Downloads 102

Authors: Yunusa Aliyu Hadejia

Abstract:

Cholera is a gastrointestinal disease caused by a bacterium called Vibrio Cholerae which spread as a result of eating food or drinking water contaminated with feaces from an infected person. In this work we proposed and analyzed the impact of isolating infected people and give them therapeutic treatment, the specific objectives of the research was to formulate a mathematical model of cholera transmission incorporating treatment class, to make analysis on stability of equilibrium points of the model, positivity and boundedness was shown to ensure that the model has a biological meaning, the basic reproduction number was derived by next generation matrix approach. The result of stability analysis show that the Disease free equilibrium was both locally and globally asymptotically stable when R_0< 1 while endemic equilibrium has locally asymptotically stable when R_0> 1. Sensitivity analysis was perform to determine the contribution of each parameter to the basic reproduction number. Numerical simulation was carried out to show the impact of the model parameters using MAT Lab Software.

Keywords: mathematical model, treatment, stability, sensitivity

Procedia PDF Downloads 99

Authors: Mouhamadou Dosso

Abstract:

This paper presents methods of spectral dichotomy of a matrix which compute spectral projectors on the subspace associated with the eigenvalues external to the parabolas described by a general equation. These methods are modifications of the one proposed in [A. N. Malyshev and M. Sadkane, SIAM J. MATRIX ANAL. APPL. 18 (2), 265-278, 1997] which uses the spectral dichotomy method of a matrix with respect to the imaginary axis. Theoretical and algorithmic aspects of the methods are developed. Numerical results obtained by applying methods presented on matrices are reported.

Keywords: spectral dichotomy method, spectral projector, eigensubspaces, eigenvalue

Procedia PDF Downloads 92

Authors: Idowu Ibikunle Albert, Atilade Adesanya Oluwafemi, Okedeyi Abiodun Sikiru, Mustapha Rilwan Adewale

Abstract:

These present-day all areas of transport have experienced large advances characterized by increases in the speeds and weight of vehicles. As a result, this paper considered the Transverse Vibration of an Elastic Beam Resting on a Variable Elastic Foundation Subjected to a moving Load. The beam is presumed to be uniformly distributed and has simple support at both ends. The moving distributed moving mass is assumed to move with constant velocity. The governing equations, which are fourth-order partial differential equations, were reduced to second-order partial differential equations using an analytical method in terms of series solution and solved by a numerical method using mathematical software (Maple). Results show that an increase in the values of beam parameters, moving Mass M, and k-stiffness K, significantly reduces the deflection profile of the vibrating beam. In the results, it was equally found that moving mass is greater than moving force.

Keywords: elastic beam, moving load, response of structure, variable elastic foundation

Procedia PDF Downloads 120

Authors: Shao-Yuan Huang

Abstract:

We study the shape of the bifurcation curve of positive solutions for the semipositone problem with the Minkowski-curvature operator. The Minkowski-curvature problem plays an important role in certain fundamental issues in differential geometry and in the special theory of relativity. In addition, it is well known that studying the multiplicity of positive solutions is equivalent to studying the shape of the bifurcation curve. By the shape of the bifurcation curve, we can understand the change in the multiplicity of positive solutions with varying parameters. In this paper, our main technique is a time-map method used in Corsato's PhD Thesis. By this method, studying the shape of the bifurcation curve is equivalent to studying the shape of a certain function T with improper integral. Generally speaking, it is difficult to study the shape of T. So, in this paper, we consider two cases that the nonlinearity is convex or concave. Thus we obtain the following results: (i) If f''(u) < 0 for u > 0, then the bifurcation curve is C-shaped. (ii) If f''(u) > 0 for u > 0, then there exists η>β such that the bifurcation curve does not exist for 0 η. Furthermore, we prove that the bifurcation is C-shaped for L > η under a certain condition.

Keywords: bifurcation curve, Minkowski-curvature problem, positive solution, time-map method

Procedia PDF Downloads 101

Authors: Mohammed Husein Mohammad Rashid

Abstract:

For a bounded linear operator T acting on a complex infinite dimensional Hilbert space ℋ, we say that T is ∗-class A operator (abbreviation T∈A*) if |T²|≥ |T*|². In this article, we prove the following assertions:(i) we establish some conditions which imply the normality of ∗-class A; (ii) we consider ∗-class A operator T ∈ ℬ(ℋ) with reducing kernel such that TX = XS for some X ∈ ℬ(K, ℋ) and prove the Fuglede-Putnam type theorem when adjoint of S ∈ ℬ(K) is dominant operators; (iii) furthermore, we extend the asymmetric Putnam-Fuglede theorem the class of ∗-class A operators.

Keywords: fuglede-putnam theorem, normal operators, ∗-class a operators, dominant operators

Procedia PDF Downloads 87

Authors: Muhammad Farooq, Ahtasham Gul

Abstract:

To meet the desired standard, it is important to monitor and analyze different engineering processes to get desired output. The bivariate distributions got a lot of attention in recent years to describe the randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed using two independent models developed by the nesting approach to study the effect of each component on reliability for better understanding. Further, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution, like mean median and quantile function, are discussed. We use inverse Gamma prior to study its frequentist properties by conducting Monte Carlo Markov Chain (MCMC) sampling scheme.

Keywords: reliability, system availability Weibull, inverse Lomax, Monte Carlo Markov Chain, Bayesian

Procedia PDF Downloads 71

Authors: Lim Yi Wei

Abstract:

Structural equation modelling (SEM) is well-known in statistics due to its flexibility and accessibility. It plays an increasingly important role in the development of the education field. The number of research publications using SEM in education has increased in recent decades. However, there is a lack of scientific review conducted on SEM in education. The purpose of this study is to investigate research trends related to SEM in education. The researcher will use Vosviewer, Datawrapper, and SciMAT to do bibliometric analysis on 5549 papers that have been published in the Scopus database in the last five years. The result will show the publication trends of the most cited documents, the top contributing authors, countries, institutions, and journals in the research field. It will also look at how they relate to each other in terms of co-citation, collaboration, and co-occurrence of keywords. This study will benefit researchers and practitioners by identifying research trends and the current state of SEM in education.

Keywords: structural equation modeling, education, bibliometric analysis, Vosviewer

Procedia PDF Downloads 98

Authors: Mohammed Husein Mohammed Rashid

Abstract:

Let Τ = U |Τ| be a polar decomposition of a bounded linear operator T on a complex Hilbert space with ker U = ker |T|. T is said to be class p-w A(s,t) if (|T*|ᵗ|T|²ˢ|T*|ᵗ )ᵗᵖ/ˢ⁺ᵗ ≥|T*|²ᵗᵖ and |T|²ˢᵖ ≥ (|T|ˢ|T*|²ᵗ|T|ˢ)ˢᵖ/ˢ⁺ᵗ with 0Keywords: class p-w A (s, t), normaloid, isoloid, finite, orthogonality

Procedia PDF Downloads 116

Authors: Abubakar Attahiru

Abstract:

Mathematics plays an important role in the real situation. The development of the study of mathematics is a result of the needs of man to survive and interact with one another in society. Mathematics is the universal language that is applied in almost every aspect of life. Mathematics gives us a way to understand patterns, define relationships, and predict the future. The changes in the content and methods of studying mathematics follow the trends in societal needs and developments. Also, the developments in mathematics affect the developments in society. Generally, education helps to develop society while the activities and needs of the society dictate e educational policy of any society. Among all the academic subjects studied at school, mathematics has distinctly contributed more to the objectives of general education of man than any other subject. This is a result of the applications of mathematics to all spheres of human endeavors’. This paper looks at the meaning of the basic concepts of mathematics, science, and technology, the application of mathematics in a real-life situation, and their relationships with society. The paper also shows how mathematics, science, and technology affect the existence and development of society and how society determines the nature of mathematics studied in society through its educational system.

Keywords: application, mathematics, real life, situation

Procedia PDF Downloads 154