Pub Date : 2020-11-16DOI: 10.11648/J.ACM.20200906.12
F. Liu
In this paper, to reduce the computational cost of solving semilinear parabolic equations on a tensor product domain Ω⊂ℝd with d = 2 or 3, some two-scale finite element discretizations are proposed and analyzed. The time derivative in semilinear parabolic equations is approximated by the backward Euler finite difference scheme. The two-scale finite element method is designed for the space discretization. The idea of the two-scale finite element method is based on an understanding of a finite element solution to an elliptic problem on a tensor product domain. The high frequency parts of the finite element solution can be well captured on some univariate fine grids and the low frequency parts can be approximated on a coarse grid. Thus the two-scale finite element approximation is defined as a linear combination of some standard finite element approximations on some univariate fine grids and a coarse grid satisfying H = O (h1/2), where h and H are the fine and coarse mesh widths, respectively. It is shown theoretically and numerically that the backward Euler two-scale finite element solution not only achieves the same order of accuracy in the H1 (Ω) norm as the backward Euler standard finite element solution, but also reduces the number of degrees of freedom from O(h-d×τ-1) to O(h-((d)+1)/2×τ-1) where τ is the time step. Consequently the backward Euler two-scale finite element method for semilinear parabolic equations is more efficient than the backward Euler standard finite element method.
本文为了减少在d = 2或3的张量积域Ω上求解半线性抛物方程的计算代价，提出并分析了几种双尺度有限元离散化方法。用后向欧拉有限差分格式逼近半线性抛物方程的时间导数。设计了双尺度有限元法进行空间离散化。双尺度有限元方法的思想是基于对张量积域上椭圆问题的有限元解的理解。有限元解的高频部分可以在一些单变量细网格上很好地捕获，低频部分可以在粗网格上近似。因此，双尺度有限元近似定义为在满足H = O (h1/2)的单变量细网格和粗网格上的一些标准有限元近似的线性组合，其中H和H分别为细网格宽度和粗网格宽度。理论和数值表明，向后欧拉双尺度有限元解不仅在H1 (Ω)范数上达到与向后欧拉标准有限元解相同的精度阶数，而且将自由度从O(h-d×τ-1)减少到O(h-(d)+1)/2×τ-1)，其中τ为时间步长。因此，用后向欧拉双尺度有限元法求解半线性抛物方程比用后向欧拉标准有限元法求解更有效。
{"title":"Two-scale Finite Element Discretizations for Semilinear Parabolic Equations","authors":"F. Liu","doi":"10.11648/J.ACM.20200906.12","DOIUrl":"https://doi.org/10.11648/J.ACM.20200906.12","url":null,"abstract":"In this paper, to reduce the computational cost of solving semilinear parabolic equations on a tensor product domain Ω⊂ℝd with d = 2 or 3, some two-scale finite element discretizations are proposed and analyzed. The time derivative in semilinear parabolic equations is approximated by the backward Euler finite difference scheme. The two-scale finite element method is designed for the space discretization. The idea of the two-scale finite element method is based on an understanding of a finite element solution to an elliptic problem on a tensor product domain. The high frequency parts of the finite element solution can be well captured on some univariate fine grids and the low frequency parts can be approximated on a coarse grid. Thus the two-scale finite element approximation is defined as a linear combination of some standard finite element approximations on some univariate fine grids and a coarse grid satisfying H = O (h1/2), where h and H are the fine and coarse mesh widths, respectively. It is shown theoretically and numerically that the backward Euler two-scale finite element solution not only achieves the same order of accuracy in the H1 (Ω) norm as the backward Euler standard finite element solution, but also reduces the number of degrees of freedom from O(h-d×τ-1) to O(h-((d)+1)/2×τ-1) where τ is the time step. Consequently the backward Euler two-scale finite element method for semilinear parabolic equations is more efficient than the backward Euler standard finite element method.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87224439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-04DOI: 10.11648/J.ACM.20200906.11
Chang Wang, Renbing Xiao
Let G be a transitive permutation group acting on a finite set Ω. For a point α of Ω, the set of the images of G acting on α is called the orbit of α under G and is denoted by αG, and the set of elements in G which fix α is called the stabilizer of α in G and is denoted by Gα. We can get some new orbits by using the natural action of the stabilizer Gα on Ω, and then we can define the suborbit of G. The suborbits of G on Ω are defined as the orbits of a point stabilizer on Ω. The number of suborbits is called the rank of G and the length of suborbits is called the subdegree of G. For finite primitive groups, the study of the rank and subdegrees of group has a long history. In this paper, we construct a class of imprimitive permutation groups of rank 4 or 5 by using imprimitive action and product action of wreath product, determine the number and the length of the suborbits, and extend the results to imprimitive permutation groups of rank m+1 and 2n+1, where m and n are positive integers.
{"title":"A Construction of Imprimitive Groups of Rank 4 or 5","authors":"Chang Wang, Renbing Xiao","doi":"10.11648/J.ACM.20200906.11","DOIUrl":"https://doi.org/10.11648/J.ACM.20200906.11","url":null,"abstract":"Let G be a transitive permutation group acting on a finite set Ω. For a point α of Ω, the set of the images of G acting on α is called the orbit of α under G and is denoted by αG, and the set of elements in G which fix α is called the stabilizer of α in G and is denoted by Gα. We can get some new orbits by using the natural action of the stabilizer Gα on Ω, and then we can define the suborbit of G. The suborbits of G on Ω are defined as the orbits of a point stabilizer on Ω. The number of suborbits is called the rank of G and the length of suborbits is called the subdegree of G. For finite primitive groups, the study of the rank and subdegrees of group has a long history. In this paper, we construct a class of imprimitive permutation groups of rank 4 or 5 by using imprimitive action and product action of wreath product, determine the number and the length of the suborbits, and extend the results to imprimitive permutation groups of rank m+1 and 2n+1, where m and n are positive integers.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88787595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-13DOI: 10.11648/j.acm.20200905.13
Uwakwe Joy Ijeoma, Inyama Simeon Chioma, O. Andrew
We formulated three compartmental model of Marek Disease model. We first determined the basic Reproduction number and the existence of Steady (Equilibrium) states (disease-free and endemic). Conditions for the local stability of the disease-free and endemic steady states were determined. Further, the Global stability of the disease-free equilibrium (DFE) and endemic equilibrium were proved using Lyponav method. We went further to carry out the sensitivity analysis or parametric dependence on R0 and later formulated the optimal control problem. We finally looked at numerical Results on poultry productivity in the presence of Marek disease and we drew five graphs to demonstrate this. The first figure shows the effect of both vaccination (v) and biosecurity measures (u) on the latently infected birds. The population of infected birds increases speedily and then remains stable without the application of any control measure, with the controls, the population increases to about 145 and then begins to reduce from day 8 till it drops to 50 on day 20 and then remains stable. With this strategy, only bird vaccination (v) is applied to control the system while the other control is set to zero. In the second figure, the effect of bird vaccination and its’ positive impact is revealed, though there is an increase to about 160 before a decrease occurs. From the third figure, as the control (u) ranges from 0.2 to 0.9, we see that the bird population still has a high level of latently infected birds. This result from figure shows that the bird population is not free from the disease, hence, the biosecurity control strategy is not effective without vaccination of susceptible birds and hence it is not preferable as the only control measure for marek disease. The numerical result in the fourth figure shows that as the latently infected bird population increases without control, with vaccination it decreases as more susceptible birds are vaccinated. From the fifth figure we observe, that as the control parameter increases, the total deaths by infection reduces, also as the age of the infection increases to the maximum age of infection which is 6 months (thatis, T=24 weeks), the number of deaths increases to 30 in a day. Hence, control measures should be applied at the early ages of infection in order to avoid high mortality rate during the outbreak of the disease.
{"title":"Age-Infection Model and Control of Marek Disease","authors":"Uwakwe Joy Ijeoma, Inyama Simeon Chioma, O. Andrew","doi":"10.11648/j.acm.20200905.13","DOIUrl":"https://doi.org/10.11648/j.acm.20200905.13","url":null,"abstract":"We formulated three compartmental model of Marek Disease model. We first determined the basic Reproduction number and the existence of Steady (Equilibrium) states (disease-free and endemic). Conditions for the local stability of the disease-free and endemic steady states were determined. Further, the Global stability of the disease-free equilibrium (DFE) and endemic equilibrium were proved using Lyponav method. We went further to carry out the sensitivity analysis or parametric dependence on R0 and later formulated the optimal control problem. We finally looked at numerical Results on poultry productivity in the presence of Marek disease and we drew five graphs to demonstrate this. The first figure shows the effect of both vaccination (v) and biosecurity measures (u) on the latently infected birds. The population of infected birds increases speedily and then remains stable without the application of any control measure, with the controls, the population increases to about 145 and then begins to reduce from day 8 till it drops to 50 on day 20 and then remains stable. With this strategy, only bird vaccination (v) is applied to control the system while the other control is set to zero. In the second figure, the effect of bird vaccination and its’ positive impact is revealed, though there is an increase to about 160 before a decrease occurs. From the third figure, as the control (u) ranges from 0.2 to 0.9, we see that the bird population still has a high level of latently infected birds. This result from figure shows that the bird population is not free from the disease, hence, the biosecurity control strategy is not effective without vaccination of susceptible birds and hence it is not preferable as the only control measure for marek disease. The numerical result in the fourth figure shows that as the latently infected bird population increases without control, with vaccination it decreases as more susceptible birds are vaccinated. From the fifth figure we observe, that as the control parameter increases, the total deaths by infection reduces, also as the age of the infection increases to the maximum age of infection which is 6 months (thatis, T=24 weeks), the number of deaths increases to 30 in a day. Hence, control measures should be applied at the early ages of infection in order to avoid high mortality rate during the outbreak of the disease.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88301795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-29DOI: 10.11648/J.ACM.20200905.12
Tariq Al-Moqri, Xiao Haijun, J. P. Namahoro, E. Alfalahi, Ibrahim Alwesabi
This study focused on exploiting machine learning algorithms for classifying and predicting injury severity of vehicle crashes in Yemen. The primary objective is to assess the contribution of the leading causes of injury severity. The selected machine learning algorithms compared with traditional statistical methods. The filtrated second data collected within two months (August-October 2015) from the two main hospitals included 156 injured patients of vehicle crashes reported from 128 locations. The data classified into three categories of injury severity: Severe, Serious, and Minor. It balanced using a synthetic minority oversampling technique (SMOTE). Multinomial logit model (MNL) compared with five machine learning classifiers: Naive Bayes (NB), J48 Decision Tree, Random Forest (RF), Support Vector Machine (SVM), and Multilayer Perceptron (MLP). The results showed that most of machine learning-based algorithms performed well in predicting and classifying the severity of the traffic injury. Out of five classifiers, RF is the best classifier with 94.84% of accuracy. The characteristics of road type, total injured person, crash type, road user, transport way to the emergency department (ED), and accident action were the most critical factors in the severity of the traffic injury. Enhancing strategies for using roadway facilities may improve the safety of road users and regulations.
{"title":"Exploiting Machine Learning Algorithms for Predicting Crash Injury Severity in Yemen: Hospital Case Study","authors":"Tariq Al-Moqri, Xiao Haijun, J. P. Namahoro, E. Alfalahi, Ibrahim Alwesabi","doi":"10.11648/J.ACM.20200905.12","DOIUrl":"https://doi.org/10.11648/J.ACM.20200905.12","url":null,"abstract":"This study focused on exploiting machine learning algorithms for classifying and predicting injury severity of vehicle crashes in Yemen. The primary objective is to assess the contribution of the leading causes of injury severity. The selected machine learning algorithms compared with traditional statistical methods. The filtrated second data collected within two months (August-October 2015) from the two main hospitals included 156 injured patients of vehicle crashes reported from 128 locations. The data classified into three categories of injury severity: Severe, Serious, and Minor. It balanced using a synthetic minority oversampling technique (SMOTE). Multinomial logit model (MNL) compared with five machine learning classifiers: Naive Bayes (NB), J48 Decision Tree, Random Forest (RF), Support Vector Machine (SVM), and Multilayer Perceptron (MLP). The results showed that most of machine learning-based algorithms performed well in predicting and classifying the severity of the traffic injury. Out of five classifiers, RF is the best classifier with 94.84% of accuracy. The characteristics of road type, total injured person, crash type, road user, transport way to the emergency department (ED), and accident action were the most critical factors in the severity of the traffic injury. Enhancing strategies for using roadway facilities may improve the safety of road users and regulations.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73886231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-18DOI: 10.20944/PREPRINTS202009.0428.V1
A. Khadim, A. Saghir, Tassaddaq Hussain
Developments of new probability models for data analysis are keen interest of importance for all fields. The log-Dagum distribution has a prominent role in the theory and practice of statistics. In this article, a new family of continuous distributions generated from a log Dagum random variable called the log-Dagum Weibull distribution is proposed. The key properties of the proposed distribution are derived. Its density function can be symmetrical, left-skewed, right-skewed and reversed-J shaped and can have increasing, decreasing, bathtub hazard rates shaped. The model parameters are estimated by the method of maximum likelihood and illustrate its importance by means of applications to real data sets.
{"title":"A log-Dagum Weibull Distribution: Properties and Characterization","authors":"A. Khadim, A. Saghir, Tassaddaq Hussain","doi":"10.20944/PREPRINTS202009.0428.V1","DOIUrl":"https://doi.org/10.20944/PREPRINTS202009.0428.V1","url":null,"abstract":"Developments of new probability models for data analysis are keen interest of importance for all fields. The log-Dagum distribution has a prominent role in the theory and practice of statistics. In this article, a new family of continuous distributions generated from a log Dagum random variable called the log-Dagum Weibull distribution is proposed. The key properties of the proposed distribution are derived. Its density function can be symmetrical, left-skewed, right-skewed and reversed-J shaped and can have increasing, decreasing, bathtub hazard rates shaped. The model parameters are estimated by the method of maximum likelihood and illustrate its importance by means of applications to real data sets.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86368173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-03DOI: 10.11648/J.ACM.20200905.11
A. M. Kozae, M. Shokry, M. Omran
Intuitionistic Fuzzy set (IFS) theory plays an important role in real life and engineering problems. There are many model involving fuzzy matrices to deal with different complicated aspects. Intuitionistic fuzzy set (IFS) is useful in providing a flexible model for developing the uncertainty and vagueness involved in making decisions where the theories of uncertainty are very useful to treat with mathematics that needs to address. In other words, the application of intuitionistic fuzzy sets instead of fuzzy sets means the introduction of another degree of freedom into a set description. Intuitionistic fuzzy set (IFS) called the generalization of fuzzy sets was proposed in K. T. Atanassov. So, we can use it in decision making. We examined the definition of IFS and puts new definitions of IFS (Intuitionistic fuzzy set) in this paper and suggested its implementation in the Corona Covid-19. For several similar real-life cases the suggested approach can be applied.
直觉模糊集(IFS)理论在现实生活和工程问题中起着重要作用。有许多涉及模糊矩阵的模型来处理各种复杂的问题。直觉模糊集(IFS)可以提供一个灵活的模型，用于开发决策中涉及的不确定性和模糊性，其中不确定性理论对于处理需要解决的数学问题非常有用。换句话说，用直觉模糊集代替模糊集意味着在集合描述中引入另一个自由度。直觉模糊集(IFS)是由K. T. Atanassov提出的，称为模糊集的泛化。所以，我们可以用它来做决策。本文对IFS的定义进行了研究，提出了IFS(直觉模糊集)的新定义，并提出了IFS在新冠肺炎疫情中的实施建议。对于几个类似的现实案例，建议的方法可以应用。
{"title":"Intuitionistic Fuzzy Set and Its Application in Corona Covid-19","authors":"A. M. Kozae, M. Shokry, M. Omran","doi":"10.11648/J.ACM.20200905.11","DOIUrl":"https://doi.org/10.11648/J.ACM.20200905.11","url":null,"abstract":"Intuitionistic Fuzzy set (IFS) theory plays an important role in real life and engineering problems. There are many model involving fuzzy matrices to deal with different complicated aspects. Intuitionistic fuzzy set (IFS) is useful in providing a flexible model for developing the uncertainty and vagueness involved in making decisions where the theories of uncertainty are very useful to treat with mathematics that needs to address. In other words, the application of intuitionistic fuzzy sets instead of fuzzy sets means the introduction of another degree of freedom into a set description. Intuitionistic fuzzy set (IFS) called the generalization of fuzzy sets was proposed in K. T. Atanassov. So, we can use it in decision making. We examined the definition of IFS and puts new definitions of IFS (Intuitionistic fuzzy set) in this paper and suggested its implementation in the Corona Covid-19. For several similar real-life cases the suggested approach can be applied.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90988987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-22DOI: 10.11648/j.acm.20200904.15
R. Dong
In this paper, through a series of analysis and testing of breast cancer detection data, the statistical rules of multiple objects and multiple indicators are analyzed in the case of their correlation. First of all, univariate diagnosis and multivariate diagnosis were performed on the data. Among them, when studying the correlation between variables, it was found that HOMA had a clear linear positive correlation with insulin content in blood. It is worth noting that some patients with breast cancer show a high degree of insulin resistance and blood insulin content, which is a feature not found in samples without breast cancer. Then, through single factor analysis of variance, we believe that there were significant differences in blood test conditions, ages, and BMI indicators of samples of different health conditions. Next, the principal component analysis was used to reduce the dimension of the data. In this study, the differences in age, BMI, and blood component content between the two groups with different health conditions can be summarized by these two independent factors. Among them, the absolute value of the MCP-1 (monocyte chemoattractant protein 1) coefficient in the main component 1 is large, reflecting the characteristics of the blood component of the sample; the load values of glucose and leptin in the main component 2 are large, reflecting similar results. Then, assuming the use of m = 3 factor model and the use of maximum likelihood method and principal component method, the original data and factor rotation data are re-analyzed, so that the variables are reduced to 3 factors for analysis. Among them, the maximum likelihood method is used to estimate the factor rotation data. The first factor reflects the insulin resistance factor attributed to insulin and HOMA indicators, and the second factor reflects the body fat and thin factor attributed to BMI and leptin. The third factor reflects the glucose content in the blood. Finally, by setting different misjudgment costs for discriminant analysis, the obtained APER is 0.1638 and EAER is 0.1872. Among them, the probability of discriminating patients with breast cancer from not having breast cancer is 0.09375, which is a low rate of misjudgment and also means the model established in this paper is efficient.
{"title":"Explore the Characteristics of Age, BMI and Blood Composition of Breast Cancer Patients Based on Multivariate Statistical Analysis","authors":"R. Dong","doi":"10.11648/j.acm.20200904.15","DOIUrl":"https://doi.org/10.11648/j.acm.20200904.15","url":null,"abstract":"In this paper, through a series of analysis and testing of breast cancer detection data, the statistical rules of multiple objects and multiple indicators are analyzed in the case of their correlation. First of all, univariate diagnosis and multivariate diagnosis were performed on the data. Among them, when studying the correlation between variables, it was found that HOMA had a clear linear positive correlation with insulin content in blood. It is worth noting that some patients with breast cancer show a high degree of insulin resistance and blood insulin content, which is a feature not found in samples without breast cancer. Then, through single factor analysis of variance, we believe that there were significant differences in blood test conditions, ages, and BMI indicators of samples of different health conditions. Next, the principal component analysis was used to reduce the dimension of the data. In this study, the differences in age, BMI, and blood component content between the two groups with different health conditions can be summarized by these two independent factors. Among them, the absolute value of the MCP-1 (monocyte chemoattractant protein 1) coefficient in the main component 1 is large, reflecting the characteristics of the blood component of the sample; the load values of glucose and leptin in the main component 2 are large, reflecting similar results. Then, assuming the use of m = 3 factor model and the use of maximum likelihood method and principal component method, the original data and factor rotation data are re-analyzed, so that the variables are reduced to 3 factors for analysis. Among them, the maximum likelihood method is used to estimate the factor rotation data. The first factor reflects the insulin resistance factor attributed to insulin and HOMA indicators, and the second factor reflects the body fat and thin factor attributed to BMI and leptin. The third factor reflects the glucose content in the blood. Finally, by setting different misjudgment costs for discriminant analysis, the obtained APER is 0.1638 and EAER is 0.1872. Among them, the probability of discriminating patients with breast cancer from not having breast cancer is 0.09375, which is a low rate of misjudgment and also means the model established in this paper is efficient.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87915752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-17DOI: 10.11648/j.acm.20200904.12
Ihsan Hishamuddin, S. S. Supadi, M. Omar
Various forms of preservation technology nowadays allow businesses to handle valuable perishable items with greater flexibility. Even with a wide variety of preservation techniques, the mathematical modelling of its implementation in EOQ literature remains rigid. The paper aims to integrate an improved preservation technology in a non-instantaneous deteriorating inventory model for businesses maximizing their average total cycle profit. The improved preservation technology furthers the delay to the time within the cycle where deterioration begins and enhances the durability of inventory that allows operators to employ a less prudent holding facility. Another improvement in this area is the accurate accumulation of preservation cost depending on the inventory level at hand. The conventional EOQ method of forming the objective function before choosing the optimal values for our two decision variables (Cycle time and level of preservation) is undertaken. The cycle time is split in two, differing in their inventory process (deterioration beginning in the second period). The time when deterioration begins is derived using the model's boundary conditions, a first attempt within the area. The optimal solution set is solved for a numerical example using an algorithm to demonstrate the model and prove the global nature of the solution. An investigation into the gains from the improved preservation technology is conducted by dissecting the effects within each individual component within the objective function. 3 separate channels by which this improved preservation technology modelling benefits the business model is found namely shifting to the higher profitable period, effects towards preservation affected costs and the returns to scale from successively increasing preservation levels. Sensitivity analysis is conducted to demonstrate and confirm the findings. The paper discovers great benefits from such an improved modelling that warrants further attention within the scope of preserved inventory models, especially on how levels of preservation could influence the traditional decision variable optimized such as cycle time or ordering frequency. Findings of the paper would have significant benefits to different inventory models with its own delay before deterioration and holding facility requirement.
{"title":"Improved Preservation Technology for Non-Instantaneous Deteriorating Inventory Using Boundary Condition Estimation","authors":"Ihsan Hishamuddin, S. S. Supadi, M. Omar","doi":"10.11648/j.acm.20200904.12","DOIUrl":"https://doi.org/10.11648/j.acm.20200904.12","url":null,"abstract":"Various forms of preservation technology nowadays allow businesses to handle valuable perishable items with greater flexibility. Even with a wide variety of preservation techniques, the mathematical modelling of its implementation in EOQ literature remains rigid. The paper aims to integrate an improved preservation technology in a non-instantaneous deteriorating inventory model for businesses maximizing their average total cycle profit. The improved preservation technology furthers the delay to the time within the cycle where deterioration begins and enhances the durability of inventory that allows operators to employ a less prudent holding facility. Another improvement in this area is the accurate accumulation of preservation cost depending on the inventory level at hand. The conventional EOQ method of forming the objective function before choosing the optimal values for our two decision variables (Cycle time and level of preservation) is undertaken. The cycle time is split in two, differing in their inventory process (deterioration beginning in the second period). The time when deterioration begins is derived using the model's boundary conditions, a first attempt within the area. The optimal solution set is solved for a numerical example using an algorithm to demonstrate the model and prove the global nature of the solution. An investigation into the gains from the improved preservation technology is conducted by dissecting the effects within each individual component within the objective function. 3 separate channels by which this improved preservation technology modelling benefits the business model is found namely shifting to the higher profitable period, effects towards preservation affected costs and the returns to scale from successively increasing preservation levels. Sensitivity analysis is conducted to demonstrate and confirm the findings. The paper discovers great benefits from such an improved modelling that warrants further attention within the scope of preserved inventory models, especially on how levels of preservation could influence the traditional decision variable optimized such as cycle time or ordering frequency. Findings of the paper would have significant benefits to different inventory models with its own delay before deterioration and holding facility requirement.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88859566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-18DOI: 10.11648/J.ACM.20200903.17
Nenad Stojanović
A simple polygon that either has equal all sides or all interior angles is called a semi-regular nonagon. In terms of this definition, we can distinguish between two types of semi-regular polygons: equilateral polygons (that have equal all sides and different interior angles) and equiangular polygons (that have equal interior angles and different sides). Unlike regular polygons, one characteristic element is not enough to analyze the metric properties of semi-regular polygons, and an additional one is needed. To select this additional characteristic element, note that the following regular triangles can be inscribed to a semi-regular equilateral nonagon by joining vertices: ∆A1 A4A7, △ A2 A5 A8, △A3 A6 A9. Now have a look at triangle △A1 A4A7. Let us use the mark φ=∡(a,b1) to mark the angle between side a of the semi-regular nonagon and side b1 of the inscribed regular triangle. In interpreting the metric properties of a semi-regular equilateral nonagon, in addition to its side, we also use the angle that such side creates with the side of one of the three regular triangles that can be inscribed to such semi-regular nonagon. We consider the way in which convexity, possibility of construction, surface area, and other properties depend on a side of the semi-regular nonagon and angle φ=∡(a,b1).
{"title":"Some Metric Properties of Semi-Regular Equilateral Nonagons","authors":"Nenad Stojanović","doi":"10.11648/J.ACM.20200903.17","DOIUrl":"https://doi.org/10.11648/J.ACM.20200903.17","url":null,"abstract":"A simple polygon that either has equal all sides or all interior angles is called a semi-regular nonagon. In terms of this definition, we can distinguish between two types of semi-regular polygons: equilateral polygons (that have equal all sides and different interior angles) and equiangular polygons (that have equal interior angles and different sides). Unlike regular polygons, one characteristic element is not enough to analyze the metric properties of semi-regular polygons, and an additional one is needed. To select this additional characteristic element, note that the following regular triangles can be inscribed to a semi-regular equilateral nonagon by joining vertices: ∆A1 A4A7, △ A2 A5 A8, △A3 A6 A9. Now have a look at triangle △A1 A4A7. Let us use the mark φ=∡(a,b1) to mark the angle between side a of the semi-regular nonagon and side b1 of the inscribed regular triangle. In interpreting the metric properties of a semi-regular equilateral nonagon, in addition to its side, we also use the angle that such side creates with the side of one of the three regular triangles that can be inscribed to such semi-regular nonagon. We consider the way in which convexity, possibility of construction, surface area, and other properties depend on a side of the semi-regular nonagon and angle φ=∡(a,b1).","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72602591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-18DOI: 10.11648/j.acm.20200904.11
E. R. Onyango, M. Kinyanjui, M. Kimathi, S. M. Uppal
In this study, a magnetohydrodynamic Jeffrey-Hamel flow of a viscous, fluid that conducts electricity and is incompressible through a divergent conduit in presence of inclined variable magnetic field with heat and mass transfer has been investigated. The solutions of the governing equations of the MHD flow are obtained numerically since they are non-linear. The numerical scheme used is implemented in a computer software program and the results presented in graphical form. The velocity profile, the temperature profiles, the effect of variable magnetic field and of varying various dimensionless numbers on the flow are analyzed. Jeffrey-Hamel flows are also applied in the diffuser development. Some of the systems include; the channel between the compressor and gas turbine engine burner, the canal at departure from a gas turbine linked to the jet pipe, the canal subsequent to the impellor of a centrifugal compressor, wind tunnels with closed circuits, and water turbine draft tubes among several others. The results provide significant information for the improvement of proficiency and performance of technologies in aerospace, chemical, civil, environmental, industrial and mechanical applications.
{"title":"Heat and Mass Transfer on MHD Jeffrey-Hamel Flow in Presence of Inclined Magnetic Field","authors":"E. R. Onyango, M. Kinyanjui, M. Kimathi, S. M. Uppal","doi":"10.11648/j.acm.20200904.11","DOIUrl":"https://doi.org/10.11648/j.acm.20200904.11","url":null,"abstract":"In this study, a magnetohydrodynamic Jeffrey-Hamel flow of a viscous, fluid that conducts electricity and is incompressible through a divergent conduit in presence of inclined variable magnetic field with heat and mass transfer has been investigated. The solutions of the governing equations of the MHD flow are obtained numerically since they are non-linear. The numerical scheme used is implemented in a computer software program and the results presented in graphical form. The velocity profile, the temperature profiles, the effect of variable magnetic field and of varying various dimensionless numbers on the flow are analyzed. Jeffrey-Hamel flows are also applied in the diffuser development. Some of the systems include; the channel between the compressor and gas turbine engine burner, the canal at departure from a gas turbine linked to the jet pipe, the canal subsequent to the impellor of a centrifugal compressor, wind tunnels with closed circuits, and water turbine draft tubes among several others. The results provide significant information for the improvement of proficiency and performance of technologies in aerospace, chemical, civil, environmental, industrial and mechanical applications.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":10.0,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76415942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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