The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assu...The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assumed to follow the Gompertz growth model and the respective predator growth function is constructed by solving ordinary differential equations. The results show that the predator population model is found to be a function of the well known exponential integral function. The solution is also given in Taylor’s series. Simulation study shows that the predator population size eventually converges either to a finite positive limit or zero or diverges to positive infinity. Under certain conditions, the predator population converges to the asymptotic limit of the prey model. More results are included in the paper.展开更多
Particle Swarm Optimization,a potential swarm intelligence heuristic,has been recognized as a global optimizer for solving various continuous as well as discrete optimization problems.Encourged by the performance of G...Particle Swarm Optimization,a potential swarm intelligence heuristic,has been recognized as a global optimizer for solving various continuous as well as discrete optimization problems.Encourged by the performance of Gompertz PSO on a set of continuous problems,this works extends the application of Gompertz PSO for solving binary optimization problems.Moreover,a new chaotic variant of Gompertz PSO namely Chaotic Gompertz Binary Particle Swarm Optimization(CGBPSO)has also been proposed.The new variant is further analysed for solving binary optimization problems.The new chaotic variant embeds the notion of chaos into GBPSO in later stages of searching process to avoid stagnation phenomena.The efficiency of both the Binary PSO variants has been tested on different sets of Knapsack Problems(KPs):0-1 Knapsack Problem(0-1 KP)and Multidimensional Knapsack Problems(MKP).The concluding remarks have made on the basis of detailed analysis of results,which comprises the comparison of results for Knapsack and Multidimensional Knapsack problems obtained using BPSO,GBPSO and CGBPSO.展开更多
In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution. We obtained some of its mathematical properties. Some structural properties of the new distribution are stud...In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution. We obtained some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.展开更多
The convolution of Nadarajah-Haghighi-G family of distributions will result <span style="font-family:Verdana;">into a more flexible distribution (Nadarajah-Haghighi Gompertz distribution) </span>...The convolution of Nadarajah-Haghighi-G family of distributions will result <span style="font-family:Verdana;">into a more flexible distribution (Nadarajah-Haghighi Gompertz distribution) </span><span style="font-family:Verdana;">than each of them individually in terms of the estimate of the characteristics in there parameters. The combination was done using Nadarajah-Haghighi </span><span style="font-family:Verdana;">(NH) generator. We investigated in the newly developed distribution some basic </span><span style="font-family:Verdana;">properties including moment, moment generating function, survival rate function, hazard rate function asymptotic behaviour and estimation of parameters. The proposed model is much more flexible and has a better representation of data than Gompertz distribution and some other model considered. A real data set was used to illustrate the applicability of the new model.</span>展开更多
This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infan...This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts.展开更多
Coronavirus disease 2019 outbreak has spread as a pandemic since the end of year 2019.This situation has been causing a lot of problems of human beings such as economic problems,health problems.The forecasting of the ...Coronavirus disease 2019 outbreak has spread as a pandemic since the end of year 2019.This situation has been causing a lot of problems of human beings such as economic problems,health problems.The forecasting of the number of infectious people is required by the authorities of all countries including Southeast Asian countries to make a decision and control the outbreak.This research is to investigate the suitable forecasting model for the number of infectious people in Southeast Asian countries.A comparison of forecasting models between logistic growth curve which is symmetric and Gompertz growth curve which is asymmetric based on the maximumof Coefficient of Determination and theminimumof RootMean Squared Percentage Error is also proposed.The estimation of parameters of the forecasting models is evaluated by the least square method.In addition,spreading of the outbreak is estimated by the derivative of the number of cumulative cases.The findings show that Gompertz growth curve is a suitable forecasting model for Indonesia,Philippines,andMalaysia and logistic growth curve suits the other countries in South Asia.展开更多
In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown ...In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.展开更多
Entering the 21st century, China’s economic development has reached new heights and the country has ascended to the world’s second largest economy. The 20 year unrelenting development in China also stimulates income...Entering the 21st century, China’s economic development has reached new heights and the country has ascended to the world’s second largest economy. The 20 year unrelenting development in China also stimulates income growth. The increased disposable income enables an ordinary Chinese family vehicle ownership which was unthinkable two decades ago. The most populous country has started a love affair with automobile just like in the United States. Annual automobile sales in China rose from 2.1 million in 2000 to 18.1 million in 2010 with a yearly growth rate of 24.3%, which spurs the vehicle ownership increase from 18.1 million in 2000 to 78.8 million in 2010, a growth rate of 15.9% The unprecedented motorization development in China is making a huge impact on all aspects of society, including negative consequences that cannot be ignored. Traffic congestion, air pollution, and dependency on imported oil are huge emerging problems threatening Chinese sustainable development. Although these problems occurred and still exist in many other developed and developing countries, they are more acute in China today. By collecting and analyzing the massive data from various sources, this paper explores the relationship between economic development and level of mobility by studying the historical developments from several developed counties and discusses the key issues in Chinese motorization development. The objective of the study is to predict the future level of motorization and its potential impacts.展开更多
对基于G om pertz函数的上证综合指数进行预测的可行性进行了分析,同时,在对上证综合指数的具体走势及实际数据进行研判的基础上,对牛市行情下上证综合指数的运行进行了预测的实证研究,得出了相应的结论,并提出了该预测方法进一步完善...对基于G om pertz函数的上证综合指数进行预测的可行性进行了分析,同时,在对上证综合指数的具体走势及实际数据进行研判的基础上,对牛市行情下上证综合指数的运行进行了预测的实证研究,得出了相应的结论,并提出了该预测方法进一步完善之处和可进一步深入研究的问题.展开更多
文摘The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assumed to follow the Gompertz growth model and the respective predator growth function is constructed by solving ordinary differential equations. The results show that the predator population model is found to be a function of the well known exponential integral function. The solution is also given in Taylor’s series. Simulation study shows that the predator population size eventually converges either to a finite positive limit or zero or diverges to positive infinity. Under certain conditions, the predator population converges to the asymptotic limit of the prey model. More results are included in the paper.
文摘Particle Swarm Optimization,a potential swarm intelligence heuristic,has been recognized as a global optimizer for solving various continuous as well as discrete optimization problems.Encourged by the performance of Gompertz PSO on a set of continuous problems,this works extends the application of Gompertz PSO for solving binary optimization problems.Moreover,a new chaotic variant of Gompertz PSO namely Chaotic Gompertz Binary Particle Swarm Optimization(CGBPSO)has also been proposed.The new variant is further analysed for solving binary optimization problems.The new chaotic variant embeds the notion of chaos into GBPSO in later stages of searching process to avoid stagnation phenomena.The efficiency of both the Binary PSO variants has been tested on different sets of Knapsack Problems(KPs):0-1 Knapsack Problem(0-1 KP)and Multidimensional Knapsack Problems(MKP).The concluding remarks have made on the basis of detailed analysis of results,which comprises the comparison of results for Knapsack and Multidimensional Knapsack problems obtained using BPSO,GBPSO and CGBPSO.
文摘In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution. We obtained some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.
文摘The convolution of Nadarajah-Haghighi-G family of distributions will result <span style="font-family:Verdana;">into a more flexible distribution (Nadarajah-Haghighi Gompertz distribution) </span><span style="font-family:Verdana;">than each of them individually in terms of the estimate of the characteristics in there parameters. The combination was done using Nadarajah-Haghighi </span><span style="font-family:Verdana;">(NH) generator. We investigated in the newly developed distribution some basic </span><span style="font-family:Verdana;">properties including moment, moment generating function, survival rate function, hazard rate function asymptotic behaviour and estimation of parameters. The proposed model is much more flexible and has a better representation of data than Gompertz distribution and some other model considered. A real data set was used to illustrate the applicability of the new model.</span>
文摘This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts.
基金The research was funding by King Mongkut’s University of Technology North Bangkok Contract No.KMUTNB-61-GOV-03-23.
文摘Coronavirus disease 2019 outbreak has spread as a pandemic since the end of year 2019.This situation has been causing a lot of problems of human beings such as economic problems,health problems.The forecasting of the number of infectious people is required by the authorities of all countries including Southeast Asian countries to make a decision and control the outbreak.This research is to investigate the suitable forecasting model for the number of infectious people in Southeast Asian countries.A comparison of forecasting models between logistic growth curve which is symmetric and Gompertz growth curve which is asymmetric based on the maximumof Coefficient of Determination and theminimumof RootMean Squared Percentage Error is also proposed.The estimation of parameters of the forecasting models is evaluated by the least square method.In addition,spreading of the outbreak is estimated by the derivative of the number of cumulative cases.The findings show that Gompertz growth curve is a suitable forecasting model for Indonesia,Philippines,andMalaysia and logistic growth curve suits the other countries in South Asia.
文摘In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.
文摘Entering the 21st century, China’s economic development has reached new heights and the country has ascended to the world’s second largest economy. The 20 year unrelenting development in China also stimulates income growth. The increased disposable income enables an ordinary Chinese family vehicle ownership which was unthinkable two decades ago. The most populous country has started a love affair with automobile just like in the United States. Annual automobile sales in China rose from 2.1 million in 2000 to 18.1 million in 2010 with a yearly growth rate of 24.3%, which spurs the vehicle ownership increase from 18.1 million in 2000 to 78.8 million in 2010, a growth rate of 15.9% The unprecedented motorization development in China is making a huge impact on all aspects of society, including negative consequences that cannot be ignored. Traffic congestion, air pollution, and dependency on imported oil are huge emerging problems threatening Chinese sustainable development. Although these problems occurred and still exist in many other developed and developing countries, they are more acute in China today. By collecting and analyzing the massive data from various sources, this paper explores the relationship between economic development and level of mobility by studying the historical developments from several developed counties and discusses the key issues in Chinese motorization development. The objective of the study is to predict the future level of motorization and its potential impacts.
