Pub Date : 2018-05-30DOI: 10.3844/JMSSP.2018.151.155
E. Balreira
The Gale-Nikaido Theorem establishes global injectivity of maps defined over rectangular regions provided the Jacobian matrix is a P-matrix. We provide a purely geometric generalization of this result in the plane by showing that if the image of each edge of the rectangular domain is realized as a graph of a function over the appropriate axis, then the map is injective. We also show that the hypothesis that the Jacobian matrix is a P-matrix is simply one way to analytically check this geometric condition.
{"title":"A Geometric Generalization of the Planar Gale-Nikaidô Theorem","authors":"E. Balreira","doi":"10.3844/JMSSP.2018.151.155","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.151.155","url":null,"abstract":"The Gale-Nikaido Theorem establishes global injectivity of maps defined over rectangular regions provided the Jacobian matrix is a P-matrix. We provide a purely geometric generalization of this result in the plane by showing that if the image of each edge of the rectangular domain is realized as a graph of a function over the appropriate axis, then the map is injective. We also show that the hypothesis that the Jacobian matrix is a P-matrix is simply one way to analytically check this geometric condition.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"18 1","pages":"151-155"},"PeriodicalIF":0.3,"publicationDate":"2018-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84745098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-05-28DOI: 10.3844/JMSSP.2018.141.150
Iis Dewi Ratih, S. Wulandari, B. Otok, Yusnada Asa Nurani
Indonesia shall fulfill the residents need of food by its heterogeneous and big resource of food. But in fact, Indonesian food security is still far from expectation because of the maintenance of food resource in Indonesia has not been maximized yet. Meanwhile, households with tuberculosis patients in Surabaya tend to classify as food-insecure. This study conduct a classification of households with tuberculosis patients food security in Surabaya by using Classification and Regression Tree (CART) and Adaptive Resampling and Combining (ARCING). The purpose of this study is to know the influential factor of households food security and the accuracy of its classification. As the result, the way households obtain foods is the most influential factor of Indonesian food security in Surabaya. Other than that, this study shows that accuracy when using ARCING is higher than CART.
{"title":"Comparison of CART and CART ARCING to Classify Household Food Security of Tuberculosis Patients in Surabaya","authors":"Iis Dewi Ratih, S. Wulandari, B. Otok, Yusnada Asa Nurani","doi":"10.3844/JMSSP.2018.141.150","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.141.150","url":null,"abstract":"Indonesia shall fulfill the residents need of food by its heterogeneous and big resource of food. But in fact, Indonesian food security is still far from expectation because of the maintenance of food resource in Indonesia has not been maximized yet. Meanwhile, households with tuberculosis patients in Surabaya tend to classify as food-insecure. This study conduct a classification of households with tuberculosis patients food security in Surabaya by using Classification and Regression Tree (CART) and Adaptive Resampling and Combining (ARCING). The purpose of this study is to know the influential factor of households food security and the accuracy of its classification. As the result, the way households obtain foods is the most influential factor of Indonesian food security in Surabaya. Other than that, this study shows that accuracy when using ARCING is higher than CART.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"82 1","pages":"141-150"},"PeriodicalIF":0.3,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80567748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-05-18DOI: 10.3844/JMSSP.2018.129.140
U. Duran, M. Acikgoz, S. Araci
In this study, we introduce a new class of generalized (p, q)-Bernoulli, (p, q)-Euler and (p, q)-Genocchi polynomials and investigate their some properties. We derive (p, q)-generalizations of some familiar formulae belonging to classical Bernoulli, Euler and Genocchi polynomials. We also obtain a (p, q)-extension of the Srivastava-Pinter addition theorem.
{"title":"On Generalized Some (p, q)-Special Polynomials","authors":"U. Duran, M. Acikgoz, S. Araci","doi":"10.3844/JMSSP.2018.129.140","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.129.140","url":null,"abstract":"In this study, we introduce a new class of generalized (p, q)-Bernoulli, (p, q)-Euler and (p, q)-Genocchi polynomials and investigate their some properties. We derive (p, q)-generalizations of some familiar formulae belonging to classical Bernoulli, Euler and Genocchi polynomials. We also obtain a (p, q)-extension of the Srivastava-Pinter addition theorem.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"11 1","pages":"129-140"},"PeriodicalIF":0.3,"publicationDate":"2018-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82853706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-05-16DOI: 10.3844/jmssp.2018.119.128
J. Dugas, Brian M. O’Connor
A previously derived set of sequences for generating prime numbers is modified by various algebraic and trigonometric manipulations. The modified sequences are then used to more efficiently generate prime numbers. The modified sequences are simplified from their original form and are much easier to implement into a computer program. It is shown by computation that the modified sequences more efficiently determine prime numbers because the modified sequences provide flexibility with their implementation. The added flexibility allows for the removal of redundancy in the overall process, which decreases the amount of data to process; thus, the efficiency of the prime number generator is significantly improved.
{"title":"The Linear and Quadratic Nature of Sequences for Determining Prime Numbers by Elimination of Composites","authors":"J. Dugas, Brian M. O’Connor","doi":"10.3844/jmssp.2018.119.128","DOIUrl":"https://doi.org/10.3844/jmssp.2018.119.128","url":null,"abstract":"A previously derived set of sequences for generating prime numbers is modified by various algebraic and trigonometric manipulations. The modified sequences are then used to more efficiently generate prime numbers. The modified sequences are simplified from their original form and are much easier to implement into a computer program. It is shown by computation that the modified sequences more efficiently determine prime numbers because the modified sequences provide flexibility with their implementation. The added flexibility allows for the removal of redundancy in the overall process, which decreases the amount of data to process; thus, the efficiency of the prime number generator is significantly improved.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"4 1","pages":"119-128"},"PeriodicalIF":0.3,"publicationDate":"2018-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90247163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-05-15DOI: 10.3844/jmssp.2018.107.118
I. L. Amerise
In this article we are concerned with a collection of multiple linear regressions that enable the researcher to gain an impression of the entire conditional distribution of a response variable given a set of explanatory variables. More specifically, we investigate the advantage of using a new method to estimate a bunch of non-crossing quantile regressions hyperplanes. The main tool is a weighting system of the data elements that aims to reduce the effect of contamination of the sampled population on the estimated parameters by diminishing the effect of outliers. The performances of the new estimators are evaluated on a number of data sets. We had considerable success with avoiding intersections and in the same time improving the global fitting of conditional quantile regressions. We conjecture that in other situations (e.g., data with high level of skewness, non-constant variances, unusual and imputed data) the method of weighted non-crossing quantiles will lead to estimators with good robustness properties.
{"title":"Quantile Regression Estimation Using Non-Crossing Constraints","authors":"I. L. Amerise","doi":"10.3844/jmssp.2018.107.118","DOIUrl":"https://doi.org/10.3844/jmssp.2018.107.118","url":null,"abstract":"In this article we are concerned with a collection of multiple linear regressions that enable the researcher to gain an impression of the entire conditional distribution of a response variable given a set of explanatory variables. More specifically, we investigate the advantage of using a new method to estimate a bunch of non-crossing quantile regressions hyperplanes. The main tool is a weighting system of the data elements that aims to reduce the effect of contamination of the sampled population on the estimated parameters by diminishing the effect of outliers. The performances of the new estimators are evaluated on a number of data sets. We had considerable success with avoiding intersections and in the same time improving the global fitting of conditional quantile regressions. We conjecture that in other situations (e.g., data with high level of skewness, non-constant variances, unusual and imputed data) the method of weighted non-crossing quantiles will lead to estimators with good robustness properties.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"1 1","pages":"107-118"},"PeriodicalIF":0.3,"publicationDate":"2018-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89621721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-05-09DOI: 10.3844/JMSSP.2018.94.106
Nneka Umeorah, Phillip Mashele
Monte-Carlo simulations have been utilized greatly in the pricing of derivative securities. Over the years, several variance reduction techniques have been developed to curb the instability, as well as, increase the simulation e?ciencies of the Monte-Carlo methods. Our approach in this research work will consider the use of antithetic variate techniques to estimate the fair prices of barrier options. Next, we use the quasi-Monte Carlo method, together with Sobol sequence to estimate the values of the same option. An extended version of the Black-Scholes model will serve as basis for the exact prices of these exotic options. The resulting simulated prices will be compared to the exact prices. The research concludes by showing some results which proves that when random numbers are generated via low discrepancy sequences in contrast to the normal pseudo-random numbers, a more efficient simulation method is ensued. This is further applicable in pricing complex derivatives without closed formsolutions.
{"title":"A Comparative Study on Barrier Option Pricing using Antithetic and Quasi Monte-Carlo Simulations","authors":"Nneka Umeorah, Phillip Mashele","doi":"10.3844/JMSSP.2018.94.106","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.94.106","url":null,"abstract":"Monte-Carlo simulations have been utilized greatly in the pricing of derivative securities. Over the years, several variance reduction techniques have been developed to curb the instability, as well as, increase the simulation e?ciencies of the Monte-Carlo methods. Our approach in this research work will consider the use of antithetic variate techniques to estimate the fair prices of barrier options. Next, we use the quasi-Monte Carlo method, together with Sobol sequence to estimate the values of the same option. An extended version of the Black-Scholes model will serve as basis for the exact prices of these exotic options. The resulting simulated prices will be compared to the exact prices. The research concludes by showing some results which proves that when random numbers are generated via low discrepancy sequences in contrast to the normal pseudo-random numbers, a more efficient simulation method is ensued. This is further applicable in pricing complex derivatives without closed formsolutions.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"146 1","pages":"94-106"},"PeriodicalIF":0.3,"publicationDate":"2018-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88644612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-04-25DOI: 10.3844/JMSSP.2018.88.93
Sami H. Altoum
In this study, the transonic gas equation will be considered. For q∈(0,1), q-deformation of transonic gas equation (q-transonic) are studied, we use q- derivative (or Jackson derivative) to solve transonic gas equation.
{"title":"q-Deformation of Transonic Gas Equation","authors":"Sami H. Altoum","doi":"10.3844/JMSSP.2018.88.93","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.88.93","url":null,"abstract":"In this study, the transonic gas equation will be considered. For q∈(0,1), q-deformation of transonic gas equation (q-transonic) are studied, we use q- derivative (or Jackson derivative) to solve transonic gas equation.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"11 1","pages":"88-93"},"PeriodicalIF":0.3,"publicationDate":"2018-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89740928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-04-03DOI: 10.3844/JMSSP.2018.79.87
H. M. Barakat, O. Khaled, N. Khalil
In this study we introduce a new method of adding two shape parameters to any baseline bivariate distribution function (df) to get a more flexible family of bivariate df's. Through the additional parameters we can fully control the type of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution, denoted by BSSN. The statistical properties of the BSSN family are studied. Moreover, via a mixture of the BSSN family and the standard bivariate logistic df, we get a more capable family, denoted by FBSSN. Theoretically, each of the marginals of the FBSSN contains all the possible types of df's with respect to the signs of skewness and excess kurtosis. In addition, each possesses very wide range of the indices of skewness and kurtosis. Finally, we compare the families BSSN and FBSSN with some important competitors (i.e., some generalized families of bivariate df's) via real data examples. AMS 2010 Subject Classification: 62-07; 62E10; 62F99.
{"title":"New Families of Distributions for Modeling Bivariate Data, with Applications","authors":"H. M. Barakat, O. Khaled, N. Khalil","doi":"10.3844/JMSSP.2018.79.87","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.79.87","url":null,"abstract":"In this study we introduce a new method of adding two shape parameters to any baseline bivariate distribution function (df) to get a more flexible family of bivariate df's. Through the additional parameters we can fully control the type of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution, denoted by BSSN. The statistical properties of the BSSN family are studied. Moreover, via a mixture of the BSSN family and the standard bivariate logistic df, we get a more capable family, denoted by FBSSN. Theoretically, each of the marginals of the FBSSN contains all the possible types of df's with respect to the signs of skewness and excess kurtosis. In addition, each possesses very wide range of the indices of skewness and kurtosis. Finally, we compare the families BSSN and FBSSN with some important competitors (i.e., some generalized families of bivariate df's) via real data examples. AMS 2010 Subject Classification: 62-07; 62E10; 62F99.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"13 1","pages":"79-87"},"PeriodicalIF":0.3,"publicationDate":"2018-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76701822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-02-10DOI: 10.3844/JMSSP.2018.56.63
S. Abbas, M. Benchohra, S. Sivasundaram
In this study, we present some results concerning the existence of weak solutions for some coupled systems of Hadamard fractional differential equations involving the both retarded and advanced arguments. Our results are obtained by using fixed point theory and the technique of measure of weak noncompactness.
{"title":"Coupled Pettis-Hadamard Fractional Differential Systems with Retarded and Advanced Arguments","authors":"S. Abbas, M. Benchohra, S. Sivasundaram","doi":"10.3844/JMSSP.2018.56.63","DOIUrl":"https://doi.org/10.3844/JMSSP.2018.56.63","url":null,"abstract":"In this study, we present some results concerning the existence of weak solutions for some coupled systems of Hadamard fractional differential equations involving the both retarded and advanced arguments. Our results are obtained by using fixed point theory and the technique of measure of weak noncompactness.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"19 1","pages":"56-63"},"PeriodicalIF":0.3,"publicationDate":"2018-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86028344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-02-10DOI: 10.3844/jmssp.2018.64.71
Vivek Devaraj, K. Kanagarajan, S. Sivasundaram
This paper deals with some existence and Ulam-Hyers-q-Mittag-Leffler stability results for q-fractional order pantograph equation. An application is made of a Darbo's fixed point theorem for the existence of solutions.
{"title":"Dynamics and Stability of q-Fractional Order Pantograph Equations With Nonlocal Condition","authors":"Vivek Devaraj, K. Kanagarajan, S. Sivasundaram","doi":"10.3844/jmssp.2018.64.71","DOIUrl":"https://doi.org/10.3844/jmssp.2018.64.71","url":null,"abstract":"This paper deals with some existence and Ulam-Hyers-q-Mittag-Leffler stability results for q-fractional order pantograph equation. An application is made of a Darbo's fixed point theorem for the existence of solutions.","PeriodicalId":41981,"journal":{"name":"Jordan Journal of Mathematics and Statistics","volume":"25 1","pages":"64-71"},"PeriodicalIF":0.3,"publicationDate":"2018-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78916647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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