Pub Date : 2020-02-05DOI: 10.20944/preprints202002.0064.v1
R. Dhaigude, C. Chesneau, Yogesh J. Bagul
In this article, we establish sharp trigonometric-polynomial bounds for unnormalized sinc function.
本文建立了非归一化sinc函数的尖锐三角多项式界。
{"title":"About trigonometric-polynomial bounds of sinc function","authors":"R. Dhaigude, C. Chesneau, Yogesh J. Bagul","doi":"10.20944/preprints202002.0064.v1","DOIUrl":"https://doi.org/10.20944/preprints202002.0064.v1","url":null,"abstract":"In this article, we establish sharp trigonometric-polynomial bounds for unnormalized sinc function.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123089239","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 : 2019-10-15DOI: 10.36753/MATHENOT.583477
E. Öztürk, Y. Yaylı
In this paper, we characterize the de Sitter space by means of spacelike and timelike curves that fully lies on it. For this purpose, we consider the tangential part of the second derivative of the unit speed curve on the hypersurface, and obtain the vector equations of the geodesics. We find the geodesics as hyperbolas, ellipses, and helices. Moreover, we give an example of null curve with constant curvature in 4−dimensional Minkowski space and we illustrate the geodesics of S 1 1 (r) × R .
{"title":"Elementary Approachs on De Sitter Space","authors":"E. Öztürk, Y. Yaylı","doi":"10.36753/MATHENOT.583477","DOIUrl":"https://doi.org/10.36753/MATHENOT.583477","url":null,"abstract":"In this paper, we characterize the de Sitter space by means of spacelike and timelike curves that fully lies on it. For this purpose, we consider the tangential part of the second derivative of the unit speed curve on the hypersurface, and obtain the vector equations of the geodesics. We find the geodesics as hyperbolas, ellipses, and helices. Moreover, we give an example of null curve with constant curvature in 4−dimensional Minkowski space and we illustrate the geodesics of S 1 1 (r) × R .","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131314114","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 : 2019-10-15DOI: 10.36753/MATHENOT.588787
H. Menken, Orhan Dişkaya
In this paper, we consider Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas sequences. We introduce the quadra Fibona-Pell,Fibona-Jacobsthal and Pell-Jacobsthal and the hexa Fibona-Pell-Jacobsthal sequences whose components are the Fibonacci, Pell and Jacobsthal sequences. We derive the Binet-like formulas, the generating functions and the exponential generating functions of these sequences. Also, we obtain some binomial identities for them.
{"title":"On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences","authors":"H. Menken, Orhan Dişkaya","doi":"10.36753/MATHENOT.588787","DOIUrl":"https://doi.org/10.36753/MATHENOT.588787","url":null,"abstract":"In this paper, we consider Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas sequences. We introduce the quadra Fibona-Pell,Fibona-Jacobsthal and Pell-Jacobsthal and the hexa Fibona-Pell-Jacobsthal sequences whose components are the Fibonacci, Pell and Jacobsthal sequences. We derive the Binet-like formulas, the generating functions and the exponential generating functions of these sequences. Also, we obtain some binomial identities for them.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129066598","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 : 2019-10-15DOI: 10.36753/MATHENOT.542272
Ö. Gelişgen, Serhat Yavuz
Polyhedra have interesting symmetries. Therefore they have attracted the attention of scientists and artists from past to present. Thus polyhedra are discussed in a lot of scientific and artistic works. There are only five regular convex polyhedra known as the platonic solids. There are many relationships between metrics and polyhedra. Some of them are given in previous studies. In this study, we introduce two new metrics, and show that the spheres of the 3-dimensional analytical space furnished by these metrics are chamfered cube and chamfered octahedron. Also we give some properties about these metrics. We show that the group of isometries of the 3-dimesional space covered by CCmetric and COmetric are the semi-direct product of Oh and T(3), where octahedral group Oh is the (Euclidean) symmetry group of the octahedron and T(3) is the group of all translations of the 3-dimensional space.
{"title":"Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces","authors":"Ö. Gelişgen, Serhat Yavuz","doi":"10.36753/MATHENOT.542272","DOIUrl":"https://doi.org/10.36753/MATHENOT.542272","url":null,"abstract":"Polyhedra have interesting symmetries. Therefore they have attracted the attention of scientists and artists from past to present. Thus polyhedra are discussed in a lot of scientific and artistic works. There are only five regular convex polyhedra known as the platonic solids. There are many relationships between metrics and polyhedra. Some of them are given in previous studies. In this study, we introduce two new metrics, and show that the spheres of the 3-dimensional analytical space furnished by these metrics are chamfered cube and chamfered octahedron. Also we give some properties about these metrics. We show that the group of isometries of the 3-dimesional space covered by CCmetric and COmetric are the semi-direct product of Oh and T(3), where octahedral group Oh is the (Euclidean) symmetry group of the octahedron and T(3) is the group of all translations of the 3-dimensional space.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134218718","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 : 2019-10-15DOI: 10.36753/MATHENOT.618335
B. Meftah, A. Souahi
In this paper, we establish a new fractional integral identity, and then we derive some new fractional Hermite-Hadamard type inequalities for functions whose derivatives are s-preinvex.
{"title":"Fractional Hermite-Hadamard Type Inequalities for Functions Whose Derivatives are s-Preinvex","authors":"B. Meftah, A. Souahi","doi":"10.36753/MATHENOT.618335","DOIUrl":"https://doi.org/10.36753/MATHENOT.618335","url":null,"abstract":"In this paper, we establish a new fractional integral identity, and then we derive some new fractional Hermite-Hadamard type inequalities for functions whose derivatives are s-preinvex.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"306 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114400839","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 : 2019-10-15DOI: 10.36753/MATHENOT.634506
Meriem Elhaddad, Faiza Limam-Belarbi
This paper concerns an approximate analysis of a Markovian multiserver infinite source retrial queuing with impatience, in which all the servers are subject to breakdown and repairs. Customer who find the total number of busy and failed servers equal to $s$,i.e, he is given to choice to enter a retrial orbit for an random amount of time before attempting to reccess an available server or enter the queue of size $q$. Customer waiting in the queue start being served as an idle or repaired server assigned to them, they can also leave the queue and enter orbit due to impatience. Customers whose service is interrupted by a failure may have the option of leaving the system entirely or returning to the orbit to repeat or resume service. We assume that each server has its own dedicated repair person, and repairs begin immediately following a failure and all process are assumed to be mutually independent. The simultaneous effect of customer balking, impatience and retrials is analyzed. We try to approximate the steady-state joint distribution of the number of customers in orbit and the number of customers in the service area using a phase-merging Algorithm.
{"title":"On the Analysis of Unreliable Markovian Multiserver Queue with Retrials and Impatience","authors":"Meriem Elhaddad, Faiza Limam-Belarbi","doi":"10.36753/MATHENOT.634506","DOIUrl":"https://doi.org/10.36753/MATHENOT.634506","url":null,"abstract":"This paper concerns an approximate analysis of a Markovian multiserver infinite source retrial queuing with impatience, in which all the servers are subject to breakdown and repairs. Customer who find the total number of busy and failed servers equal to $s$,i.e, he is given to choice to enter a retrial orbit for an random amount of time before attempting to reccess an available server or enter the queue of size $q$. Customer waiting in the queue start being served as an idle or repaired server assigned to them, they can also leave the queue and enter orbit due to impatience. Customers whose service is interrupted by a failure may have the option of leaving the system entirely or returning to the orbit to repeat or resume service. We assume that each server has its own dedicated repair person, and repairs begin immediately following a failure and all process are assumed to be mutually independent. The simultaneous effect of customer balking, impatience and retrials is analyzed. We try to approximate the steady-state joint distribution of the number of customers in orbit and the number of customers in the service area using a phase-merging Algorithm.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130012945","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 : 2019-10-15DOI: 10.36753/MATHENOT.578638
P. Agarwal, A. Çetinkaya, Shilpi Jain, İ. O. Kıymaz
In 2014, S-generalized beta function which consist of seven parameters, defined and studied by Srivastava et al. [H. M. Srivastava, P. Agarwal and S. Jain, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput., 247 (2014), pp. 348-352]. In this paper, by using S-generalized beta function, we introduce a new generalization of Mittag-Leffler function. This new generalization of Mittag-Leffler function is consist of eleven parameters. We also investigate some of its certain properties such as integral representations, recurrence formulas and derivative formulas by using classical and fractional derivatives. Furthermore, we determine its Mellin, beta and Laplace integral transforms.
2014年，Srivastava等定义并研究了由7个参数组成的s -广义beta函数[H]。M. Srivastava, P. Agarwal和S. Jain，广义高斯超几何函数的生成函数，应用。数学。第一版。书刊，247 (2014)，pp. 348-352]。本文利用s -广义beta函数，引入了Mittag-Leffler函数的一种新的推广。这种新推广的Mittag-Leffler函数由11个参数组成。我们还利用经典导数和分数阶导数研究了它的积分表示、递归公式和导数公式等性质。进一步，我们确定了它的Mellin，和拉普拉斯积分变换。
{"title":"S-generalized Mittag-Leffler Function and its Certain Properties","authors":"P. Agarwal, A. Çetinkaya, Shilpi Jain, İ. O. Kıymaz","doi":"10.36753/MATHENOT.578638","DOIUrl":"https://doi.org/10.36753/MATHENOT.578638","url":null,"abstract":"In 2014, S-generalized beta function which consist of seven parameters, defined and studied by Srivastava et al. [H. M. Srivastava, P. Agarwal and S. Jain, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput., 247 (2014), pp. 348-352]. In this paper, by using S-generalized beta function, we introduce a new generalization of Mittag-Leffler function. This new generalization of Mittag-Leffler function is consist of eleven parameters. We also investigate some of its certain properties such as integral representations, recurrence formulas and derivative formulas by using classical and fractional derivatives. Furthermore, we determine its Mellin, beta and Laplace integral transforms.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122194350","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 : 2019-10-15DOI: 10.36753/MATHENOT.634516
E. Ünlüyol, Yeter Erdaş, Seren Salaş
In this study, firstly the definition of operator $(alpha,m)$-convex function is defined. Secondly, a new lemma is given. Then, new theorems are obtained in terms of this lemma. Finally, they are applied for synchronous and asynchronous functions.
{"title":"Operator $(alpha,m)$-convex functions and applications for synchronous and asynchronous functions","authors":"E. Ünlüyol, Yeter Erdaş, Seren Salaş","doi":"10.36753/MATHENOT.634516","DOIUrl":"https://doi.org/10.36753/MATHENOT.634516","url":null,"abstract":"In this study, firstly the definition of operator $(alpha,m)$-convex function is defined. Secondly, a new lemma is given. Then, new theorems are obtained in terms of this lemma. Finally, they are applied for synchronous and asynchronous functions.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124828795","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 : 2019-10-15DOI: 10.36753/MATHENOT.634513
N. Irmak, Naime Demirtaş
In this paper, we combine the important concepts which are Fuzzy numbers and Fibonacci, Lucas numbers. We introduce the concepts of Fuzzy Fibonacci and Fuzzy Lucas numbers by this combination. By this motivation, we provide a bridge between the areas Fuzzy sets and number theory. Afterwards, we generalize their well-known properties by the definitions of Fuzzy Fibonacci and Lucas numbers.
{"title":"Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties","authors":"N. Irmak, Naime Demirtaş","doi":"10.36753/MATHENOT.634513","DOIUrl":"https://doi.org/10.36753/MATHENOT.634513","url":null,"abstract":"In this paper, we combine the important concepts which are Fuzzy numbers and Fibonacci, Lucas numbers. We introduce the concepts of Fuzzy Fibonacci and Fuzzy Lucas numbers by this combination. By this motivation, we provide a bridge between the areas Fuzzy sets and number theory. Afterwards, we generalize their well-known properties by the definitions of Fuzzy Fibonacci and Lucas numbers.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114612061","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 : 2019-10-15DOI: 10.36753/MATHENOT.566448
Feng Qi (祁锋), Bai-Ni Guo (郭白妮)
In the note, by virtue of the Fa`a di Bruno formula and two identities for the Bell polynomials of the second kind, the authors derive three relations among the Bell polynomials, central factorial numbers of the second kind, and central Bell polynomials.
本文利用Fa a di Bruno公式和第二类贝尔多项式的两个恒等式，导出了贝尔多项式、第二类中心阶乘数和中心贝尔多项式之间的三种关系。
{"title":"Relations among Bell polynomials, central factorial numbers, and central Bell polynomials","authors":"Feng Qi (祁锋), Bai-Ni Guo (郭白妮)","doi":"10.36753/MATHENOT.566448","DOIUrl":"https://doi.org/10.36753/MATHENOT.566448","url":null,"abstract":"In the note, by virtue of the Fa`a di Bruno formula and two identities for the Bell polynomials of the second kind, the authors derive three relations among the Bell polynomials, central factorial numbers of the second kind, and central Bell polynomials.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131455247","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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