Pub Date : 1900-01-01DOI: 10.12988/imf.2022.912329
O. Gok, Esra Uluocak
In this paper, we investigate the notions of Dunford-Pettis operators and M -weakly compact operators in the unbounded norm topology ver-sion on Banach lattices. We characterize Banach lattices on which all operators are unbounded demi Dunford-Pettis operator and unbounded M -weakly demicompact operator
{"title":"On unbounded demi Dunford-Pettis operators","authors":"O. Gok, Esra Uluocak","doi":"10.12988/imf.2022.912329","DOIUrl":"https://doi.org/10.12988/imf.2022.912329","url":null,"abstract":"In this paper, we investigate the notions of Dunford-Pettis operators and M -weakly compact operators in the unbounded norm topology ver-sion on Banach lattices. We characterize Banach lattices on which all operators are unbounded demi Dunford-Pettis operator and unbounded M -weakly demicompact operator","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"203 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133882249","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}
The 80/20 rule and the 7 ± 2 law are examples of difficult to explain empirical facts. According to the 80/20 rule, in each activity, 20% of the people contribute to the 80% of the results. The 7± 2 law means that we divide objects into 7 ± 2 groups – i.e., into 5 to 9 groups. In this paper, we show that there is a relation between these two facts: namely, we show that, because of the 80/20 rule, the number of classes cannot be smaller than 5. Thus, the 80/20 rule explains the lower bound (5) on the 7 ± 2 law. 1 Formulation of the Problem Difficult-to-explain empirical facts. There are several difficult-to-explain empirical facts. • For example, there is a ubiquitous 80/20 rule, according to which, in each human activity, 80% of the results come from 20% of the participants. For example, 20% of the people own 80% of all the wealth, 20% of researchers publish 80% of all the papers, etc.; see, e.g., [1, 2] and references therein. • There is a known phenomenon in psychology called a 7 ± 2 law (see, e.g., [4, 5]), according to which each person usually classifies everything into a certain number of classes C; depending on the person, this number ranges from 7 − 2 = 5 to 7 + 2 = 9 classes.
{"title":"80/20 Rule partially explains 7+/-2 law: general system-based analysis","authors":"Griselda Acosta, Eric Smith, V. Kreinovich","doi":"10.12988/imf.2019.9833","DOIUrl":"https://doi.org/10.12988/imf.2019.9833","url":null,"abstract":"The 80/20 rule and the 7 ± 2 law are examples of difficult to explain empirical facts. According to the 80/20 rule, in each activity, 20% of the people contribute to the 80% of the results. The 7± 2 law means that we divide objects into 7 ± 2 groups – i.e., into 5 to 9 groups. In this paper, we show that there is a relation between these two facts: namely, we show that, because of the 80/20 rule, the number of classes cannot be smaller than 5. Thus, the 80/20 rule explains the lower bound (5) on the 7 ± 2 law. 1 Formulation of the Problem Difficult-to-explain empirical facts. There are several difficult-to-explain empirical facts. • For example, there is a ubiquitous 80/20 rule, according to which, in each human activity, 80% of the results come from 20% of the participants. For example, 20% of the people own 80% of all the wealth, 20% of researchers publish 80% of all the papers, etc.; see, e.g., [1, 2] and references therein. • There is a known phenomenon in psychology called a 7 ± 2 law (see, e.g., [4, 5]), according to which each person usually classifies everything into a certain number of classes C; depending on the person, this number ranges from 7 − 2 = 5 to 7 + 2 = 9 classes.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130294827","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}
Let A be a unital algebra with a nontrivial idempotent e1. A map φ : A → A is anti-commuting if [φ(a), b] = −[a, φ(b)] holds for all a, b ∈ A. In this paper, we give a general form of φ on A; particularly, if A is prime, then such maps are either central-valued maps or of the forms a 7→ za+ f(a) for all a ∈ A, where z is in the center of A and f is a central-valued map. Mathematics Subject Classification: 47B47, 47B49, 46L10
{"title":"Nonlinear anti-commuting maps of unital algebras with idempotents","authors":"Liqin Feng, X. Qi","doi":"10.12988/imf.2019.9524","DOIUrl":"https://doi.org/10.12988/imf.2019.9524","url":null,"abstract":"Let A be a unital algebra with a nontrivial idempotent e1. A map φ : A → A is anti-commuting if [φ(a), b] = −[a, φ(b)] holds for all a, b ∈ A. In this paper, we give a general form of φ on A; particularly, if A is prime, then such maps are either central-valued maps or of the forms a 7→ za+ f(a) for all a ∈ A, where z is in the center of A and f is a central-valued map. Mathematics Subject Classification: 47B47, 47B49, 46L10","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115528763","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 : 1900-01-01DOI: 10.12988/imf.2022.912302
Xiantao Wang, Yuanguo Zhu
This paper studies a dynamic optimal investment decision of defined contribution (DC) pension with inflation. Fund managers invest capital in different assets to minimize the quadratic loss function. Considering financial market complexity and incompleteness of information, we use optimal control under uncertain optimistic value criterion to build an optimal control model for DC pension plan. The equation of optimality for the optimal control problem is used to get the optimal pension investment strategy. Finally, a numerical experiment is given as an illustration. Mathematics Subject Classification: 91G80
{"title":"Optimal control of defined contribution pension plan under uncertain optimistic value criterion","authors":"Xiantao Wang, Yuanguo Zhu","doi":"10.12988/imf.2022.912302","DOIUrl":"https://doi.org/10.12988/imf.2022.912302","url":null,"abstract":"This paper studies a dynamic optimal investment decision of defined contribution (DC) pension with inflation. Fund managers invest capital in different assets to minimize the quadratic loss function. Considering financial market complexity and incompleteness of information, we use optimal control under uncertain optimistic value criterion to build an optimal control model for DC pension plan. The equation of optimality for the optimal control problem is used to get the optimal pension investment strategy. Finally, a numerical experiment is given as an illustration. Mathematics Subject Classification: 91G80","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126298660","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 : 1900-01-01DOI: 10.12988/imf.2022.912312
Chiara Brambilla, L. Grosset
In this paper, we analyse a new formulation of Stackelberg differential games. We assume that the Leader can control not only the dynamics of the game, but also the length of the programming interval. This formulation of a free final time Stackelberg differential game is not explicitly considered in the literature and presents some interesting issues. After a formal definition of this kind of differential game, we show, using a practical example, the main difficulties associated with this new definition. We close the article by presenting two open questions related to this issue.
{"title":"Free final time Stackelberg differential games","authors":"Chiara Brambilla, L. Grosset","doi":"10.12988/imf.2022.912312","DOIUrl":"https://doi.org/10.12988/imf.2022.912312","url":null,"abstract":"In this paper, we analyse a new formulation of Stackelberg differential games. We assume that the Leader can control not only the dynamics of the game, but also the length of the programming interval. This formulation of a free final time Stackelberg differential game is not explicitly considered in the literature and presents some interesting issues. After a formal definition of this kind of differential game, we show, using a practical example, the main difficulties associated with this new definition. We close the article by presenting two open questions related to this issue.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122967601","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 : 1900-01-01DOI: 10.12988/imf.2022.912327
B. Y. Disca, M. G. Domingo
The concept of H − cordial graphs is introduced by Ibrahim Cahit in 1996. Ibrahim Cahit used the symbol H to represent Hadamard Matrices. He claims that H − cordial graphs can be useful to construct Hadamard matrices since any n x n Hadamard matrix gives an H − cordial labeling for the bipartite graph. In this paper we investigate H − and H 2 − cordial graphs obtained by duplication of a vertex, duplication of a vertex by a new edge and duplication of an edge by a new vertex in some graph elements on crown graph.
H -亲切图的概念是由Ibrahim Cahit在1996年提出的。Ibrahim Cahit使用符号H来表示Hadamard矩阵。他声称H -亲切图可以用来构造Hadamard矩阵，因为任何n x n个Hadamard矩阵都给出了二部图的H -亲切标记。本文研究了冠图上若干图元中由顶点复制、新边复制顶点和新顶点复制边得到的H−和H 2−诚恳图。
{"title":"H- and H2- cordial labeling of graphs in the context of some graph operations on crown graph","authors":"B. Y. Disca, M. G. Domingo","doi":"10.12988/imf.2022.912327","DOIUrl":"https://doi.org/10.12988/imf.2022.912327","url":null,"abstract":"The concept of H − cordial graphs is introduced by Ibrahim Cahit in 1996. Ibrahim Cahit used the symbol H to represent Hadamard Matrices. He claims that H − cordial graphs can be useful to construct Hadamard matrices since any n x n Hadamard matrix gives an H − cordial labeling for the bipartite graph. In this paper we investigate H − and H 2 − cordial graphs obtained by duplication of a vertex, duplication of a vertex by a new edge and duplication of an edge by a new vertex in some graph elements on crown graph.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115457640","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 : 1900-01-01DOI: 10.12988/imf.2023.912383
Rita Vincenti
In [1] the author proves that by starting from two projectively equivalent curves in two independent spaces, a 2-dimensional ruled variety can be generated by the lines joining corresponding points of the two curves, the order of the variety being the sum of the orders of them. In this note we prove that result can be extended to any pair of projectively equivalent irreducible varieties of same dimension lying in two complementary spaces
{"title":"A generalization to varieties of a result about curves","authors":"Rita Vincenti","doi":"10.12988/imf.2023.912383","DOIUrl":"https://doi.org/10.12988/imf.2023.912383","url":null,"abstract":"In [1] the author proves that by starting from two projectively equivalent curves in two independent spaces, a 2-dimensional ruled variety can be generated by the lines joining corresponding points of the two curves, the order of the variety being the sum of the orders of them. In this note we prove that result can be extended to any pair of projectively equivalent irreducible varieties of same dimension lying in two complementary spaces","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"176 12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120967310","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 : 1900-01-01DOI: 10.12988/imf.2022.912316
M. G. Domingo, A. Racca
A graph labeling is an assignment of integers to the vertices or edges or both subject to some conditions. The concept of cordial labeling was introduced by Ibrahim Cahit in 1987 as a weaker version of graceful and harmonious labeling. A product cordial labeling of a graph 𝐺 = (𝑉(𝐺), 𝐸(𝐺)) is a function 𝑓: 𝑉(𝐺) → {0,1} with each edge 𝑢𝑣 assign label 𝑓(𝑢)𝑓(𝑣) , such that the number of vertices with label 0 and the number of vertices with label 1 differ at most by 1, and the number of edges with label 0 and the number of edges with label 1 differ by at most 1. In this paper we investigate product cordial labeling of the graphs obtained by duplication of some graph elements in crown, helm and wheel graph.
{"title":"Product cordial graph in the context of some graph operations on crown, helm, and wheel graph","authors":"M. G. Domingo, A. Racca","doi":"10.12988/imf.2022.912316","DOIUrl":"https://doi.org/10.12988/imf.2022.912316","url":null,"abstract":"A graph labeling is an assignment of integers to the vertices or edges or both subject to some conditions. The concept of cordial labeling was introduced by Ibrahim Cahit in 1987 as a weaker version of graceful and harmonious labeling. A product cordial labeling of a graph 𝐺 = (𝑉(𝐺), 𝐸(𝐺)) is a function 𝑓: 𝑉(𝐺) → {0,1} with each edge 𝑢𝑣 assign label 𝑓(𝑢)𝑓(𝑣) , such that the number of vertices with label 0 and the number of vertices with label 1 differ at most by 1, and the number of edges with label 0 and the number of edges with label 1 differ by at most 1. In this paper we investigate product cordial labeling of the graphs obtained by duplication of some graph elements in crown, helm and wheel graph.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129765227","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 : 1900-01-01DOI: 10.12988/imf.2022.912301
A. Fässler, Alagu S. Somasundaram
Parametrizations of 4 × 4 squares which allow to generate individual examples, using birthdays or other personally preferred numbers are developed. This will be done for magic squares that are delightful, perfect, skew symmetric, most perfect and pandiagonal (also called diabolic). Furthermore, the parametrizations explain the construction of famous historical magic squares. Also an idea for an artwork containing mathematics is given, called MathArt. 1 Historical Introduction Magic squares are always of interest to people irrespective of age and their acquaintance with mathematics. Earlier, magic squares appeared often on temples, in paintings and on mythological objects. Magic squares first appeared in ancient China, before they became an active subject westwards. They played a remarkable role in India, later in the Arabic world, in medieval Islam and finally in Europe and America. Legend has it that the first magic square is over 4000 years old. It is said that 12 Albert Fässler and Alagu S. Somasundaram the mystical Emperor Yu in China discovered small black and white circles on the shell of a turtle that had emerged from the Lo river. The arrangement of the circles representing the numbers 1 to 9 were structured in a special 3 × 3 square (see [2]). Here is the modern design of the so-called Lo Shu magic square
参数化的4 × 4平方，允许生成单独的例子，使用生日或其他个人喜欢的数字开发。这将是为神奇的正方形，是令人愉快的，完美的，斜对称的，最完美的和泛对角线(也称为恶魔)。此外，参数化还解释了著名历史幻方的构造。还提出了一种包含数学的艺术作品的想法，称为MathArt。不论年龄大小和对数学的了解程度，魔方总是能引起人们的兴趣。早些时候，魔方经常出现在寺庙、绘画和神话物品上。魔方最早出现在中国古代，后来在西方成为一项活跃的学科。他们在印度，后来在阿拉伯世界，在中世纪的伊斯兰教，最后在欧洲和美洲发挥了显著的作用。传说第一个魔法广场有4000多年的历史。据说12阿尔伯特Fässler和神秘的中国禹皇帝Alagu S. Somasundaram在一只乌龟的壳上发现了黑色和白色的小圆圈，这只乌龟是从罗河中出现的。代表数字1到9的圆圈排列在一个特殊的3 × 3正方形中(见[2])。这是现代设计的所谓罗树魔术广场
{"title":"Personal and historical magic squares","authors":"A. Fässler, Alagu S. Somasundaram","doi":"10.12988/imf.2022.912301","DOIUrl":"https://doi.org/10.12988/imf.2022.912301","url":null,"abstract":"Parametrizations of 4 × 4 squares which allow to generate individual examples, using birthdays or other personally preferred numbers are developed. This will be done for magic squares that are delightful, perfect, skew symmetric, most perfect and pandiagonal (also called diabolic). Furthermore, the parametrizations explain the construction of famous historical magic squares. Also an idea for an artwork containing mathematics is given, called MathArt. 1 Historical Introduction Magic squares are always of interest to people irrespective of age and their acquaintance with mathematics. Earlier, magic squares appeared often on temples, in paintings and on mythological objects. Magic squares first appeared in ancient China, before they became an active subject westwards. They played a remarkable role in India, later in the Arabic world, in medieval Islam and finally in Europe and America. Legend has it that the first magic square is over 4000 years old. It is said that 12 Albert Fässler and Alagu S. Somasundaram the mystical Emperor Yu in China discovered small black and white circles on the shell of a turtle that had emerged from the Lo river. The arrangement of the circles representing the numbers 1 to 9 were structured in a special 3 × 3 square (see [2]). Here is the modern design of the so-called Lo Shu magic square","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130698321","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 : 1900-01-01DOI: 10.12988/imf.2023.912379
Xuejiao Zi, Zhaoli Ma
In this article, an iterative algorithm is proposed for solving the split feasibility problem and fixed point problem of Bregman totally quasi-asymptotically nonexpansive mapping in p -uniformly convex and uniformly smooth real Banach spaces. We obtained and proved the strong convergence theorem of the iterative scheme presented. Then, our main result is used to solve split feasibility problem and equilibrium problem.
{"title":"The split feasibility problem and fixed point problem of Bregman totally quasi-asymptotically non-expansive mapping in Banach spaces","authors":"Xuejiao Zi, Zhaoli Ma","doi":"10.12988/imf.2023.912379","DOIUrl":"https://doi.org/10.12988/imf.2023.912379","url":null,"abstract":"In this article, an iterative algorithm is proposed for solving the split feasibility problem and fixed point problem of Bregman totally quasi-asymptotically nonexpansive mapping in p -uniformly convex and uniformly smooth real Banach spaces. We obtained and proved the strong convergence theorem of the iterative scheme presented. Then, our main result is used to solve split feasibility problem and equilibrium problem.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114411466","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：