Pub Date : 2023-12-14DOI: 10.1142/s1793557123502455
Fazlahmad Abbasnia, K. Khashyarmanesh, Ahmad Erfanian
{"title":"Common zero-divisor graph over a commutative ring","authors":"Fazlahmad Abbasnia, K. Khashyarmanesh, Ahmad Erfanian","doi":"10.1142/s1793557123502455","DOIUrl":"https://doi.org/10.1142/s1793557123502455","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"16 S4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138975376","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 : 2023-12-01DOI: 10.1142/s1793557123502431
Pankaj Kumar, Riddhi
If j = 2 in (C6) , we obtain (3.7) a 2 001 + a 2 011 + a QQ1 a Q11 = 1. Using (3.6) and (3.7) along with the fact that a 0 0 1 = 1, we see that # 0 1 1 = 0. Since all the variables in (C7) have already been uniquely determined, we proceed to (C8), where we obtain c 2-~ 2 and (3.9) a 2 , + 2 + a a = i, (3.8) a 2 0Q1 + a 1 0 1 + 2 a 0 0 1 a 1 0 1 = 1 so that a 101 = 0. From (C10), we obtain and (3.11) a 2 010 + al lQ + a 0 1 0 a 1 1 0 = 1, so that a 110-0. From (C12) , we obtain, after simplification, (3.12) al ±1 + 2a l l x = 0 and (3.13) a 2 11 + a 1±1 = 0, so that a 111 = 0. We have now uniquely determined all 27 coefficients in (3.1). Thus, is the only reduced local permutation polynomial in three variables over Z 3 and, hence, there is precisely one reduced Latin cube of order three. If we list the cube in terms of the three Latin squares of order three which form its different levels, we can list the only reduced Latin cube of order three as 012 120 201 120 201 012 201 012 120. In this paper, we wish to derive some combinatorial identities (partly known, partly apparently new) by combining well-known recurrence relations with known forms for characteristic polynomials of paths and cycles (i.e., of their adjacency matrices). We also obtain some extensions of known results .
如果j = 2 in (C6)，我们得到(3.7)a 2001 + a 2011 + a QQ1 a Q11 = 1。使用(3.6)和式(3.7)以及a 0 0 1 = 1的事实，我们看到# 0 1 1 = 0。由于(C7)中的所有变量已经唯一确定，我们继续(C8)，在这里我们得到c2 -~ 2和(3.9)a 2， + 2 + a a = i， (3.8) a 2 q1 + a 101 + 2 a 0 01 a 101 = 1，因此a 101 = 0。由式(C10)可得，式(3.11)a 2010 + al lQ + a 110 + a 110 = 1，则a 110-0。由式(C12)，化简后得到(3.12)al±1 + 2a l l x = 0和(3.13)a 2 11 + a 1±1 = 0，则a 111 = 0。我们现在唯一地确定了(3.1)中的所有27个系数。因此，是z3上唯一的三个变量的约简局部排列多项式，因此，有一个3阶的约简拉丁立方体。如果我们根据构成其不同层次的三个三阶拉丁方阵列出该立方体，我们可以列出唯一的三阶拉丁方阵为012 120 201 120 201 012 201 012 120。在本文中，我们希望通过将已知的递归关系与已知形式的路径和环的特征多项式(即它们的邻接矩阵)结合起来，推导出一些组合恒等式(部分已知，部分显然是新的)。我们还得到了一些已知结果的推广。
{"title":"Some combinatorial identities","authors":"Pankaj Kumar, Riddhi","doi":"10.1142/s1793557123502431","DOIUrl":"https://doi.org/10.1142/s1793557123502431","url":null,"abstract":"If j = 2 in (C6) , we obtain (3.7) a 2 001 + a 2 011 + a QQ1 a Q11 = 1. Using (3.6) and (3.7) along with the fact that a 0 0 1 = 1, we see that # 0 1 1 = 0. Since all the variables in (C7) have already been uniquely determined, we proceed to (C8), where we obtain c 2-~ 2 and (3.9) a 2 , + 2 + a a = i, (3.8) a 2 0Q1 + a 1 0 1 + 2 a 0 0 1 a 1 0 1 = 1 so that a 101 = 0. From (C10), we obtain and (3.11) a 2 010 + al lQ + a 0 1 0 a 1 1 0 = 1, so that a 110-0. From (C12) , we obtain, after simplification, (3.12) al ±1 + 2a l l x = 0 and (3.13) a 2 11 + a 1±1 = 0, so that a 111 = 0. We have now uniquely determined all 27 coefficients in (3.1). Thus, is the only reduced local permutation polynomial in three variables over Z 3 and, hence, there is precisely one reduced Latin cube of order three. If we list the cube in terms of the three Latin squares of order three which form its different levels, we can list the only reduced Latin cube of order three as 012 120 201 120 201 012 201 012 120. In this paper, we wish to derive some combinatorial identities (partly known, partly apparently new) by combining well-known recurrence relations with known forms for characteristic polynomials of paths and cycles (i.e., of their adjacency matrices). We also obtain some extensions of known results .","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":" 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138614019","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 : 2023-11-23DOI: 10.1142/s179355712350239x
Gurpreet Kaur, S. Nagpal
{"title":"Radius problems for Ratios of analytic functions involving sigmoid domain","authors":"Gurpreet Kaur, S. Nagpal","doi":"10.1142/s179355712350239x","DOIUrl":"https://doi.org/10.1142/s179355712350239x","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"286 ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139244830","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 : 2023-11-23DOI: 10.1142/s1793557123502406
Soufiane Hadji
{"title":"Common Local spectral properties for the Operator Products","authors":"Soufiane Hadji","doi":"10.1142/s1793557123502406","DOIUrl":"https://doi.org/10.1142/s1793557123502406","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"8 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139245998","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 : 2023-11-23DOI: 10.1142/s179355712350242x
N. Nhung, Lê Ngọc Quỳnh, Pham Duc Thoan
{"title":"A generalization of uniqueness theorems of meromorphic mappings from complete kahler manifolds","authors":"N. Nhung, Lê Ngọc Quỳnh, Pham Duc Thoan","doi":"10.1142/s179355712350242x","DOIUrl":"https://doi.org/10.1142/s179355712350242x","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"4 10","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139244127","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 : 2023-11-23DOI: 10.1142/s1793557123502418
Anupam Das, Mohsen Rabbani, Bipan Hazarika
{"title":"An iterative algorithm to approximate the solution of a weighted fractional integral equation","authors":"Anupam Das, Mohsen Rabbani, Bipan Hazarika","doi":"10.1142/s1793557123502418","DOIUrl":"https://doi.org/10.1142/s1793557123502418","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"12 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139243863","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 : 2023-11-16DOI: 10.1142/s1793557123502352
B. Khoshnood Gharalar, A. Moussavi
{"title":"Weakly p.q.-Baer skew Hurwitz series rings","authors":"B. Khoshnood Gharalar, A. Moussavi","doi":"10.1142/s1793557123502352","DOIUrl":"https://doi.org/10.1142/s1793557123502352","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"25 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139267034","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 : 2023-11-16DOI: 10.1142/s1793557123502364
Sandeep Malik, R. K. Sharma
{"title":"Describing the Group of Units of Integral Grouprings ℤD8 and ℤD12","authors":"Sandeep Malik, R. K. Sharma","doi":"10.1142/s1793557123502364","DOIUrl":"https://doi.org/10.1142/s1793557123502364","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"24 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139269946","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 : 2023-11-16DOI: 10.1142/s1793557123502376
Saraswati Bajaj, P. Panigrahi
{"title":"Universal adjacency spectrum of the commuting and non-commuting graphs on AC-groups","authors":"Saraswati Bajaj, P. Panigrahi","doi":"10.1142/s1793557123502376","DOIUrl":"https://doi.org/10.1142/s1793557123502376","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"63 5","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139267523","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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