Indian Journal of Pure and Applied Mathematics最新文献

{"title":"Convergence properties of new $$alpha $$ -Bernstein–Kantorovich type operators","authors":"Ajay Kumar, Abhishek Senapati, Tanmoy Som","doi":"10.1007/s13226-024-00577-5","DOIUrl":"https://doi.org/10.1007/s13226-024-00577-5","url":null,"abstract":"<p>In the present paper, we introduce a new sequence of <span>(alpha -)</span>Bernstein-Kantorovich type operators, which fix constant and preserve Korovkin’s other test functions in a limiting sense. We extend the natural Korovkin and Voronovskaja type results into a sequence of probability measure spaces. Then, we establish the convergence properties of these operators using the Ditzian-Totik modulus of smoothness for Lipschitz-type space and functions with derivatives of bounded variations.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140572994","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}

{"title":"Clear graph of a ring","authors":"Shabir Ahmad Mir, Cihat Abdioğlu, Nadeem ur Rehman, Mohd Nazim, Muhammed Akkafa, Ece Yetkin Çelikel","doi":"10.1007/s13226-024-00581-9","DOIUrl":"https://doi.org/10.1007/s13226-024-00581-9","url":null,"abstract":"<p>This research article introduces the concept of the clear graph associated with a ring <span>({mathcal {R}})</span> with identity, denoted as <span>(Cr({mathcal {R}}))</span>. This graph comprises vertices of the form <span>({(x,u):)</span> <i>x</i> is a unit regular element of <i>R</i> and <i>u</i> is a unit of <span>({mathcal {R}})</span>} and two distinct vertices (<i>x</i>, <i>u</i>) and (<i>y</i>, <i>v</i>) are adjacent if and only if either <span>(xy=yx=0)</span> or <span>(uv=vu=1)</span>. This research article also focuses on a specific subgraph of <span>(Cr({mathcal {R}}))</span> denoted as <span>(Cr_2({mathcal {R}}))</span>, which is formed by vertices <span>({(x,u) :x)</span> is a nonzero unit regular element of <span>(R })</span>. The significance of <span>(Cr_2({mathcal {R}}))</span> within the context of <span>(Cr{({mathcal {R}})})</span> is explored in the article. Taken <span>(Cr_2({mathcal {R}}))</span> into consideration, we found connectedness, regularity, planarity, and outer planarity. Moreover, we characterized the ring <span>({mathcal {R}})</span> for which <span>(Cr_2({mathcal {R}}))</span> is unicyclic, a tree and a split graph. Finally, we have found genus one of <span>(Cr_2({mathcal {R}}))</span>.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602938","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}

{"title":"Stratified bundles on the Hilbert Scheme of n points","authors":"Saurav Holme Choudhury","doi":"10.1007/s13226-024-00576-6","DOIUrl":"https://doi.org/10.1007/s13226-024-00576-6","url":null,"abstract":"<p>Let <i>k</i> be an algebraically closed field of characteristic <span>(p &gt; 3)</span> and <i>S</i> be a smooth projective surface over <i>k</i> with <i>k</i>-rational point <i>x</i>. For <span>(n ge 2)</span>, let <span>(S^{[n]})</span> denote the Hilbert scheme of <i>n</i> points on <i>S</i>. In this note, we compute the fundamental group scheme <span>(pi ^{text {alg}}(S^{[n]}, {tilde{nx}}))</span> defined by the Tannakian category of stratified bundles on <span>(S^{[n]})</span>.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140572902","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}

{"title":"On some super-congruences for the coefficients of analytic solutions of certain differential equations","authors":"Guo-Shuai Mao, Hao Zhang","doi":"10.1007/s13226-024-00582-8","DOIUrl":"https://doi.org/10.1007/s13226-024-00582-8","url":null,"abstract":"<p>In this paper, we prove some congruences involving the coefficients <span>({A_{n}}_{n=0,1,2,ldots })</span> of the analytic solution <span>(y_0(z)=sum _{n=0}^infty A_nz^n)</span> of certian differential eqution <span>({mathcal {D}}y=0)</span> normalized by the condition <span>(y_0(0)=A_0=1)</span>, where <span>({mathcal {D}})</span> is a 4th-order linear differential operator.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"2014 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140572991","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}

{"title":"Ground state solutions to critical Schrödinger–Possion system with steep potential well","authors":"Xiuming Mo, Mengyao Li, Anmin Mao","doi":"10.1007/s13226-024-00580-w","DOIUrl":"https://doi.org/10.1007/s13226-024-00580-w","url":null,"abstract":"<p>We study the following critical Schrödinger-Possion system with steep potential well </p><span>$$begin{aligned} left{ begin{aligned}&amp;-Delta u+(1+lambda V(x))u+phi u=f(u)+|u|^4u,&amp;text {in} {mathbb {R}}^{3},&amp;-Delta phi =u^2,&amp;text {in} {mathbb {R}}^{3}, end{aligned}right. end{aligned}$$</span><p>where <span>(lambda &gt;0)</span> is a positive parameter, <span>(V:{mathbb {R}}^{3}rightarrow {mathbb {R}})</span> is a continuous function and <i>f</i> is a continuous subcritical nonlinearity. Under some certain assumptions on <i>V</i> and <i>f</i>, for any <span>(lambda ge lambda _0&gt;0)</span>, we prove the existence of a ground state solution via variational methods. Moreover, the concentration behavior of the ground state solution is also described as <span>(lambda rightarrow infty )</span>. Our results extends that in Jiang[11](J. Differ. Equ. 2011) and Zhao[21](J. Differ. Equ. 2013) to the critical growth case.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573165","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}

{"title":"Total graph of a lattice","authors":"Pravin Gadge, Vinayak Joshi","doi":"10.1007/s13226-024-00551-1","DOIUrl":"https://doi.org/10.1007/s13226-024-00551-1","url":null,"abstract":"<p>In this paper, we prove that the study of the subgraph <span>(T(Z^*(L)))</span> of the total graph <i>T</i>(<i>L</i>) of a lattice <i>L</i> is essentially the study of the zero-divisor graph of a poset. Also, we prove that the graph <span>(T^c(Z^*(L)))</span> is weakly perfect whereas <span>(T(Z^*(L)))</span> is not weakly perfect. The graph <span>(T(Z^*(L)))</span> and its complement <span>(T^c(Z^*(L)))</span> are shown to be a perfect graph if and only if <i>L</i> has at most four atoms. In the concluding section, we establish that, in the context of a commutative reduced ring <i>R</i>, the total graph, the annihilating ideal graph, the complement of the co-annihilating ideal graph, and the complement of the comaximal ideal graph coincide.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313405","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}

{"title":"Compressed Cayley graph of groups","authors":"","doi":"10.1007/s13226-024-00567-7","DOIUrl":"https://doi.org/10.1007/s13226-024-00567-7","url":null,"abstract":"<h3>Abstract</h3> <p>Let <em>G</em> be a group and let <em>S</em> be a subset of <span> <span>(G setminus {e})</span> </span> with <span> <span>(S^{-1} subseteq S)</span> </span>, where <em>e</em> is the identity element of <em>G</em>. The Cayley graph <span> <span>(mathrm {{{,textrm{Cay},}}}(G,S))</span> </span> is a graph whose vertices are the elements of <em>G</em> and two distinct vertices <span> <span>(g,hin G)</span> </span> are adjacent if and only if <span> <span>(g^{-1} hin S)</span> </span>. Let <span> <span>(S subseteq Z(G))</span> </span>. Then the relation <span> <span>( sim )</span> </span> on <em>G</em>, given by <span> <span>(asim b)</span> </span> if and only if <span> <span>(Sa=Sb)</span> </span>, is an equivalence relation. Let <span> <span>(G_E)</span> </span> be the set of equivalence classes of <span> <span>(sim )</span> </span> on <em>G</em> and let [<em>a</em>] be the equivalence class of the element <em>a</em> in <em>G</em>. Then <span> <span>(G_E)</span> </span> is a group with operation <span> <span>([a].[b]=[ab])</span> </span>. Also, let <span> <span>(S_E)</span> </span> be the set of equivalence classes of the elements of <em>S</em>. The compressed Cayley graph of <em>G</em> is introduced as the Cayley graph <span> <span>({{,textrm{Cay},}}(G_E,S_E))</span> </span>, which is denoted by <span> <span>({{,textrm{Cay},}}_E(G,S))</span> </span>. In this paper, we investigate some relations between <span> <span>(mathrm {{{,textrm{Cay},}}}(G,S))</span> </span> and <span> <span>({{,textrm{Cay},}}_E(G,S))</span> </span>. Also, we prove that <span> <span>(mathrm {{{,textrm{Cay},}}}(G,S))</span> </span> is a <span> <span>({{,textrm{Cay},}}_E(G,S))</span> </span>-generalized join of certain empty graphs. Moreover, we describe the structure of the compressed Cayley graph of <span> <span>(mathbb {Z}_n)</span> </span> by introducing a subset <em>S</em> such that <span> <span>({{,textrm{Cay},}}_E(mathbb {Z}_n,S))</span> </span> and <span> <span>({{,textrm{Cay},}}(mathbb {Z}_n,S))</span> </span> are not isomorphic, and we describe the Laplacian spectrum of <span> <span>({{,textrm{Cay},}}(mathbb {Z}_n,S))</span> </span>.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301956","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}

{"title":"On L(2, 1)-labeling of zero-divisor graphs of finite commutative rings","authors":"Annayat Ali, Rameez Raja","doi":"10.1007/s13226-024-00574-8","DOIUrl":"https://doi.org/10.1007/s13226-024-00574-8","url":null,"abstract":"<p>For a simple graph <span>(mathcal {G}= (mathcal {V}, mathcal {E}))</span>, an <i>L</i>(2, 1)-labeling is an assignment of non-negative integer labels to vertices of <span>(mathcal {G})</span>. An <i>L</i>(2, 1)-labeling of <span>(mathcal {G})</span> must satisfy two conditions: adjacent vertices in <span>(mathcal {G})</span> should get labels which differ by at least two, and vertices at a distance of two from each other should get distinct labels. The <span>(lambda )</span>-number of <span>(mathcal {G})</span>, denoted by <span>(lambda (mathcal {G}))</span>, represents the smallest positive integer <span>(ell )</span> for which an <i>L</i>(2, 1)-labeling exists, the vertices of <span>(mathcal {G})</span> are provided labels from the set <span>({0, 1, dots , ell })</span>. Let <span>(Gamma (R))</span> be a zero-divisor graph of a finite commutative ring <i>R</i> with unity. In <span>(Gamma (R))</span>, vertices represent zero-divisors of <i>R</i>, and two vertices <i>x</i> and <i>y</i> are adjacent if and only if <span>(xy = 0)</span> in <i>R</i>. The methodology of the research involves a detailed investigation into the structural aspects of zero-divisor graphs associated with specific classes of local and mixed rings, such as <span>(mathbb {Z}_{p^n})</span>, <span>(mathbb {Z}_{p^n} times mathbb {Z}_{q^m})</span>, and <span>(mathbb {F}_{q}times mathbb {Z}_{p^n})</span>. This exploration leads us to compute the exact value of <i>L</i>(2, 1)-labeling number of these graphs.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201819","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}

{"title":"Sufficient conditions for component factors in a graph","authors":"Hongzhang Chen, Xiaoyun Lv, Jianxi Li","doi":"10.1007/s13226-024-00575-7","DOIUrl":"https://doi.org/10.1007/s13226-024-00575-7","url":null,"abstract":"<p>Let <i>G</i> be a graph and <span>(mathcal {H})</span> be a set of connected graphs. A spanning subgraph <i>H</i> of <i>G</i> is called an <span>(mathcal {H})</span>–factor if each component of <i>H</i> is isomorphic to a member of <span>(mathcal {H})</span>. In this paper, we first present a lower bound on the size (resp. the spectral radius) of <i>G</i> to guarantee that <i>G</i> has a <span>({P_2,, C_n: nge 3})</span>–factor (or a perfect <i>k</i>–matching for even <i>k</i>) and construct extremal graphs to show all this bounds are best possible. We then provide a lower bound on the signless laplacian spectral radius of <i>G</i> to ensure that <i>G</i> has a <span>({K_{1,j}:1le jle k})</span>–factor, where <span>(kge 2 )</span> is an integer. Moreover, we also provide some Laplacian eigenvalue (resp. toughness) conditions for the existence of <span>({P_2,, C_{n}:nge 3})</span>–factor, <span>(P_{ge 3})</span>–factor and <span>({K_{1,j}: 1le jle k})</span>–factor in <i>G</i>, respectively. Some of our results extend or improve the related existing results.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201821","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}

{"title":"Ramanujan-type congruences for partition k-tuples with 5-cores","authors":"Manjil P. Saikia, Abhishek Sarma, Pranjal Talukdar","doi":"10.1007/s13226-024-00566-8","DOIUrl":"https://doi.org/10.1007/s13226-024-00566-8","url":null,"abstract":"<p>We prove several Ramanujan-type congruences modulo powers of 5 for partition <i>k</i>-tuples with 5-cores, for <span>(k=2, 3, 4)</span>. We also prove some new infinite families of congruences modulo powers of primes for <i>k</i>-tuples with <i>p</i>-cores, where <i>p</i> is a prime.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201817","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}