http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
ALGEBRA BUNDLES WHOSE m-DIMENSIONAL COHOMOLOGY MODULES ARE ZERO
R. Rajendra,B.S. Kiranagi 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.3
Let§ be an algebra bundle and Ƞ be a §-bimodule bundle over a compact Hausdorff space X. Here we prove that the m-dimensional cohomology module Hm(§, Ƞ)is isomorphic to Hm−1(§, ˜ C(§, Ƞ)), where ˜ C(§, Ƞ) is a § bimodule bundle. If we denote Km(F),m = 1, 2, 3, ..., the class of all algebra bundles whose m-dimensional cohomology modules are all zero then it is shown that K1(F) is strictly contained in K2(F) and K2(F) is strictly contained in K3(F). Further we show that if an algebra bundle § is nilpotent then it does not belong to K3(F).
R. RAJENDRA,P. SIVA KOTA REDDY,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.2
The stress of a vertex in a graph had been introduced by Shimbel in 1953 as the number of geodesics (shortest paths) passing through it. A topological index of a chemical structure (molecular graph) is a number that correlates given chemical structure with a chemical reactivity or physical property. In this paper, we introduce two new topological indices for graphs called rst and second stress indices by means of the notion of stress of a vertex. Further, we establish some inequalities, prove some fundamental results and compute these stress indices for some standard graphs. These two indices are expected to give new applications in chemistry and social science problems as the notion of stress of a vertex depends on the geodesics passing through that vertex and may lead to new notions related to graphs.
R. RAJENDRA,P. SIVA KOTA REDDY,C. N. HARSHAVARDHANA 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.1
A topological index of a chemical structure (graph) is a number that correlates the chemical structure with chemical reactivity or physical properties. There are several topological indices have been defined on graphs using degrees of vertices/edges, for instance first and second Zagreb indices. In this paper, we introduce a new topological index for graphs called Tosha index using tension on edges. Further, we establish some inequalities and compute Tosha index for some standard graphs.
Set-prime graph of a finite group
R. RAJENDRA,P.Siva Kota Reddy,K. V. Madhusudhan 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.3
Let S be a non-empty set of positive integers. We dene the set-prime graph GS( ) of a given nite group of order n with respect to S, as a graph with vertex set V (GS( )) = and any two vertices a and b are adjacent in GS( ) if and only if (o(a); o(b)) 2 S. In this paper, we observe that order prime and general order prime graphs are special cases of set-prime graphs and we investigate some properties of set-prime graphs of nite groups.
R. RAJENDRA,P. S. Guruprasad,K. BHARGAVA,P. SIVA KOTA REDDY 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.2
In this paper, we present a new representation of partitions of positive integers using labeled trees. Labeled trees representing a partition of an integer n is called a partition-tree of n. We discuss some results involving partition-trees, energy of an integer with respect to partition-trees, and gracefulness of the default labeling of partition trees.
SOME RESULTS ON ORDER PRIME GRAPHS AND GENERAL ORDER PRIME GRAPHS
R. RAJENDRA,P. SIVA KOTA REDDY 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.2
The order prime graph OP(Γ) of a nite group Γ is a graph with the vertex set V (OP(Γ)) = Γ and any two distinct vertices a and b are adjacent in OP(Γ) if and only if (o(a), o(b)) = 1. The general order prime graph GOP(Γ) of Γ is a graph with vertex set V (GOP(Γ)) = Γ and any two distinct vertices a and b are adjacent in GOP(Γ) if and only if (o(a), o(b)) = 1 or p, where p is a prime and p < n. In this paper, we discuss some results involving eigenvalues and energy of order prime graphs and general order prime graphs of nite groups. Further, we dene the order prime graphs of a nite group Γ with respect to subsets(subgroups) of Γ and investigate some properties.
Squares stress sum index for graphs
R. Rajendra,P. SIVA KOTA REDDY,C. N. HARSHAVARDHANA,Khaled A. A. Alloush 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.4
Squares stress sum index for graphs
On general order prime graph of a finite group
R. RAJENDRA,P. S. K. Reddy 장전수학회 2014 Proceedings of the Jangjeon mathematical society Vol.17 No.4
On general order prime graph of a finite group
On pull back Lie algebra bundles
R. RAJENDRA,B.S. Kiranagi,RANJITHA KUMAR 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.4
In this paper, given a Lie algebra bundle ε over a topological space X and a continuous map f : Y → X, we construct a pull back Lie algebra bundle f^*(ξ ) over Y and we show that a pull back Lie algebra bundle of a semisimple Lie algebra bundle is also semisimple. We prove that given a Lie algebra bundle ε over X and homotopic continuous maps f_0, f_1 : Y → X, the induced pull back bundles f^*_0 (ξ ) and f^*_1 (ξ ) are isomorphic if Y is compact Hausdorff. Also, we construct an example to show that this result is not true for weak Lie algebra bundles.
A note on prime graph of a finite ring
R. RAJENDRA,P.Siva Kota Reddy,H. Mangala Gowramma,P. S. Hemavathi 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.3
Sathyanaryana et al. (2010) introduced the concept of prime graph of an associative ring R and studied some properties in their paper. We found that a correction to be made in the statement of the rst theorem of their paper. In this paper, we investigate some properties of prime graphs of nite rings and give a corrected version of the said result. We establish a formula for nding the number of edges in the prime graph of the ring of residue classes modulo n by using the gcd-sum function. Further, we discuss some results regarding eigenvalues and energy of prime graphs of nite rings.