Papers by Manjunatha Prasad Karantha
'Rao-regular matrix'is an important notion in the study of regular matrices over a commut... more 'Rao-regular matrix'is an important notion in the study of regular matrices over a commutative ring. The purpose of this article is to make an exhaustive review of properties of Rao-regular matrices with some new observations and showcase some very important applications of the same notion. Also, we present a some results on the characterization of Rao- regulatr (X,Y) inverse.
Journal of Algebra and Its Applications, 2021
In this paper, the notion of “strongly unit regular element”, for which every reflexive generaliz... more In this paper, the notion of “strongly unit regular element”, for which every reflexive generalized inverse is associated with an inverse complement, is introduced. Noting that every strongly unit regular element is unit regular, some characterizations of unit regular elements are obtained in terms of inverse complements and with the help of minus partial order. Unit generalized inverses of given unit regular element are characterized as sum of reflexive generalized inverses and the generators of its annihilators. Surprisingly, it has been observed that the class of strongly regular elements and unit regular elements are the same. Also, several classes of generalized inverses are characterized in terms of inverse complements.
In this article, an iterative method for estimating the core-EP inverse is proposed and the conve... more In this article, an iterative method for estimating the core-EP inverse is proposed and the convergence properties of the same has been discussed. Also, numerical examples with different values of parameters and the criteria for stopping the iteration are presented.
Stress is an important centrality measure of graphs applicableto the study of social and biologic... more Stress is an important centrality measure of graphs applicableto the study of social and biological networks. We study the stress of paths, cycles, fans andwheels. We determine the stress of a cut vertex of a graph G, when G has at most two cutvertices. We have also identified the graphs with minimum stress and maximum stress in thefamily of all trees of order $n$ and in the family of all complete bipartite graphs of order n.
Journal of Algebra and Its Applications
In this paper, the concept of “Inverse Complemented Matrix Method”, introduced by Eagambaram (201... more In this paper, the concept of “Inverse Complemented Matrix Method”, introduced by Eagambaram (2018), has been reestablished with the help of minus partial order and several new properties of complementary matrices and the inverse of complemented matrix are discovered. Class of generalized inverses and outer inverses of given matrix are characterized by identifying appropriate inverse complement. Further, in continuation, we provide a condition equivalent to the regularity condition for a matrix to have unique shorted matrix in terms of inverse complemented matrix. Also, an expression for shorted matrix in terms of inverse complemented matrix is given.
In this article, an iterative method for estimating the core-EP inverse is proposed and the conve... more In this article, an iterative method for estimating the core-EP inverse is proposed and the convergence properties of the same are discussed. Also, numerical examples with different values of parameters and the criteria for stopping the iteration are presented.
The Journal of Analysis
In the present paper, we introduce several generalizations of core-nilpotent decomposition of a s... more In the present paper, we introduce several generalizations of core-nilpotent decomposition of a square matrix and study their properties. Well known decompositions such as core-EP decomposition and EP-nilpotent decompositions are discussed as special cases.
Journal of Radioanalytical and Nuclear Chemistry
The \( ^{232} {\text{Th}}\left( {{\text{n}},2{\text{n}}} \right)^{231} {\text{Th}} \) reaction cr... more The \( ^{232} {\text{Th}}\left( {{\text{n}},2{\text{n}}} \right)^{231} {\text{Th}} \) reaction cross sections were measured at the neutron energies of 10.49 ± 0.29, 14.46 ± 0.26, 18.36 ± 0.24 MeV and 15.03 ± 0.003 MeV. For the first three energies, \( ^{7} {\text{Li}}\left( {{\text{p}},{\text{n}}} \right) \) reaction as a neutron source at the BARC-TIFR Pelletron accelerator facility was used. For the latter energy, \( ^{3} {\text{H}}\left( {{\text{d}},{\text{n}}} \right) \) neutron source using the PURNIMA neutron generator facility was used. The experiments were carried out using the activation method and off-line \( \upgamma \)-ray spectrometric technique. Covariance information of various attributes of cross section was propagated to obtain the covariance matrix for the reaction cross sections. The experimental resuts obtained with reference to the two different neutron sources are then compared with the values of evaluated nuclear data files such as ENDF/B-VIII.0, JENDL 4.0, JEFF-3.2, ROSFOND-2010, TENDL-2017 and the theoretical values from TALYS-1.9 code.
Electronic Journal of Linear Algebra
For the class of matrices over a field, the notion of `rank of a matrix' as defined by `the d... more For the class of matrices over a field, the notion of `rank of a matrix' as defined by `the dimension of subspace generated by columns of that matrix' is folklore and cannot be generalized to the class of matrices over an arbitrary commutative ring. The `determinantal rank' defined by the size of largest submatrix having nonzero determinant, which is same as the column rank of given matrix when the commutative ring under consideration is a field, was considered to be the best alternative for the `rank' in the class of matrices over a commutative ring. Even this determinantal rank and the McCoy rank are not so efficient in describing several characteristics of matrices like in the case of discussing solvability of linear system. In the present article, the `rank--function' associated with the matrix as defined in [{\it Solvability of linear equations and rank--function}, K. Manjunatha Prasad, \url{http://dx.doi.org/10.1080/00927879708825854}] is discussed and the ...
Bulletin of Kerala Mathematics Association, Special Issue, 2018
In this article, an iterative method for estimating the core-EP inverse is proposed and the conve... more In this article, an iterative method for estimating the core-EP inverse is proposed and the convergence properties of the same has been discussed. Also, numerical examples with different values of parameters and the criteria for stopping the iteration are presented.
Journal of Radioanalytical and Nuclear Chemistry
The cross sections for the 93Nb(n,2n)92mNb, 93Nb(n,α)90mY and the 92Mo(n,p)92mNb reactions have b... more The cross sections for the 93Nb(n,2n)92mNb, 93Nb(n,α)90mY and the 92Mo(n,p)92mNb reactions have been measured with respect to the 197Au(n,2n)196Au monitor reaction at the incident neutron energy of 14.78 ± 0.19 MeV by employing methods of activation and off-line γ-ray spectrometry. The covariance analysis was carried out by taking into consideration of partial uncertainties in different attributes and correlation among the attributes. The present data have been compared with the literature data available in EXFOR, evaluated data of different libraries and theoretical values based on TALYS-1.8 code.
Radiochimica Acta
The 59Co(n, 2n)58Co reaction cross sections relative to the cross sections of the 115In(n, n′)115... more The 59Co(n, 2n)58Co reaction cross sections relative to the cross sections of the 115In(n, n′)115mIn reaction have been measured at the effective neutron energies of 11.98 and 15.75 MeV by using activation and off-line γ-ray spectrometric technique. Neutron beam used in the present experiment was generated from the 7Li(p, n)7Be reaction with the proton energies of 14 and 18 MeV at the 14UD BARC-TIFR Pelletron facility, Mumbai. We also present the covariance information by taking into account the sources of error and the correlations between the attributes influencing the measurements. The 59Co(n, 2n)58Co reaction cross sections from the present work are then compared with the values from different evaluated nuclear data libraries. The micro-correlation technique suggested by Smith was modified to generate the covariance matrix for the measurements of reaction cross sections as the efficiencies of detector for the sample and monitor are correlated.
Journal of Radioanalytical and Nuclear Chemistry
The 59Co(n, γ)60Co reaction cross sections have been measured relative to the cross sections of t... more The 59Co(n, γ)60Co reaction cross sections have been measured relative to the cross sections of the 115In $$\left( {n,\gamma } \right)$$n,γ116mIn monitor reaction at the effective neutron energies of 11.98 and 15.75 MeV by using activation and off-line γ-ray spectrometric technique. We generate and present the covariance information by taking into account various attributes influencing the uncertainties and also the correlations between them. The 59Co(n, γ)60Co reaction cross sections from the present work have been compared with evaluated nuclear data libraries and theoretical values based on computer code TALYS-1.8.
Linear Algebra and its Applications
Abstract We consider matrices over a commutative ring and characterize the class of outer inverse... more Abstract We consider matrices over a commutative ring and characterize the class of outer inverses for which Jacobi type identities can be extended. We obtain a necessary and sufficient condition for the existence of Rao-regular Drazin inverse in terms of sum of principal minors of A k for some k . Also, we obtain determinantal formula for the Rao-regular Drazin inverse. Conjectures are formulated which give expressions for outer inverse and the conjectures are proved in some special cases.
International Journal of E-Business Research
Development of Micro, Small and Medium Enterprise (MSME) sector in India has been a priority issu... more Development of Micro, Small and Medium Enterprise (MSME) sector in India has been a priority issue. They constitute 95 percent of total industrial units, provide huge employment opportunities and contribute significantly to GDP. Prior research indicates that B2B e-marketplace offers ample opportunities for MSMEs to access global markets and enhances their competitiveness. There is limited empirical research on B2B e-marketplace use by Indian MSMEs, as also on the factors that influence their adoption. As adoption of B2B e-marketplace is in its growth stage in India, there is a need to understand the factors that influence the adoption. Based on the theoretical frameworks of Diffusion of Innovation, Institutional theory and Transaction cost theory, a conceptual framework that identifies organization, environment, product and e-marketplace related factors influencing adoption is developed. Using the data from 122 MSMEs, the significant factors that influence adoption of B2B e-marketpl...
Linear Algebra and its Applications, 2016
We characterize the elements with outer inverse in a semigroup S, and provide explicit expression... more We characterize the elements with outer inverse in a semigroup S, and provide explicit expressions for the class of outer inverses b of an element a such that bS⊆yS and Sb⊆Sx, where x, y are any arbitrary elements of S. We apply this result to characterize pairs of outer inverses of given elements from an associative ring R, satisfying absorption laws extended for the outer inverses. We extend the result on right–left symmetry of aR⊕bR=(a+b)R (Jain–Prasad, 1998) to the general case of an associative ring. We conjecture that ‘given an outer inverse x of a regular element a in a semigroup S, there exists a reflexive generalized inverse y of a such that x≤−y’ and prove the conjecture when S is an associative ring.
Linear Algebra and its Applications, 2000
A closed form representation is given for the matrix S that sweeps out a single column. This incl... more A closed form representation is given for the matrix S that sweeps out a single column. This includes the integer as well as the unitary and regular cases. The closed form is built up from the 2 × 2 case. The product rule for adjoints is used to show that the dual of this procedure is precisely the completion procedure, which completes a single column to a matrix B such that SB = BS = diagonal. This construction underlines the fact that the completion and elimination processes are complementary. By permuting rows suitably, the matrices may be assumed to be in lower Hessenberg form.
In literature, we have several partial orders on subclasses of rectan-gular matrices of same size... more In literature, we have several partial orders on subclasses of rectan-gular matrices of same size and some which are dominated by known "Minus Partial Order". Star partial order ([3]) on rectangular matrices of size, Sharp order ([6]) on class of square matrices of same size and of index one, and the Core partial order ([2]) are such partial orders dominated by minus partial order to name a few. It is well known that the m × n matrices B and A − B decomposes the given matrix A under minus partial order (i.e., B, A − B ≤ − A) is equivalent to say that the column spaces of B and A − B decomposes the column space of the matrix A (i.e., C(B) ⊕ C(A − B) = C(A)). The same is true for the row spaces. In fact, there is one to one correspondence between matrix decompositions with reference to minus partial order, column space decompositions and row space decompositions. The characteri-zation of the partial orders such as star partial order and sharp order involve both column space ...
We give necessary and sufficient conditions for the existence of Khatri inverse, pointing out an ... more We give necessary and sufficient conditions for the existence of Khatri inverse, pointing out an error in a condition given by Khatri. We also establish a generalized Cramer's rule to find minimum N-norm M-least-squares solution.
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Papers by Manjunatha Prasad Karantha