Bio

Prof. NZIMBI BERNARD MUTUKU

Personal Information

Areas Of Specialization

Pure Mathematics - Mathematical Analysis (Operator Theory)

Research Interests

Application of Operator Theory in Telecommunications (signal processing) , image processing and systems control

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Publications


Submitted

MUTUKU, DRNZIMBIBERNARD, P PROFPOKHARIYALGANESH, M PROFKHALAGAIJAIRUS.  Submitted.  Linear operators for which T* and T^2 commute. Global Journal of Pure and Applied Mathematics(GJPAM),2012, to appear. : Global Journal of Pure and Applied Mathematics(GJPAM), 2012, to appear Abstract

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In Press

Nzimbi, BM, Kiratu BN, Sitati IN, Kipkemoi ST.  In Press.  Remarks on the Murray-von Neumann equivalence of projections. International Journal of Pure and Applied Mathematics(IJPMAS)-accepted June 6, 2016.
Nzimbi, BM, Luketero SW, Sitati IN, Musundi SW, Mwenda E.  In Press.  On almost-similarity and metric equivalence of operators. Pioneer Journal of Mathematics and Mathematical Sciences(PJMMS)-accepted June 14, 2016.
MUTUKU, DRNZIMBIBERNARD, KIBET DRMOINDISTEPHEN, P PROFPOKHARIYALGANESH.  In Press.  W_4-Curvature tensor on a A-Einstein Sasakian manifold. Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS). : Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS) Abstract

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2020

SO Pambo, Moindi SK, Nzimbi BM.  2020.  A study of eta-Ricci soliton on W_5-semi symmetric LP sasakian manifolfds. International Journal of Statistics and Applied Mathematics 2. 5(5):25-29. AbstractWebsite

In this paper, we study ƞ-Ricci solitons on Lorentzian para-Sasakian manifold satisfying
R(ξ,X)•W_5(Y,Z)U=0 and W_5(ξ,X)•R(Y,Z)U=0 conditions.
We prove that on a Lorentzian para-Sasakian manifold (M,ξ,ƞ,g), the Ricci curvature tensor satisfying
any one of the given conditions, the existence of ƞ-Ricci soliton then implies that (M,g) is Einstein
manifold. We also conclude that in these cases, there is no Ricci soliton on M, with the potential vector
field ξ (the killing vector)

B.M. Nzimbi, Luketero SW.  2020.  Weyl and Browder theorems for operators with or without SVEP at zero. International Journal of Statistics and Applied Mathematics. 5(3):11-24. AbstractWebsite

The study of operators having some special spectral properties like Weyl's theorem, Browder's theorem
and the SVEP has been of important interest for some time now. The SVEP is very useful in the study of
the local spectral theory. In this paper, we explore the single-valued extension property (SVEP) for some
operators on Hilbert spaces. We characterize operators with or without SVEP at zero and those where
Weyl's and Browder's theorems hold. It is shown that if a Fredholm operator has no SVEP at zero, then
zero is an accumulation point of the spectrum of the operator. It is also shown that quasi similar Fredholm
operators have equal Weyl spectrum.

Bernard M. Nzimbi, Luketero SW.  2020.  On unitary quasi-equivalence of operators. International Journal of Mathematics and Its Applications. 8(1):207-215. AbstractWebsite

In this paper we investigate unitary quasi-equivalence of operators in Hilbert spaces. We characterize operators that are
unitarily quasi-equivalent. We also investigate equivalence relations closely related to unitary quasi-equivalence. We give
and prove conditions under which unitary quasi-equivalence coincides with other operator equivalence relations

2019

Njagi, L, Nzimbi BM, Moindi SK.  2019.  On Pseudo-inverses and Duality of Frames in Hilbert Spaces. International Journal of Mathematics and its Applications (IJMAA). 7(2):75-88. AbstractWebsite

In this paper, we show how to find dual frames using the notion of singular value decomposition and pseudo-inverses of an operator in a Hilbert space. We will also show how properties of dual frames are linked to the spectral properties of the dual frame operator and the Grammian

Loyford Njagi, Bernard Nzimbi, Moindi S.  2019.  A note on analysis and synthesis operators of a frame and reconstruction of a signal from frame coefficients. International Journal of Statistics and Applied Mathematics. 4(5):93-99. AbstractWebsite

We discuss basic properties of Analysis and synthesis operators a frame. The structure of matrix
representation of the Synthesis operator is also analysed. This matrix is what most frame constructions in
fact focus on. The frame operator which is just the joining together of the analysis and synthesis
operators is fundamental for the reconstruction of signals from frame coefficients

Njagi, L, Nzimbi BM, Moindi SK.  2019.  A note on isomorphy and unitary isomorphy of Hilbert space frames. International Journal of Mathematics Trends and Technology(IJMTT). 65(1):15-30.

2018

Njagi, L, Nzimbi BM, Moindi SK.  2018.  On finite dimensional Hilbert space frames, dual and normalized frames and pseudo-inverse of the frame operator. Advance Research in Mathematics and Statistics. 5(11):1-14.
Njagi, L, Nzimbi BM, Moindi SK.  2018.  On analysis and synthesis operators and characterization of the synthesis matrix of a frame in terms of the frame operator. Advance Research in Mathematics and Statistics. 5(12):1-10.
Nzimbi, BM.  2018.  A note on some equivalences of operators and topology of invariant subspaces. Mathematics and Computer Science . 3(5):102-112.

2015

Njagi, L, Nzimbi BM, Mwenda E.  2015.  Subdegrees and suborbital graphs of symmetric groups Sn (n=3,4,5) acting on unordered pairs. Global Educational Research Journal. 3(7):333-345.
Sitati, IN, Musundi SW, Nzimbi BM, Kikete DW.  2015.  A note on quasi-similarity of operators in Hilbert spaces. International Journal of Mathematical Archives. 6(7):49-54.

2014

Mwenda, E, Musundi SW, Nzimbi BM, Marani VN, Njagi L.  2014.  Distribution of spectrum in a direct sum decomposition of operators into normal and completely non-normal operators. International Journal of Modern Mathematical Sciences. 11(3):118-124.

2013

Moindi, SK, Pokhariyal GP, Nzimbi BM.  2013.  W_2-Recurrent LP-Sasakian manifold. Universal Journal of Mathematics and Mathematical Sciences(UJMMS). 3(2):119-128.
Moindi, SK, Pokhariyal GP, Nzimbi BM.  2013.  w_4-curvature tensor on A-Einstein Sasakian manifold. Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS).
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2013.  A note on A-self-adjoint and A-skew-adjoint operators and their extensions. Pioneer Journal of Mathematics and Mathematical Sciences(PJMMS). 7(1):1-36.
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2013.  A note on A-self-adjoint and A-skew-adjoint operators and their extensions. Pioneer Journal of Mathematics and Mathematical Sciences(PJMMS). 7(1):1-36.
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2013.  A note on metric equivalence of some operators. Far East Journal of Mathematical Sciences(FJMS). 75(2):301-318.
Musundi, SW, Sitati IN, Nzimbi BM, Murwayi AL.  2013.  On almost similarity operator equivalence relation. IJRRAS. 15(3):293-299.

2012

Mille, JK, Nzimbi BM, Moindi SK.  2012.  On characterization of class R_1 of non-normal operators in a Hilbert space. Pioneer Journal of Mathematics and Mathematical Sciences(PJMMS). 5(1):137-142.
Sitati, IN, Musundi SW, Nzimbi BM, Kirimi J.  2012.  On similarity and quasisimilarity equivalence relations. Bull. Soc. Math. Serv. and Standards. 1(2):151-171.
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2012.  A note on a-self -adjoint and a-skew -adjoint operators and their extensions. AbstractA note on a-self -adjoint and a-skew -adjoint operators and their extensions

In this paper we introduce the notions of an A-self-adjoint, an A-skewadjoint linear operator, where A is a self-adjoint and invertible operator and related classes of operators, which generalize some known classes of operators. We investigate some properties of these operators and show that these operators share some properties with some known classes of operators. We prove some results on some equivalence of these operators and investigate conditions under which these operators are self-adjoint, unitary, skew-adjoint, normal, hyponormal, quasinormal or binormal. We also attempt to locate the spectra of such operators

2011

Nzimbi, BM.  2011.  Linear Algebra II-ODL Programme. , Nairobi: University of Nairobi

2010

Moindi, SK, Pokhariyal GP, Nzimbi BM.  2010.  Study of W_4-curvature tensor on Sasakian manifold. Kenya Journal of Sciences. 14(1):1-8.
MUTUKU, DRNZIMBIBERNARD, KIBET DRMOINDISTEPHEN, P PROFPOKHARIYALGANESH.  2010.  Stephen Moindi Kibet, G.P. Pokhariyal and B.M. Nzimbi, Study of W_4 Curvature tensor on Sasakian Manifold, Kenya J. Sciences(KJS), Vol. 14, No.1 2010, 1-8. Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS). : Kenya Journal of Sciences(KJS), Abstract
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2008

Nzimbi, BM, Pokhariyal GP, Khalagai JM.  2008.  A note on similarity, almost-similarity and equivalence of operators. Far East Journal of Mathematical Sciences(FJMS). 28(2):305-317.
MUTUKU, DRNZIMBIBERNARD, P PROFPOKHARIYALGANESH, M PROFKHALAGAIJAIRUS.  2008.  A note on Similarity, Almost-Similarity and Equivalence of Operators. Far East Mathematics Journal. 28(2(February 2008)):305-317.: Kenya Journal of Sciences(KJS), AbstractWebsite

The almost-similar and similar relations between operators on finite-dimensional Hilbert spaces are investigated. It is shown that almost-similar operators share some properties with some other classes of operators. Various results on almost-similarity and similarity are proved. An attempt is made to classify those operators where almost-similarity implies similarity. We investigate some properties of corresponding parts of operators which enjoy these equivalence relations.

1999

MUTUKU, DRNZIMBIBERNARD.  1999.  On Decomposition of Operators in Hilbert Spaces. Far East Mathematics Journal, Vol 28, Issue 2(February 2008), 305-317.. , Nairobi: University of Nairobi Abstract

The almost-similar and similar relations between operators on finite-dimensional Hilbert spaces are investigated. It is shown that almost-similar operators share some properties with some other classes of operators. Various results on almost-similarity and similarity are proved. An attempt is made to classify those operators where almost-similarity implies similarity. We investigate some properties of corresponding parts of operators which enjoy these equivalence relations.

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