Dejenie Alemayehu Lakew

Dejenie Alemayehu Lakew
Hampton University | HIU · Department of Mathematics

Ph.D.
Professor(Asst.) Mathematics Department, Hampton University

About

31
Publications
101,389
Reads
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29
Citations
Citations since 2016
10 Research Items
7 Citations
201620172018201920202021202201234
201620172018201920202021202201234
201620172018201920202021202201234
201620172018201920202021202201234
Introduction
Dejenie Alemayehu Lakew (PhD) is a mathematician with rich experience in teaching, research and publications. His dictum is that mathematics is both useful and beautiful, it is a study of abstract structures of logic, reason and imagination. He taught undergraduate & graduate courses in his long teaching career, author, co-author of articles in peer reviewed journals, and reviewer/editor. Areas of research: Analysis - hypercomplex analysis, functional analysis, operator theory, PDEs, ODEs.
Additional affiliations
August 2019 - present
Hampton University
Position
  • Professor (Assistant)
July 2017 - present
Stratford University
Position
  • Full Time Faculty
Description
  • Modern mathematics in algebra, college algebra, statistics, intermediate mathematics.
July 2017 - May 2019
Stratford University
Position
  • Full Time faculty
Description
  • On boundary value problems of first and second order of the Dirac operator
Education
August 1996 - July 2000
University of Arkansas
Field of study
  • Mathematics (Clifford analysis and PDEs)
September 1987 - June 1988
Addis Ababa University
Field of study
  • Mathematics
September 1980 - July 1984
Addis Ababa University
Field of study
  • Mathematics

Publications

Publications (31)
Article
Full-text available
In article [1], the initial value problems (IVPs) studied were the ones that have solutions that are algebraic. In this article, initial value problems of difference equations of first and second order whose solutions are transcendental sequences, not algebraic are considered. Again, the discrete Laplace transform method and its inverse transform a...
Article
Full-text available
In this short research article, we establish new results of initial value problems of discrete differential equations. The particular difference equations we consider at the moment are the ones with solutions that are generated as algebraic sequences, sequences of polynomials or of rational expressions. These results are obtained by a transform met...
Preprint
Full-text available
In this short article we show solutions of first, second and higherorder PDEs develop as sums of functions that are orthogonal, the parts that evolve from the trace values of solutions on the boundary and the ones that evolve from values of the differential equations in the interior of the domain.That is, for the first order Cauchy BVP : Du=f in /O...
Preprint
Full-text available
We investigate more initial value problems of difference equations of first and second order whose solutions are transcendental sequences using the method of the discrete Laplace transform and its inverse.
Presentation
Full-text available
Mathematics is ubiquitous, not peculiar to humans but in nature, it is the lingua franca and modes vivendi of nature and the paper describes this phenomena.
Data
The theme of this short article is to investigate an orthogonal decomposition of the Sobolev space W^{1, 2}(Ω) as W^{1, 2}(Ω) = A^{2,2}(Ω)⊕D²(W₀^{3, 2}(Ω)) and look at some of the properties of the inner product therein and the distance defined from the inner product. We also determine the dimension of the orthogonal difference space W^{1,2}(Ω)⊖(W₀...
Data
Full-text available
The main theme of this paper is to construct Clifford analytic-complete function systems in the general-ized Bergman spaces: BpCln:=kerD∩LpCln, and B(p;2)Cln:=kerD^2∩LpCln. These systems are used to approximate null solutions of elliptic partial differential equations of the Dirac /D and Laplace /Delta operators over an unbounded domains /Omega in...
Article
Full-text available
The theme of this short article is to investigate an orthogonal decomposition of the Sobolev space W^{1,2}(Ω) as W^{1,2}(Ω)=A^{2,2}(Ω)⊕D²(W₀^{3,2}(Ω)) and look at some properties of the inner product therein and the distance defined from the inner product. We also determine the dimension of the orthogonal difference space W^{1,2}(Ω)⊖(W₀^{1,2}(Ω))^{...
Article
Full-text available
We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions, particularly between those which are non zero constant multiples of each other and between functions from the kernel s...
Research
Full-text available
We obtain further results of the discrete Laplace transform of transcendental sequences and solve initial value problems with a mix of algebraic and transcendental solutions.
Article
Full-text available
In this short article we show an orthogonal decomposition of the Hilbert space as ℒ²(Ω)=A²(Ω)⊕(d/(dx))(W₀^{1,2}(Ω)), define orthogonal projections and see some of its properties. We display some decomposition of elementary functions as corollaries.
Article
Full-text available
In this article we define the spherical π operator over domains in the (n-1)- unit sphere S^{n-1} of Rⁿ and develop new and analogous results. We introduce a spherical Dirac operator Γ_{α}: = Γ_{ω}+α for α in ℂ and Γ_{ω} = ω ^ D_{ω}, the anti-symmetric Grassmanian product of ω and D_{ω} = ∑_{j=1}ⁿe_{j}∂_{w_{j}}. We use a Gugenbauer polynomial Ψ_{α}...
Article
Full-text available
In this article we develop few of the analogous theoretical results of Clifford analysis over Orlicz-Sobolev spaces and study mapping properties of the Dirac operator and the Teodorescu transform over these function spaces. We also get analogous decomposition results of Clifford valued Orlicz spaces and the generalized Orlicz-Sobolev spaces.
Article
Full-text available
In this short note, we study an ordinary differential operator of infinite order defined by: ∑_{n=0}^{∞}((Dⁿ)/(n!))=:e^{D} where D:=(d/(dx))
Article
Full-text available
We present norm estimates for solutions of first and second order elliptic BVPs of the Dirac operator considered over a bounded and smooth domain of the n-dimension Euclidean space. The solutions whose norms to be estimated are in some Sobolev spaces and the boundary conditions as traces of solutions and their derivatives are in some Slobodeckij sp...
Article
Full-text available
In this short article, we study different problems described as initial value problems of discrete differential equations and develop a transform method called the sigma transform, a discrete version of the continuous Laplace transform to generate solutions as rational functions of integers to these initial value problems. Particularly we look how...
Article
Full-text available
The main aim of this article is to study the hypercomplex π-operator over ${\mathbb{C}^{n+1}}$ via real, compact, n + 1-dimensional manifolds called domain manifolds. We introduce an intrinsic Dirac operator for such types of domain manifolds and define an intrinsic π-operator, study its mapping properties and introduce a Clifford–Beltrami equati...
Article
Full-text available
In this paper we study singular integral operators which are hyper or weak over Lipschitz or Holder spaces and over weghted Sobolev spaces defined on unbounded domains in the standard $n$-D space $R^n$ for $n>0$. The $\pi$-operator in this case is one of the hyper integral operators which has been studied extensively than other hyper singular integ...
Article
Full-text available
In this article, we define the spherical $\pi$-operator over domains in the $(n-1)$-D unit sphere $S^n$ of $R^n$ and develop new and analogous results on the operator it self and its mapping properties. We introduce the spherical Dirac operator $\Gamma_\alpha$ as an $\alpha$- shift of of $\Gamma_omega$, where $\Gamma_omega$ is the negative of the w...
Article
Full-text available
In this short note, we present few results on the use of the discrete Laplace transform in solving first and second order initial value problems of discrete differential equations.
Article
Full-text available
We introduce mollifiers in Clifford analysis setting and construct a sequence of $\C^{\infinity}$-functions that approximate a $\gamma$-regular function and a solution to a non homogeneous BVP of an in homogeneous Dirac like operator in certain Sobolev spaces over bounded domains whose boundary is not that wild. One can extend the smooth functions...
Article
Full-text available
In this paper, we construct $\gamma$-regular $Cl_n$-minimal function systems in the generalized Bergman space : $W^{2,k}_\gamma(\Omega,Cl_n) which are $\gamma$-regular, Clifford valued over $\Omega$ that are used to approximate null solutions of the in-homogeneous Dirac operator in the best way.
Article
Full-text available
For Ω a sufficiently smooth unbounded domain in ℝn we develop a decomposition result for the Sobolev space . We also use modified Cauchy-Green type kernels to construct Clifford analytic-complete function systems in the generalized Bergman space , where D l is the l-th iterate of the Dirac operator, l is a positive integer less than n and n/(n − l...
Article
Full-text available
The main theme of this paper is to construct Clifford analytic-complete function systems in the generalized Bergman spaces: BpCln(Ω):=kerD(Ω)∩LpCln(Ω), and Bp,2Cln(Ω):=ker▵(Ω)∩LpCln(Ω). These systems are used to approximate null solutions of elliptic partial differential equations of the Dirac and Laplace operators over an unbounded domain Ω in ℝn.
Conference Paper
By using a sophisticated maximum principle, three over determined problems for elliptic equations in two variables are discussed.
Conference Paper
By using a sophisticated maximum principle, three over determined problems for elliptic equations in two variables are discussed
Article
In this article we define the spherical ��,Sn 1 operator over domains in the (n 1)D unit sphere Sn 1 of Rn and develop new and analogous results. We introduce a spherical Dirac operator � := !+�, where � 2 C and ! = ! ^ D! , the anti-symmetric Grassmanian product of ! with D! = n X i=1 ei @ @!i. We use a Gegenbauer polynomial �n�(! �) as a Cauchy k...

Questions

Questions (37)
Question
Consider the two:
*. " A weak divergence CDC method for biharmonic equation on triangular and tetrahedral meshes " by ..... and
*. " Chlodosky type - Bernstein Stancu operator of Korvokin -type approximation theorems .. " by ...
Both are titles of articles written for mathematics journals. The first clearly indicates that it is a mathematics paper, while the second, barely with list of names of individuals in sequence.
We all know that mathematics of man is as old as mankind and that of nature is as old as nature itself. Mathematicians study and write, extrapolate and expand the kingdom of mathematical knowledge freely with no taking possession of any kind. But a recent phenomena is unique, in which a mathematics article is barely understood to be mathematics, instead chains of names of humans. The above two examples describe what I am discussing. Just imagine, all those results in mathematics since antiquity, written in the name of those who established them (which many of them will be unknown), then we are in real estate business, and the very meaning of mathematics and its universality, ubiquities-ness lose its flavor.
Let us keep mathematics - mathematical.

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Projects

Projects (4)
Project
Extend the location concept from material point to area, and scrutinize the ramifications. Connect to Tti and first order gravity concepts.
Project
To prove that solutions of first, second and higher order PDEs evolve as sums of functions that are orthogonal with respect to the inner product of a Sobolev space W^{k,2}(Ω) for k= 1, 2, 3,... The components are the parts that evolve from the trace values of solutions on the boundary ∂Ω of the domain and the ones that evolve from values of the differential equations in the interior of the domain Ω. I use the symbol ⊎ to denote an orthogonal sum of functions that are from orthogonal sum ⊕ of function subspaces.
Project
The them of this project is to open a forum of acknowledgement to our former academic advisers who initiate, acclimate and guide us in to the frontiers of our fields of research and be reasons to our achievements. I share an article about my doctoral research adviser Prof. John Ryan of the University of Arkansas, his academic works, his doctoral students and his scholarly achievements in the field of Clifford Analysis. The writer of the article is Prof. Wolfgang Sprößig, Department of Mathematics and Informatics, Institute of Applied Analysis, TU Bergakademie Freiberg, Germany, a lead mathematician in Clifford analysis and applications. Acknowledge your former academic advisers by sharing their names and academic achievements here in this forum, their human dimensions as well if need be.