Papers by Dr. Farid O. Farid
Journal of Information Science Theory and Practice, 2021
We introduce a new research assessment measure, called the research excellence index. The measure... more We introduce a new research assessment measure, called the research excellence index. The measure, which we denote by REindex, accurately assesses the research performance of a researcher. The methodology used in deriving the RE-index tackles many of the flaws of popular research performance indicators such as publication counts, citation counts, and the h and g indices. A dataset is introduced, which takes advantage of the wide coverage of Scopus and the Library of Congress, and, at the same time, deals with the Scopus database depth problem. For an academic publication x, a prestige-type and length scores are assigned, and if x is published in an academic periodical publication J, the stature of J is identified through a quartile score. The three scores are used to assign a value score to every academic publication, and cited academic publications are given citation scores that encompass both cases of including and excluding self-citations. The foregoing scores are used to derive another set of scores measuring the combined qualitative and quantitative aspects of the creative work, citations of creative work, informative work and citations of informative work of a researcher. The scores take into consideration co-authorship. From these scores, two versions of the RE-index for a researcher are derived, covering the cases of including and excluding self-citations. The new measure is calculated for two mathematicians.
Advances in Linear Algebra & Matrix Theory, 2017
We study the relations between several classes of matrices with variants of the diagonal dominanc... more We study the relations between several classes of matrices with variants of the diagonal dominance property, and identify those classes which form pairs of incomparable classes. For an incomparable pair () 1 2 , X X of classes of matrices with variants of the diagonal dominance property, we also study the problem of providing sufficient conditions for the matrices in i X to be in j X with { } { } , 1, 2 i j =. The article is a continuation of a series of articles on the topic and related topics by the author; see [1] [2] [3] [4].
Linear Algebra and its Applications, 2011
In this paper, we analyze the relation between some classes of matrices with variants of the diag... more In this paper, we analyze the relation between some classes of matrices with variants of the diagonal dominance property. We establish a sufficient condition for a generalized doubly diagonally dominant matrix to be invertible. Sufficient conditions for a matrix to be strictly generalized diagonally dominant are also presented. We provide a sufficient condition for the invertibility of a cyclically diagonally dominant matrix. These sufficient conditions do not assume the irreducibility of the matrix.
Proceedings Mathematical Sciences, 1999
In this paper we show that for a bounded linear operator A on a complex Hilbert space H, the poin... more In this paper we show that for a bounded linear operator A on a complex Hilbert space H, the points on the boundary of the numerical range of A with infinite curvature and unique tangent are in the essential spectrum of A, thus positively answering a conjecture raised by Hubner in [3].
Proceedings of the American Mathematical Society, 1991
In this paper, upper bounds for the difference between the eigenvalues and the eigenvectors of a ... more In this paper, upper bounds for the difference between the eigenvalues and the eigenvectors of a closed linear operator D D and those of D + F D + F , where F F is a bounded linear operator, are given in terms of the norm of F F . These results are applied to approximate the eigenvalues and the eigenvectors of a diagonally infinite matrix by those of its corresponding diagonal matrix.
Linear Algebra and its Applications, 1995
We develop some basic properties of finite diagonally dominant matrices. These properties are use... more We develop some basic properties of finite diagonally dominant matrices. These properties are used to establish a necessary and sufficient condition for a finite diagonally dominant matrix with nonzero diagonal entries to be singular. This condition relates the nonstrict diagonally dominant rows of the matrix to the difference between the principal arguments of the nonzero entries along each column in these rows. The infinite dimensional case is also studied, where a sufficient condition for the invertibility of the matrix operator in the sequence space CO defined by a diagonally dominant infinite matrix A with nonzero diagonal entries is introduced. This sufficient condition improves some of the earlier results. When the sequence space is lP, p E [ 1, oo), we establish a necessary and sufficient condition for the matrix operator in ZP defined by the matrix A to have a bounded inverse on lP.
Linear Algebra and its Applications, 1991
This paper is concerned with the problem of determining the location of eigenvalues for diagonall... more This paper is concerned with the problem of determining the location of eigenvalues for diagonally dominant, unbounded, infinite matrix operators acting on I,, for some 1 Q p <m. The results are established using the continuity in the generalized sense of a family of closed operators A(p), p E [O, 11. 1.
Linear Algebra and its Applications, 1992
It is shown that for a pair (A, B) of n X n matrices, where the eigenvalues of A lie on a straigh... more It is shown that for a pair (A, B) of n X n matrices, where the eigenvalues of A lie on a straight line L, and the eigenvalues of B lie on a ray with initial point on L,, the spectral distance between A and B is bounded from above by the spectral norm of their difference. The more general case where the eigenvalues of B lie on a straight line intersecting L, is also discussed. 27 is denoted by 4 /?a~. The scalar (dot) product of crp and ;;'r is denoted by :fi. 2~. SPECTRAL VARIATION FOR TWO MATRICES In the linear space C", the inner product of two points a = (QI 1,. and p = (pi,. .. , &) is defined as where P. is the complex conjugate of pj. We d enote a diagonal matrix whose jth diagonal entry is oj, j = 1,
Linear Algebra and its Applications, 1998
We construct two classes of 3 × 3 and 4 × 4 real symmetric matrices, and establish sufficient con... more We construct two classes of 3 × 3 and 4 × 4 real symmetric matrices, and establish sufficient conditions for the spectrum of a matrix A in each class to be disjoint from its kth order Gershgorin region. This provides a partial answer to a question raised by Newman and Thompson. The problem of providing sufficient conditions for the localization of the spectrum of a matrix in its kth order Gershgorin region is also discussed.
Canadian Journal of Mathematics, 1994
Recently A. Gutek, D. Hart, J. Jamison and M. Rajagopalan have obtained many significiant results... more Recently A. Gutek, D. Hart, J. Jamison and M. Rajagopalan have obtained many significiant results concerning shift operators on Banach spaces. Using a result of Holsztynski they classify isometric shift operators on C(X) for any compact Hausdorff space X into two (not necessarily disjoint) classes. If there exists an isometric shift operator T: C(X) → C(X) of type II, they show that X is necessarily separable. In case T is of type I, they exhibit a paticular infinite countable set of isolated points in X. Under the additional assumption that the linear functional Γ carrying f ∊ C(X) to Tf(p) ∊ is identically zero, they show that D is dense in X. They raise the question whether D will still be dense in X even when Γ ≠ 0. In this paper we give a negative answer to this question. In fact, given any integer l ≥ 1, we construct an example of an isometric shift operator T: C(X) —> C(X) of type I with X \ having exactly / elements, where is the closure of D in X.
Linear Algebra and its Applications, 2008
We study the question: For which (r, n) can a linear r-field on the (n − 1)-sphere in an n-dimens... more We study the question: For which (r, n) can a linear r-field on the (n − 1)-sphere in an n-dimensional real linear space be deformed through a continuous path of linear r-fields into an orthonormal r-field. We provide complete answers for the cases: (r, n) = (2, 4), (3, 4), and provide several partial results for the cases (r, n) = (2, 2m), where m is an even integer satisfying m 4. Characterizations of linear r-fields are pivotal in the investigation.
Linear and Multilinear Algebra, 2017
Lemma 2.6: In item (1), note that the condition JL B 1 = 0 is simpler than the corresponding cond... more Lemma 2.6: In item (1), note that the condition JL B 1 = 0 is simpler than the corresponding condition in Corollary 2.6 of the reference [34] by virtue of the assumption GL B 1 = 0 in the lemma. Also, there is a 4th condition R F JL B 1 = 0 in Corollary 2.6 of the reference [34], but this condition is satisfied by virtue of the condition JL B 1 = 0 in the lemma.
Linear and Multilinear Algebra, 2011
Linear Algebra and its Applications, 2013
Linear Algebra and its Applications, 2012
for adjointable operators between Hilbert C *-modules, and provide an expression for the general ... more for adjointable operators between Hilbert C *-modules, and provide an expression for the general Hermitian solution to the system. We present necessary and sufficient conditions for the existence of a unique Hermitian solution to the systems A
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Papers by Dr. Farid O. Farid