On a matrix group constructed from an {R,s+1,k}-potent matrix

Let R∈C^(n×n) be a {k}-involutory matrix (that is, R^k=I_n) for some integer k≥2, and let s be a nonnegative integer. A matrix A∈C^(n×n) is called an {R,s+1,k}-potent matrix if A satisfies R A = A^(s+1) R. In this paper, a matrix group corresponding to a fixed {R,s+1,k}-potent matrix is explicitly constructed, and properties of this group are derived and investigated. This group is then reconciled with the classical matrix group G_A that is associated with a generalized group invertible matrix A. Let R∈Cn×n be a {k}-involutory matrix (that is, Rk=In) for some integer k≥2, and let s be a nonnegative integer. A matrix A∈Cn×n is called an {R,s+1,k}-potent matrix if A satisfies RA=As+1R. In this paper, a matrix group corresponding to a fixed {R,s+1,k}-potent matrix is explicitly constructed, and properties of this group are derived and investigated. This group is then reconciled with the classical matrix group GA that is associated with a generalized group invertible matrix A

The first Chevalley-Eilenberg cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122-133], we defined the transverse bundle V^k to a decreasing family of k foliations F_i on a manifold M. We have shown that there exists a (1,1) tensor J of V^k such that Jk≠0, J^(k+1) = 0 and we defined by L_J(V^k) the Lie Algebra of vector fields X on V^k such that, for each vector field Y on V^k, [X,JY]=J[X,Y]. In this note, we study the first Chevalley-Eilenberg Cohomology Group, i.e. the quotient space of derivations of L_J(V^k) by the subspace of inner derivations, denoted by H^1(L_J(V^k))

Theoretical Framework of the filmed Interview in Communication Studies

In the Social Sciences today, there are a variety of ways to approach the various areas of investigation and a wide range of observational methods. Depending on academic background and research interests, researchers explore and emphasize certain approaches and categorizations at the expense of others in the implementation of their audiovisual investigations. These observations lead us to first question the definition of image in its connection to the object of research and its status and, secondly, to identify the diversity of current practices and uses. Indeed, the status of an image changes according to the media used and the contexts of reception. The circulation of images promotes exchange and connection between the various groups of actors. If we awkwardly accompany images, we risk unwittingly betraying their original meaning. Furthermore, there is the possibility of conflicts or unintended distortions linked to the activities of projection and identification. Our goal will be to propose a methodological framework and establish an initial model for all researchers in Communication Studies using the audiovisual method. Finally, the researcher accepts not only to properly conduct his research, but also to present an audiovisual project taking into account from the start advantages, constraints, issues of influence and scientific impact

A Note on k-generalized projections

In this note, we investigate characterizations for k-generalized projections (i.e., A^k =A*) on Hilbert spaces. The obtained results generalize those for generalized projections on Hilbert spaces in [Hong-Ke Du, Yuan Li, The spectral characterization of generalized projections, Linear Algebra Appl. 400 (2005) 313-318] and those for matrices in [J. Benítez, N. Thome, Characterizations and linear combinations of k-generalized projectors, Linear Algebra Appl. 410 (2005) 150-159]

The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem

The inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal {k+1}-potent matrix are considered. First, we study the existence of the solutions of the associated inverse eigenvalue problem and present an explicit form for them. Then, when such a solution exists, an expression for the solution to the corresponding optimal approximation problem is obtained

Further results on generalized centro-invertible matrices

This paper deals with generalized centro-invertible matrices introduced by the authors in Lebtahi et al. (Appl. Math. Lett. 38, 106-109, 2014). As a first result, we state the coordinability between the classes of involutory matrices, generalized centro-invertible matrices, and {K}-centrosymmetric matrices. Then, some characterizations of generalized centro-invertible matrices are obtained. A spectral study of generalized centro-invertible matrices is given. In addition, we prove that the sign of a generalized centro-invertible matrix is {K}-centrosymmetric and that the class of generalized centro-invertible matrices is closed under the matrix sign function. Finally, some algorithms have been developed for the construction of generalized centro-invertible matrices

Properties of a matrix group associated to a {K,s+1}-potent matrix

In a previous paper, the authors introduced and characterized a new kind of matrices called {K, s+1}-potent. In this paper, an associated group to a {K, s+1}-potent matrix is explicitly constructed and its properties are studied. Moreover, it is shown that the group is a semidirect product of Z_2 acting on Z_(s+1)^2−1. For some values of s, more specifications on the group are derived. In addition, some illustrative examples are given

Left bundle branch block and coronary artery disease: Accuracy of dipyridamole thallium-201 single-photon emission computed tomography in patients with exercise anteroseptal perfusion defects

Background: Reduced septal or anteroseptal uptake of thallium-201 during exercise is frequently observed in patients with left bundle branch block (LBBB) even in the absence of left anterior descending (LAD) coronary artery disease. The purpose of this study was to evaluate prospectively the accuracy of dipyridamole201TI single-photon emission computed tomography (SPECT) in detecting LAD coronary artery disease in patients with LBBB and septal or anteroseptal perfusion defects on exercise201TI SPECT. Methods and Results: Twelve consecutive patients (10 men and two women) with complete LBBB and septal or anteroseptal perfusion defects on exercise201TI SPECT underwent dipyridamole201TI SPECT. The delay between dipyridamole and exercise was 2 to 30 days. Coronary angiography was performed during this period in all patients. Six (50%) of 12 patients with exercise perfusion defects showed normal perfusion after dipyridamole; all had normal coronary angiograms. The remaining six patients also had positive results of dipyridamole studies, two with moderate and four with severe septal or anteroseptal perfusion defects. Coronary angiography showed significant (>50%) LAD coronary artery stenosis in three patients; three patients with severe septal or anteroseptal perfusion defects after dipyridamole had normal coronary angiograms. Neither the evaluation of apical involvement nor the presence of dilated ventricles, decreased left ventricular ejection fraction, or wall motion abnormalities could help to identify (or explain) false-positive results. Conclusion: This study confirms that dipyridamole is more accurate than exercise in excluding LAD coronary artery disease. However, there are still false-positive results and the severity of the septal or anteroseptal perfusion defect does not add additional information to identify LAD coronary artery disease. Coronary angiography is thus necessary for positive dipyridamole study results to identify coronary artery disease as a major prognostic factor in patients with LBB

Inverse eigenvalue problem for normal J-hamiltonian matrices

A complex square matrix A is called J-hamiltonian if AJ is hermitian where J is a normal real matrix such that J^2=−I_n. In this paper we solve the problem of finding J-hamiltonian normal solutions for the inverse eigenvalue problem

Algorithms for solving the inverse problem associated with KAK =A^(s+1)

In previous papers, the authors introduced and characterized a class of matrices called {K,s+1}-potent. Also, they established a method to construct these matrices. The purpose of this paper is to solve the associated inverse problem. Several algorithms are developed in order to find all involutory matrices K satisfying K A^(s+1) K = A for a given matrix A∈C^(n×n) and a given natural number s. The cases s=0 and s≥ are separately studied since they produce different situations. In addition, some examples are presented showing the numerical performance of the methods