In this paper we discuss different properties of DMP-inverse of a square matrix introduced by Malik and Thome On a new generalized inverse for matrices of an arbitrary index. Applied Mathematics and ...Computation. 2014;226: 575-580. We characterize DMP-inverse of a square matrix as an outer inverse with prescribed range and null space, as a
-inverse and as a Drazin inverse. Also we present several different characterizations based on its range and null space as well some algebraic ones.
Deep learning techniques are required for the analysis of synoptic (multi-band and multi-epoch) light curves in massive data of quasars, as expected from the Vera C. Rubin Observatory Legacy Survey ...of Space and Time (LSST). In this follow-up study, we introduce an upgraded version of a conditional neural process (CNP) embedded in a multi-step approach for the analysis of large data of quasars in the LSST Active Galactic Nuclei Scientific Collaboration data challenge database. We present a case study of a stratified set of u-band light curves for 283 quasars with very low variability ∼0.03. In this sample, the CNP average mean square error is found to be ∼5% (∼0.5 mag). Interestingly, besides similar levels of variability, there are indications that individual light curves show flare-like features. According to the preliminary structure–function analysis, these occurrences may be associated with microlensing events with larger time scales of 5–10 years.
The diagnostics of the physical properties of the broad line region (BLR) of active galactic nuclei (AGN) is still an interesting question. Here we present an overview of our recent investigations of ...the physics of the BLR using the broad emission lines.
We present the results of the long-term optical monitoring campaign of active galactic nuclei (AGN) coordinated by the Special Astrophysical Observatory of the Russian Academy of Science. This ...campaign has produced a remarkable set of optical spectra, since we have monitored for several decades different types of broad-line (type 1) AGN, from a Seyfert 1, double-peaked line, radio loud and radio quiet AGN, to a supermassive binary black hole candidate. Our analysis of the properties of the broad line region (BLR) of these objects is based on the variability of the broad emission lines. We hereby give a comparative review of the variability properties of the broad emission lines and the BLR of seven different type 1 AGNs, emphasizing some important results, such as the variability rate, the BLR geometry, and the presence of the intrinsic Baldwin effect. We are discussing the difference and similarity in the continuum and emission line variability, focusing on what is the impact of our results to the supermassive black hole mass determination from the BLR properties.
The main purpose of this paper is to investigate inequalities on symmetric sums of diagonalizable and positive definite tensors. In particular, we generalize the well-known Hlawka and Popoviciu ...inequalities to the case of diagonalizable and positive definite tensors. As corollaries, we extend Hlawka and Popoviciu inequalities for the combinatorial determinant, permanent and immanant of tensors, and generalized tensor functions.
An extensive matrix class over a complex Banach algebra is considered from the point of view of its quasinilpontency, nilpotency, as well as Drazin and generalized Drazin invertibilities. The ...matrices belonging to the class are obtained by alterations of a
2
×
2
anti-triangular matrix with one undetermined entry, and the general expression characterizing the class involves powers of the anti-triangular matrix. The main result of the paper determines those values of the powers for which the quasinilpontency of a matrix from the class is equivalent to the quasinilpontency of its undetermined entry. Similar result was established with respect to the nilpotency as well. The paper provides also related observations concerned with relationships between the Drazin and generalized Drazin invertibilities of the matrix and the entry. Though rooted in the work of Drazin published in the mid-twentieth century, the investigations carried out in the paper were inspired by and build upon recent results concerned with the Drazin invertibility.
Background/Aim. Coronary artery anomalies are an uncommon but important cause of chest pain, and in some cases of hemodynamically significant abnormalities, sudden cardiac death. The aim of the ...research was to establish the prevalence of the coronary arteries anomalies in our population. Methods. The study group included 1,562 patients (810 men, 752 women, average age 64.3 ? 12.0 years; range 32?80 years) who were scheduled for 64-slice computed tomography (MSCT), which enables detailed visualization of coronary arteries and heart anatomy. All examinations were made due to suspicion (atypical chest pain, angina equivalent symptoms or multiple risk factors for cardiovascular disease) or assumption of progression of coronary artery disease. Results. From January 2010 till December 2014 a total number of 1,562 patients were sent for evaluation of coronary arteries. The coronary anomalies were found in 45 (2.88%) patients. The most frequent coronary anomaly seen in our population group was absence of left main trunk with the separate origin of the left anterior descending artery (LAD) and left circumflex artery (LCx) originating from a left coronary sinus (LCS). This was found in 12 patients (an incidence of 0.77% or 26.7% of all coronary anomalies). Anomalous location of coronary ostium outside normal aortic sinuses in our study was present as right coronary artery (RCA) that arises from left anterior sinus in 5 (0.32%) patients and left coronary artery from non-coronary sinus in two (0.13%) patients. Conclusion. Knowledge of anomalies of the coronary arteries and their recognition on the multislice computed tomography is of great importance for the further planning of a possible therapeutic treatment. Coronary anomalies that are considered insignificant will require no further therapeutic treatment. But the detection of malignant coronary anomalies will certainly save many lives.
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