Procrustes problem for the inverse eigenvalue problem of normal (skew) JJ-Hamiltonian matrices and normal JJ-symplectic matrices

A square complex matrix $A$ is called (skew) $J$-Hamiltonian if $AJ$ is (skew) hermitian where $J$ is a real normal matrix such that $J^2=-I$, where $I$ is the identity matrix. In this paper, we solve the Procrustes problem to find normal (skew) $J$-Hamiltonian solutions for the inverse eigenvalue problem. In addition, a similar problem is investigated for normal $J$-symplectic matrices.Comment: 25 page

Electron microscopy study of CeOx–Pd/α-Al2O3 catalysts for methane dry reforming

We have investigated the interaction between Pd and Ce in a 0.47 wt % CeOx–Pd 1 wt %/ -Al2O3 catalyst that is used in the reforming reaction of CH4 with CO2. The freshly reduced catalyst was characterized by various electron microscopy techniques, such as elemental mapping, Z-contrast imaging, and electron energy-loss spectroscopy to understand the role of Ce on a microscopic scale. The high spatial resolution elemental mapping indicates that CeOx is located in close proximity of the palladium nanoparticles. High-resolution lattice images and energy-loss spectra obtained in the vicinity of the Pd particles show an anisotropic distribution of CeOx crystallites limited to the interface region between Pd and the substrate but not covering the surface of the Pd nanoparticles. Energy-loss near edge fine structure of Pd M edges reveals that the Pd nanoparticles are not oxidized.Fil: Moreno, M. S.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Wang, Feiya. National Institute for Nanotechnology; CanadáFil: Malac, M.. National Institute for Nanotechnology; CanadáFil: Kasama, T.. University of Cambridge; Reino UnidoFil: Gigola, Carlos Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Costilla, Ignacio Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Sánchez, M. D.. Universidad Nacional del Sur. Departamento de Física; Argentin

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

A weak group inverse for rectangular matrices

[EN] In this paper, we extend the notion of weak group inverse to rectangular matrices (called WweightedWGinverse) by using the weighted core EP inverse recently investigated. This new generalized inverse also generalizes the well-known weighted group inverse given by Cline and Greville. In addition, we give several representations of the W-weighted WG inverse, and derive some characterizations and properties.First author was partially supported by UNRC (Grant PPI 18/C472) and CONICET (Grant PIP 112-201501-00433CO). Third author was partially supported by Ministerio de Economia, Industria y Competitividad of Spain (Grants DGI MTM2013-43678-P and Red de Excelencia MTM2017-90682-REDT).Ferreyra, DE.; Orquera, V.; Thome, N. (2019). A weak group inverse for rectangular matrices. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3727-3740. https://doi.org/10.1007/s13398-019-00674-9S372737401134Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58, 681–697 (2010)Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Appl. Math. Comput. 236, 450–457 (2014)Bajodah, A.H.: Servo-constraint generalized inverse dynamics for robot manipulator control design. Int. J. Robot. Autom. 25, (2010). https://doi.org/10.2316/Journal.206.2016.1.206-3291Campbell, S.L., Meyer Jr., C.D.: Generalized Inverses of Linear transformations. SIAM, Philadelphia (2009)Cline, R.E., Greville, T.N.E.: A Drazin inverse for rectangular matrices. Linear Algebra Appl. 29, 53–62 (1980)Dajić, A., Koliha, J.J.: The weighted g-Drazin inverse for operators. J. Aust. Math. Soc. 2, 163–181 (2007)Doty, K.L., Melchiorri, C., Bonivento, C.: A theory of generalized inverses applied to robotics. Int. J. Rob. Res. 12, 1–19 (1993)Drazin, M.P.: Pseudo-inverses in associate rings and semirings. Am. Math. Mon. 65, 506–514 (1958)Ferreyra, D.E., Levis, F.E., Thome, N.: Revisiting of the core EP inverse and its extension to rectangular matrices. Quaest. Math. 41, 265–281 (2018)Ferreyra, D.E., Levis, F.E., Thome, N.: Maximal classes of matrices determining generalized inverses. Appl. Math. Comput. 333, 42–52 (2018)Gigola, S., Lebtahi, L., Thome, N.: The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem. J. Comput. Appl. Math. 291, 449–457 (2016)Hartwig, R.E.: The weighted $$*$$ ∗ -core-nilpotent decomposition. Linear Algebra Appl. 211, 101–111 (1994)Kirkland, S.J., Neumann, M.: Group inverses of M-matrices and their applications. Chapman and Hall/CRC, London (2013)Malik, S., Thome, N.: On a new generalized inverse for matrices of an arbitrary index. Appl. Math. Comput. 226, 575–580 (2014)Male $${{\check{\rm s}}}$$ s ˇ ević, B., Obradović, R., Banjac, B., Jovović, I., Makragić, M.: Application of polynomial texture mapping in process of digitalization of cultural heritage. arXiv:1312.6935 (2013). Accessed 14 June 2018Manjunatha Prasad, K., Mohana, K.S.: Core EP inverse. Linear Multilinear Algebra 62, 792–802 (2014)Mehdipour, M., Salemi, A.: On a new generalized inverse of matrices. Linear Multilinear Algebra 66, 1046–1053 (2018)Meng, L.S.: The DMP inverse for rectangular matrices. Filomat 31, 6015–6019 (2017)Mosić, D.: The CMP inverse for rectangular matrices. Aequaetiones Math. 92, 649–659 (2018)Penrose, R.: A generalized inverse for matrices. Proc. Cambrid. Philos. Soc. 51, 406–413 (1955)Soleimani, F., Stanimirović, P.S., Soleymani, F.: Some matrix iterations for computing generalized inverses and balancing chemical equations. Algorithms 8, 982–998 (2015)Xiao, G.Z., Shen, B.Z., Wu, C.K., Wong, C.S.: Some spectral techniques in coding theory. Discrete Math. 87, 181–186 (1991)Wang, H.: Core-EP decomposition and its applications. Linear Algebra Appl. 508, 289–300 (2016)Wang, H., Chen, J.: Weak group inverse. Open Math. 16, 1218–1232 (2018)Wei, Y.: A characterization for the $$W$$ W -weighted Drazin inverse and a Crammer rule for the $$W$$ W -weighted Drazin inverse solution. Appl. Math. Comput. 125, 303–310 (2002

Italian multicenter study on infection hazards during dental practice: Control of environmental microbial contamination in public dental surgeries

Background. The present study assessed microbial contamination in Italian dental surgeries. Methods. An evaluation of water, air and surface microbial contamination in 102 dental units was carried out in eight Italian cities. Results. The findings showed water microbial contamination in all the dental surgeries; the proportion of water samples with microbial levels above those recommended decreased during working. With regard to Legionella spp., the proportion of positive samples was 33.3%. During work activity, the index of microbial air contamination (IMA) increased. The level of microbial accumulation on examined surfaces did not change over time. Conclusion. These findings confirm that some Italian dental surgeries show high biocontamination, as in other European Countries, which highlights the risk of occupational exposure and the need to apply effective measures to reduce microbial loads

Statistical studies of sunspots

We perform two statistical studies of monthly mean sunspots one of them by considering the Daubechies 4-wavelet analysis and the other one by using the multiple linear regression method. We found that the Hurst’s parameters of the fractional Brownian motion is equal to = 0.98 manifesting the long memory of the data set. The proposed second method is used for solar cycles 16 and 23 and the results are remarkably good in comparison to the predictions made by solar dynamo and precursor methods. A weak correlation is found among the maximum amplitude of a cycle and the other ones related to the prior seven and twelve cycles. An early prediction of the maximum smoothed international sunspot number for cycles 24 and 25 are 128 and 161, respectively

Use of a tetragonal structure composed of yttrium-stabilized zirconium oxide in dentistry: a study of the ceramic-zirconia interface.

Objective The introduction of yttrium-stabilized zirconia (Y-TZP) has opened new frontiers in the fields of dental-material esthetics and biocompatibility. In a previous report, we analyzed the capacity of Y-TZP to withstand maximum loading (static resistance) and the repeated application of loads lesser than those that provoke fracture (fatigue resistance). The aim of this study was to evaluate the adhesion between Y-TZP and its ceramic support (shear resistance). Materials and methods To assess this characteristic, we developed a new testing protocol to be used with specially designed cylindrical samples with ceramic covering on a zirconia base. The research was carried out in two phases: the aim of the first was to identify the approach that produced the best adhesion; the second phase aimed at identifying the mechanical and/or physical mechanisms responsible for the zirconia/ceramic adhesion. Results In the first phase, we found that the surface finish of the zirconia was the sole factor that influenced final adhesion. In the second phase, our findings showed that this adhesion is essentially due to micromechanical and physical interactions, which were not dependent on the contact pressure between the two materials or on the geometric characteristics of the ceramic covering. Conclusions On the whole, the best final result was obtained when the zirconia was subjected to surface finishing with a diamond rotary instrument, but even in this case adhesion was inferior to that achieved with a gold-alloy base

L’ossido di zirconio a struttura tetragonale. Test di resistenza alla fatica

Negli ultimi anni, i pazienti che necessitano di protesi sono diventati sempre più giovani. Il fatto che le ceramiche essenzialmente costituite da metalli che si trovano al massimo stato ossidativi siano materiali chimicamente inerti rende meno tossica rispetto ad altri bio-materiali l’inevitabile piccola quantità di frammenti che si generano a causa dell’usura. I restauri dentali sono soggetti a forze occlusali intermittenti