The difference and sum of projectors

AbstractThe aim of this paper is to present new results on the invertibility of the sum of projectors, and new relations between the nonsingularity of the difference and the sum of projectors. We also give simple proofs, without referring to rank theory, of some results on the nonsingularity of the difference of projectors obtained by Groß and Trenkler [SIAM J. Matrix Anal. Appl. 21 (1999) 390]

Uticaj vremena taloženja na strukturu završne prevlake nikla na aluminijumu

The microstructure of the chemical coating of zinc on aluminum, as well as electrodeposited nickel coating on chemically deposited zinc were investigated with change of one parameter only-deposition time. Based on the structural characteristics of top coating of nickel, the optimum time for deposition of nickel coating was determine at the same conditions. Structural characteristics of metallic coatings were investigated by scanning tunneling microscopy (STM).Ispitivana je mikrostruktura hemijske prevlake cinka na aluminijumu, kao i prevlake nikla koja je elektrohemijski taložena na hemijsku prevlaku cinka uz promenu samo jednog parametara-vremena taloženja. Na osnovu strukturnih karakteristika završne prevlake nikla, ustanovljeno je optimalno vreme taloženja prevlaka nikla pri datim uslovima. Strukturne karakteristike metalnih prevlaka ispitivane su skenirajućom tunelirajućom mikroskopijom (STM)

Uticaj pripreme površine aluminijuma na površinsku hrapavost

Aluminum samples were electrochemically polished in one of three solutions for electrochemical polishing. On those samples the surface roughness was measured. The effect of the anode treatment on surface roughness was also investigated. The zinc coating was deposited on chemically and electrochemically treated aluminum samples, and afterwards the surface roughness of these samples was measured. Based on the results it was determined that from all of the solutions for electrochemical polishing, the most efficient solution is the solution number II. Aluminum samples treated with this solution are the least rough. It was determined that chemically deposited zinc coating on previously chemically and electrochemically treated samples leads to significant lowering of surface roughness. The anodic treatment of aluminum surface significantly lowers surface roughness also.Uzorci aluminijuma su podvrgavani elektrohemijskom glačanju u jednom od tri rastvora za elektrohemijsko glačanje. Na tako pripremljenim uzorcima merena je površinska hrapavost. Takođe je ispitivan i uticaj anadne obrade na površinsku hrapavost aluminijuma. Na hemijski i elektrohemijski pripremljene uzorke aluminijuma, taložena je prevlaka cinka hemijskim putem, a potom merena površinska hrapavost ovakvih uzoraka. Na osnovu dobijenih rezultata ustanovljeno je da je od ispitivanih rastvora za elektrohemijsko glačanje najefikasniji rastvor II. Uzorci aluminijuma tretirani u ovom rastvoru imaju najmanju hrapavost. Ustanovljeno je da usled taloženja hemijske prevlake cinka na prethodno hemijski i elektrohemijski tretirane uzorke dolazi do znatnog smanjenja površinske hrapavosti. Anodna obrada uzoraka takođe značajno smanjuje površinsku hrapavost

Equalities of ideals associated with two projections in rings with involution

In this article we study various right ideals associated with two projections (self-adjoint idempotents) in a ring with involution. Results of O.M. Baksalary, G. Trenkler, R. Piziak, P.L. Odell and R. Hahn about orthogonal projectors (complex matrices which are Hermitian and idempotent) are considered in the setting of rings with involution. New proofs based on algebraic arguments, rather than finite-dimensional and rank theory, are given.The authors thank the anonymous reviewer for his\her useful suggestions, which helped to improve the original version of this article. The second author is supported by Grant No. 174007 of the Ministry of Science, Technology and Development, Republic of Serbia.Benítez López, J.; Cvetkovic-Ilic, D. (2013). Equalities of ideals associated with two projections in rings with involution. Linear and Multilinear Algebra. 61(10):1419-1435. doi:10.1080/03081087.2012.743026S141914356110Baksalary, O. M., & Trenkler, G. (2009). Column space equalities for orthogonal projectors. Applied Mathematics and Computation, 212(2), 519-529. doi:10.1016/j.amc.2009.02.042Benítez, J. (2008). Moore–Penrose inverses and commuting elements of C∗-algebras. Journal of Mathematical Analysis and Applications, 345(2), 766-770. doi:10.1016/j.jmaa.2008.04.062Green, J. A. (1951). On the Structure of Semigroups. The Annals of Mathematics, 54(1), 163. doi:10.2307/1969317Harte, R. (1992). On generalized inverses in C*-algebras. Studia Mathematica, 103(1), 71-77. doi:10.4064/sm-103-1-71-77Harte, R. (1993). Generalized inverses in C*-algebras II. Studia Mathematica, 106(2), 129-138. doi:10.4064/sm-106-2-129-138Koliha, J. J. (2000). Elements of C*-algebras commuting with their Moore-Penrose inverse. Studia Mathematica, 139(1), 81-90. doi:10.4064/sm-139-1-81-90Koliha, J. J., Cvetković-Ilić, D., & Deng, C. (2012). Generalized Drazin invertibility of combinations of idempotents. Linear Algebra and its Applications, 437(9), 2317-2324. doi:10.1016/j.laa.2012.06.005Koliha, J. J., & Rakočević, V. (2003). Invertibility of the Difference of Idempotents. Linear and Multilinear Algebra, 51(1), 97-110. doi:10.1080/030810802100023499Mary, X. (2011). On generalized inverses and Green’s relations. Linear Algebra and its Applications, 434(8), 1836-1844. doi:10.1016/j.laa.2010.11.045Von Neumann, J. (1936). On Regular Rings. Proceedings of the National Academy of Sciences, 22(12), 707-713. doi:10.1073/pnas.22.12.707Patrı́cio, P., & Puystjens, R. (2004). Drazin–Moore–Penrose invertibility in rings. Linear Algebra and its Applications, 389, 159-173. doi:10.1016/j.laa.2004.04.006Piziak, R., Odell, P. L., & Hahn, R. (1999). Constructing projections on sums and intersections. Computers & Mathematics with Applications, 37(1), 67-74. doi:10.1016/s0898-1221(98)00242-

Uticaj pripreme površine aluminijuma na površinsku hrapavost

Aluminum samples were electrochemically polished in one of three solutions for electrochemical polishing. On those samples the surface roughness was measured. The effect of the anode treatment on surface roughness was also investigated. The zinc coating was deposited on chemically and electrochemically treated aluminum samples, and afterwards the surface roughness of these samples was measured. Based on the results it was determined that from all of the solutions for electrochemical polishing, the most efficient solution is the solution number II. Aluminum samples treated with this solution are the least rough. It was determined that chemically deposited zinc coating on previously chemically and electrochemically treated samples leads to significant lowering of surface roughness. The anodic treatment of aluminum surface significantly lowers surface roughness also.Uzorci aluminijuma su podvrgavani elektrohemijskom glačanju u jednom od tri rastvora za elektrohemijsko glačanje. Na tako pripremljenim uzorcima merena je površinska hrapavost. Takođe je ispitivan i uticaj anadne obrade na površinsku hrapavost aluminijuma. Na hemijski i elektrohemijski pripremljene uzorke aluminijuma, taložena je prevlaka cinka hemijskim putem, a potom merena površinska hrapavost ovakvih uzoraka. Na osnovu dobijenih rezultata ustanovljeno je da je od ispitivanih rastvora za elektrohemijsko glačanje najefikasniji rastvor II. Uzorci aluminijuma tretirani u ovom rastvoru imaju najmanju hrapavost. Ustanovljeno je da usled taloženja hemijske prevlake cinka na prethodno hemijski i elektrohemijski tretirane uzorke dolazi do znatnog smanjenja površinske hrapavosti. Anodna obrada uzoraka takođe značajno smanjuje površinsku hrapavost

Uticaj vremena taloženja na strukturu završne prevlake nikla na aluminijumu

The microstructure of the chemical coating of zinc on aluminum, as well as electrodeposited nickel coating on chemically deposited zinc were investigated with change of one parameter only-deposition time. Based on the structural characteristics of top coating of nickel, the optimum time for deposition of nickel coating was determine at the same conditions. Structural characteristics of metallic coatings were investigated by scanning tunneling microscopy (STM).Ispitivana je mikrostruktura hemijske prevlake cinka na aluminijumu, kao i prevlake nikla koja je elektrohemijski taložena na hemijsku prevlaku cinka uz promenu samo jednog parametara-vremena taloženja. Na osnovu strukturnih karakteristika završne prevlake nikla, ustanovljeno je optimalno vreme taloženja prevlaka nikla pri datim uslovima. Strukturne karakteristike metalnih prevlaka ispitivane su skenirajućom tunelirajućom mikroskopijom (STM)

Potential of TiO2 with various au nanoparticles for catalyzing mesotrione removal from wastewaters under sunlight

Nowadays, great focus is given to the contamination of surface and groundwater because of the extensive usage of pesticides in agriculture. The improvements of commercial catalyst TiO2 activity using different Au nanoparticles were investigated for mesotrione photocatalytic degradation under simulated sunlight. The selected system was 2.43 × 10−3% Au–S–CH2–CH2–OH/TiO2 (0.5 g/L) that was studied by transmission electron microscopy and ultraviolet-visible (UV-Vis) spectroscopy. It was found that TiO2 particles size was ~20 nm and ~50 nm, respectively. The Au nanoparticles were below 10 nm and were well distributed within the framework of TiO2 . For 2.43 × 10−3% Au–S–CH2–CH2–OH/TiO2 (0.5 g/L), band gap energy was 2.45 eV. In comparison to the pure TiO2, addition of Au nanoparticles generally enhanced photocatalytic removal of mesotrione. By examining the degree of mineralization, it was found that 2.43 × 10−3% Au–S–CH2–CH2–OH/TiO2 (0.5 g/L) system was the most efficient for the removal of the mesotrione and intermediates. The effect of tert-butanol, NaF and ethylenediaminetetraacetic acid disodium salt on the transformation rate suggested that the relative contribution of various reactive species changed in following order: h+ >•OHads >•OHbulk. Finally, several intermediates that were formed during the photocatalytic treatment of mesotrione were identified. © 2020 by the authors. Licensee MDPI, Basel, Switzerland

Ethnomusicology Matters:Influencing Social and Political Realities

This book gathers international voices from the field of ethnomusicology discussing the socio-political relevance of the discipline. The articles draw from contemporary discourses that take into account the role of music and dance in shaping social and political realities. An important field connected to political relevance is heritage, either in connection with the UNESCO or with archives. Ontologies of indigenous groups and their relevance in knowledge production is discussed in ethnomusicology nowadays as well as the possibilities of decolonising the discipline. Two articles from ethno-choreology explore dance from the gender perspective and in the post-socialist political structures. Different approaches from applied ethnomusicology deal with social justice, participatory dialogical practice, and the socio-political relevance of performance. Forced migration is seen as comprehensive topic for future ethnomusicology. The contents of the book mirror influential discourses of ethnomusicology today that will definitely shape the future development of the discipline

Origin of photocatalytic activity enhancement in Pd/Pt-deposited anatase N-TiO2-experimental insights and DFT study of the (001) surface

In pursuit of the ideal photocatalyst, cheap and stable semiconductor TiO2 is considered to be a good choice if one is able to reduce its band gap and decrease the recombination rate of charge carriers. The approach that offers such improvements for energy conversion applications is the modification of TiO2 with nitrogen and noble metals. However, the origin of these improvements and possibilities for further design of single-atom catalysts are not always straightforward. To shed light on the atomic-scale picture, we modeled the nitrogen-doped (001) anatase TiO2 surface as a support for palladium and platinum single-atom deposition. The thermodynamics of various synthesis routes for Pd/Pt deposition and nitrogen doping is considered based on density functional theory (DFT)-calculated energies, highlighting the effect of nitrogen doping on metal dimer formation and metal-support interaction. XPS analysis of the valence band of the modified TiO2 nanocrystals, and the calculated charge transfer and electronic structure of single-atom catalysts supported on the (001) anatase TiO2 surface provide an insight into modifications occurring in the valence zone of TiO2 due to nitrogen doping and Pd/Pt deposition at the surface. DFT results also show that substitutional nitrogen doping significantly increases metal-support interaction, while interstitial nitrogen doping promotes only Pt-support interaction. © the Owner Societies

Sequential targeted exome sequencing of 1001 patients affected by unexplained limb-girdle weakness

Several hundred genetic muscle diseases have been described, all of which are rare. Their clinical and genetic heterogeneity means that a genetic diagnosis is challenging. We established an international consortium, MYO-SEQ, to aid the work-ups of muscle disease patients and to better understand disease etiology. Exome sequencing was applied to 1001 undiagnosed patients recruited from more than 40 neuromuscular disease referral centers; standardized phenotypic information was collected for each patient. Exomes were examined for variants in 429 genes associated with muscle conditions. We identified suspected pathogenic variants in 52% of patients across 87 genes. We detected 401 novel variants, 116 of which were recurrent. Variants in CAPN3, DYSF, ANO5, DMD, RYR1, TTN, COL6A2, and SGCA collectively accounted for over half of the solved cases; while variants in newer disease genes, such as BVES and POGLUT1, were also found. The remaining well-characterized unsolved patients (48%) need further investigation. Using our unique infrastructure, we developed a pathway to expedite muscle disease diagnoses. Our data suggest that exome sequencing should be used for pathogenic variant detection in patients with suspected genetic muscle diseases, focusing first on the most common disease genes described here, and subsequently in rarer and newly characterized disease genes