Compact operators, the essential spectrum and the essential numerical range

Some properties of bounded operators on Hilbert space concerned with matrix representations in orthonormal bases are presented. In particular, the classes of operators with columns or diagonals converging to 0 are described

A note on compact operators and operator matrices

In this note two properties of compact operators acting on a separable Hilbert space are discussed. In the first part a characterization of compact operators is obtained for bounded operators represented as tri-block diagonal matrices with finite blocks. It is also proved that one can obtain such a tri-block diagonal matrix representation for each bounded operator starting from any orthonormal basis of the underlying Hilbert space by an arbitrary small Hilbert-Schmidt perturbation. The second part is devoted to the so-called Hummel\u27s property of compact operators: each compact operator has a uniformly small orthonormal basis for the underlying Hilbert space. The class of all bounded operators satisfying Hummel\u27s condition is determined

On a class of module maps of Hilbert C*-modules

The paper describes some basic properties of a class of module maps of Hilbert C*-modules. In Section 1 ideal submodules are considered and the canonical Hilbert C*-module structure on the quotient of a Hilbert C*-module over an ideal submodule is described. Given a Hilbert C*-module V, an ideal submodule $V_{inss}$, and the quotient $V/V_{inss}$, canonical morphisms of the corresponding C*-algebras of adjointable operators are discussed. In the second part of the paper a class of module maps of Hilbert C*-modules is introduced.Given Hilbert C*-modules V and W and a morphism $varphi : ass rightarrow bss$ of the underlying cez-algebras, a map $Phi : V rightarrow W$ belongs to the class under consideration if it preserves inner products modulo $varphi$: $langle Phi(x), Phi(y) rangle = varphi(langle x,y rangle)$ for all $x,y in V$. It is shown that each morphism Φ of this kind is necessarily a contraction such that the kernel of Φ is an ideal submodule of V. A related class of morphisms of the corresponding linking algebras is also discussed

Boundedness properties of fermionic operators

The fermionic second quantization operator $d\Gamma(B)$ is shown to be bounded by a power $N^{s/2}$ of the number operator $N$ given that the operator $B$ belongs to the $r$-th von Neumann-Schatten class, $s=2(r-1)/r$. Conversely, number operator estimates for $d\Gamma(B)$ imply von Neumann-Schatten conditions on $B$. Quadratic creation and annihilation operators are treated as well.Comment: 15 page

Selection of the optimal hard facing (HF) technology of damaged forging dies based on cooling time t8/5

In exploitation, the forging dies are exposed to heating up to very high temperatures, variable loads: compressive, impact and shear. In this paper, the reparatory hard facing of the damaged forging dies is considered. The objective was to establish the optimal reparatory technology based on cooling time t8/5 . The verification of the adopted technology was done by investigation of the hard faced layers microstructure and measurements of hardness within the welded layers’ characteristic zones. Cooling time was determined theoretically, numerically and experimentally

Selection of the optimal hard facing (HF) technology of damaged forging dies based on cooling time t8/5

In exploitation, the forging dies are exposed to heating up to very high temperatures, variable loads: compressive, impact and shear. In this paper, the reparatory hard facing of the damaged forging dies is considered. The objective was to establish the optimal reparatory technology based on cooling time t8/5. The verification of the adopted technology was done by investigation of the hard faced layers microstructure and measurements of hardness within the welded layers’ characteristic zones. Cooling time was determined theoretically, numerically and experimentally

High-density ceramics obtained by andesite basalt sintering

In the present study, andesite basalt originated from the deposit site “Donje Jarinje”, Serbia, was examined as a potential raw material for high-density ceramics production. The production of high-density ceramics included dry milling, homogenization, cold isostatic pressing and sintering in the air. To determine the optimal processing parameters the sintering was conducted at 1040, 1050, 1060, 1070 and 1080°C, and afterwards the sintering duration was varied from 30 to 240min at the optimal sintering temperature of 1060°C. Characterization of the starting and sintered materials included the estimation of particle size distribution, density, hardness and fracture toughness complemented with X-ray diffraction, optical light microscopy, scanning electron microscopy and energy dispersive spectroscopy analysis. Phase transformations did not occur during processing in the investigated temperature range from 1040 to 1080°C. The obtained research results showed that 99.5% of relative density and the highest hardness and fracture toughness values of 6.7GPa and 2.2MPa•m1/2, respectively, were achieved for the andesite basalt sintered at 1060°C for 60min in the air. The results of the present study confirmed that the sintered andesite basalt can be used as a high-density ceramic material for various industrial applications

Supplementary data for the article: Čolić, S. D.; Bakić, I. V.; Dabić Zagorac, D. Č.; Natić, M. M.; Smailagić, A. T.; Pergal, M. V.; Pešić, M. B.; Milinčić, D. D.; Rabrenović, B. B.; Fotirić Akšić, M. M. Chemical Fingerprint and Kernel Quality Assessment in Different Grafting Combinations of Almond Under Stress Condition. Scientia Horticulturae 2021, 275, 109705. https://doi.org/10.1016/j.scienta.2020.109705

Supplementary material for: [https://doi.org/10.1016/j.scienta.2020.109705]Related to published version: [https://cherry.chem.bg.ac.rs/handle/123456789/4081

The suitability of apricot for dried fruit production by the combined technology

The apricot is considered as one of the most delicious temperate fruit, a highly appreciated stone fruit and a valuable raw material for processing. The Republic of Serbia is one of the leading apricot producers in Southeast Europe, but the assortment is limited by a small number of cultivars harvested, mostly in the ripening season of “Magyar kajszi”. In order to introduce the most suitable cultivars in the production, having high yield and high quality for consumption and various forms of processing, introduced and domestic cultivars have been intensively studied. In Serbia, apricots are mostly marketed fresh and processed for jams and spirits, but demand for high-quality dried fruits is increasing. To preserve the nutritional and sensory quality of fresh apricots, choosing the best drying technique is significant, and the most preferred technique is the reduction of moisture through convective drying. The aim of the paper was to compare the potential of the apricot cultivars “Magyar kajszi”, “Novosadska rodna”, “NS-4” and “NS-6” for dried fruit production by two-phase technology – combined osmotic and convective drying, as well as the profitability of apricot drying on small family farms. Cultivars “NS-4” and “Novosadska rodna” were found to be suitable for combined drying technology. The highest score in the sensory evaluation of the dried apricots was given to “NS-4”, and then to “Novosadska rodna”. The results indicate that the combined osmotic and convective drying of apricot rather than selling fresh fruits can be a profitable and important added value tool for small family farms

Andesite Basalt as a Natural Raw Material for Obtaining Glass-Ceramics

The industrial requirements in the 21st century are environmentally friendly and light construction materials with good physical-mechanical properties manufactured from cheap natural raw materials available in large quantities. One of these materials is basalt. Basalt is a natural igneous rock of volcanic origin, with a significant amount in Serbia. Basalt belongs to the group of non-hazardous and eco-friendly materials. Andesite basalt aggregate from the "Donje Jarinje" site, Serbia, was used as the starting natural raw material for obtaining the glass-ceramic material. The aggregate is from 2 to 5 mm in size. The aggregate was milled in the tungsten-carbide vibrating cup mill for 30 min to obtain a fine powder for synthesis. The homogenization of andesite basalt powder and binder was carried out in the mortar and pestle for 10 min. The paraplast was used as a binder with a content of 0.6 wt.%. After that, uniaxial pressing of the powder at a pressure of 50 MPa was performed. A forming green compact, cold isostatic pressing was performed with a pressure of 230 MPa to increase its density. The sintering was carried out at the temperature of 1060 °C for 60 min in the air. The sintered glass-ceramic sample was a relative density of 99.5%, a macrohardness of 6.7 GPa and a fracture toughness of 2.2 MPa·m1/2 [1]. The andesite basalt powder was characterized using the laser light diffraction method, X-ray diffraction method and scanning electron microscopy. Sintered glassceramic material was characterized using the X-ray diffraction method, Archimedes principle, scanning electron and optical light microscopy and the Vickers hardness test. The glass-ceramic material obtained by sintering andesite basalt powder could be used for various industrial applications in the civil engineering, mechanical, chemical, and petrochemical industries, as well as for the making of containers to store nuclear waste.VII Conference of The Serbian Society for Ceramic Materials, 7CSCS-2023, June 14-16, 2023, Belgrade, Serbi