Canonical matrices of bilinear and sesquilinear forms

Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of F. A method for reducing the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings is used to construct the canonical matrices. This method has its origins in representation theory and was devised in [V.V. Sergeichuk, Math. USSR-Izv. 31 (1988) 481-501].Comment: 44 pages; misprints corrected; accepted for publication in Linear Algebra and its Applications (2007

A regularization algorithm for matrices of bilinear and sesquilinear forms

We give an algorithm that uses only unitary transformations and for each square complex matrix constructs a *congruent matrix that is a direct sum of a nonsingular matrix and singular Jordan blocks.Comment: 18 page

Piezoelectric polymer/ceramic nanostructures for mechanical energy harvesting

Vibration-based mechanical energy is one of the most accessible energy source in the surroundings. Harvesting this type of energy exhibits a great potential for remote/wireless sensing, charging batteries, and powering electronic devices. Piezoelectric and ferroelectric materials, including PZT, BaTiO3, ZnO, polyvinylidene fluoride (PVDF), etc., can be used for converting ambient mechanical energy into electricity. Based on these materials, a variety of micro- or nanoelectromechanical systems can be developed for harvesting energies from random vibrations, mechanical waves, or body movements like walking, running, or typing. Recent investigations on nanocomposites of electroactive ceramics and ferroelectric polymers exploit this approach in order to produce new multifunctional materials for mechanical energy harvesting. Taking into account that mechanical activation is one of the methods for modification of physico-chemical properties of the filler, in this study we investigate the influence of mechanical activation of ZnO particles on structural properties of ZnO/polyvinylidene fluoride nanocomposites. The nanocomposite films were prepared by solution casting method and investigated by X-ray diffraction (XRD) method and Raman spectroscopy, while the microstructure morphology has been analyzed by scanning electron microscope (SEM). Presented results will enable optimization of PVDF processing techniques for the production of new mechanical energy harvesting devices

Glycogen and gold nanoparticle bioconjugates: controlled plasmon resonance via glycogen-induced nanoparticle aggregation

Hybrid nanosystems composed of glycogen biopolymers and gold nanoparticles were prepared by an in situ non-toxic synthetic procedure. Transmission electron microscopy (TEM) and various spectroscopic methods (optical absorption, X-ray photoelectron and photoluminescence spectroscopy) were used for the characterization of the obtained bioconjugates. The gold nanoparticles formed in the presence of glycogen were spherical in shape and approximately 15 nm in diameter. The TEM micrographs show that the nanoparticles aggregated on the surface of the glycogen biomolecules. This effect induced a shift of the surface plasmon resonance band towards higher wavelengths on an increase in gold ion concentration. Effective medium theory calculations were carried out in order to explain the observed redshift of the plasmon band in the absorption spectra of the Au-glycogen colloids. The interactions of the gold nanoparticles with glycogen strongly affected the photoluminescence of the glycogenin protein incorporated into its structure. The Au-glycogen hydrocolloids exhibited good chemical stability in the presence of saline, phosphate buffered saline, alanine, histidine and D-glucose

The content of calcium, phosphorus and magnesium in the blood serum of sheep depending on the season and physiological state

The large number of sheep, especially the ones that spend the majority of time on pastures, is been fed with the meals, which do not contain all the necessary mineral substances. The level of calcium, phosphorus and magnesium on natural pastures is too low in relation to the needs of sheep. Therefore, the irregularity in the feeding of sheep occurs because of the absence of the other food sources. These irregularities are in the range from the acute mineral deficit or illness to the mild temporary forms, which could hardly diagnose, but they affect the level of production. The content of calcium, phosphorus and magnesium in the blood serum of sheep, as one of the indicators of the supplementation of sheep with these substances, has given in this paper. The average level of calcium in the blood serum of the control group of sheep was 2.61 mmol/l, phosphorus 1.04mmol/l and magnesium 1.31 mmol/l of serum. In the blood serum of the tested group, the average contents of calcium was 2.33 mmol/l, phosphorus 0.92 mmol/l and magnesium 1.37 mmol/l

Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence

We construct the Hasse diagrams $G_2$ and $G_3$ for the closure ordering on the sets of congruence classes of $2\times 2$ and $3\times 3$ complex matrices. In other words, we construct two directed graphs whose vertices are $2\times 2$ or, respectively, $3\times 3$ canonical matrices under congruence and there is a directed path from $A$ to $B$ if and only if $A$ can be transformed by an arbitrarily small perturbation to a matrix that is congruent to $B$. A bundle of matrices under congruence is defined as a set of square matrices $A$ for which the pencils $A+\lambda A^T$ belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of $2\times 2$ or $3\times 3$ matrices have the same properties with respect to perturbations. We construct the Hasse diagrams $G_2^{\rm B}$ and $G_3^{\rm B}$ for the closure ordering on the sets of congruence bundles of $2\times 2$ and, respectively, $3\times 3$ matrices. We find the isometry groups of $2\times 2$ and $3\times 3$ congruence canonical matrices.Comment: 34 page

Targeted Synthesis of Ceramic-Polymer Nanocomposites

It is well known that materials used in nano-electro-mechanical systems (NEMS) must simultaneously satisfy numerous requirements for chemical, structural, mechanical and electrical properties. Taking into account that the application of targeted synthesis principles is fundamental for development of these materials, in this article the results of the investigation of the nano-scale grain size effects, grain/particle size induced structural transformations, the evolution of the particle structure during targeted synthesis process and microstructure modeling of ceramic-polymer nanocomposites, has been presented. The nanocomposite BT,ST/PVDF films were prepared by pulsed laser deposition (PLD) method and investigated by X-ray diffraction (XRD) method and Raman spectroscopy, while the microstructure morphology has been analyzed by scanning electron microscope (SEM). It was found that PLD of BT,ST on PVDF substrate offers a new set of opportunities for development of advanced flexible piezo-films for the next generation of NEMS, which applications span the aero-space industry, communications, defense systems, national security, health care, information technology and environmental monitoring

Synchrotron radiation photoemission spectroscopy study of the valence band electronic structure of Ag-Ag2S Janus nanoparticles for the development of nanomotors propelled by NIR light

Silver-silver sulfide (Ag-Ag2S) hybrid nanosystem which consists of plasmonic metal Ag and narrow band gap semiconductor Ag2S is typically studied as a photocatalyst under visible and NIR light [1,2]. Janus morphology of this system is especially interesting due to the possibility of initiating two different chemical reactions that are spatially separated on two halves of the system. Here, we present the fabrication of Ag-Ag2S Janus nanoparticles and the examination of their valence electronic structure. For the investigation of the electronic structure of isolated nanoparticles, we performed synchrotron radiation vacuum ultraviolet photoelectron spectroscopy using the velocity map imaging (VMI) technique. By using two different photon energies, hν = 9.5 eV and hν = 11 eV, we obtained angle-resolved photoelectron images. Photoemission spectra and the dependence of the asymmetry parameter α on the binding energy are derived from VMI images using modified p-Basex inversion method [3]. In addition, we coupled Ag-Ag2S nanoparticles to the TiO2 and studied the actuation of obtained hybrid nanosystem in a liquid medium under visible and NIR light.IX International School and Conference on Photonics : PHOTONICA2023 : book of abstracts; August 28 - September 1, 2023; Belgrad

Hlapljivi sastojci šljivovice

Gas chromatography and GC/MS methods were used to detect volatile components of three home-made natural old plum brandy samples and one sample of industrially-produced plum brandy. Gas chromatography and gas chromatography-mass spectrometric analysis of this extracts led to the identification of 99 components, including 46 esters, 7 hydrocarbons (alkanes and alkenes), 3 aldehydes, 9 alcohols, 1 lactone, 1 ketone, 8 acetals, 14 terpenes, 8 acids and 2 phenols. Ethyl esters of C8–C18 acids were the most abundant in all samples. In addition, the content of methanol, ethanol and higher alcohols C3–C5 was determined.Metode plinske kromatografije i kombinacija plinske kromatografije i masene spektrometrije upotrijebljene su za detekciju hlapljivih komponenti u tri uzorka domaće šljivovice i jednom industrijski proizvedenom uzorku. Plinskokromatografskom metodom i kombinacijom plinskokromatografske i masene spektrometrijske analize ekstrakata identificirano je 99 komponenata, od čega su 46 esteri, 7 ugljikovodici (alkani i alkeni), 3 aldehidi, 9 alkoholi, 1 lakton, 1 keton, 8 acetali, 14 terpeni, 8 kiseline i 2 fenoli. U svim uzorcima dominantni su bili etil esteri C8-C18 kiselina. Osim toga određ|en je udeo metanola, etanola i viših alkohola C3-C5