A degree problem for the compositum of two number fields*

The triplet (a, b, c) of positive integers is said to be compositum-feasible if there exist number fields K and L of degrees a and b, respectively, such that the degree of their compositum KL equals c. We determine all compositum-feasible triplets (a, b, c) satisfying a ≤ b and b ∈ {8, 9}. This extends the classification of compositum-feasible triplets started by Drungilas, Dubickas, and Smyth [5]. Moreover, we obtain several results related to triplets of the form (a, a, c). In particular, we prove that the triplet (n, n, n(n ? 2)) is not compositum-feasible, provided that n ≥ 5 is an odd integer.

     

Light Engineering and Silicon Diffractive Optics Assisted Nonparaxial Terahertz Imaging

The art of light engineering unveils a world of possibilities through the meticulous manipulation of photonic properties such as intensity, phase, and polarization. Precision control over these properties finds application in a variety of fields spanning communications, light–matter interactions, laser direct writing, and imaging. Terahertz (THz) range, nestled between microwaves and infrared light, stands out for its remarkable ability to propagate with minimal losses in numerous dielectric materials and compounds, making THz imaging a powerful tool for noninvasive control and inspection. In this study, a rational framework for the design and optimal assembly of nonparaxial THz imaging systems is established. The research is centered on lensless photonic systems composed solely of high-resistivity silicon-based nonparaxial elements such as the Fresnel zone plate, the Fibonacci lens, the Bessel axicon, and the Airy zone plate, all fabricated using laser ablation technology. Through a comprehensive examination through illumination engineering and scattered light collection from raster-scanned samples in a single-pixel detector scheme, the imaging systems are evaluated via diverse metrics including contrast, resolution, depth of field, and focus. These findings chart an exciting course toward the development of compact and user-friendly THz imaging systems where sensors and optical elements seamlessly integrate into a single chip.     

Control of light polarization by acousto-optic diffraction from leaky acoustic wave in LiNbO₃

The acousto-optic control of light polarization due to diffraction by leaky acoustic waves in ZX-LiNbO? has been demonstrated. The randomly polarized light of 633 nm wavelength is converted by the anisotropic diffraction into two beams with mutually orthogonal polarizations, the relative intensities of which depend on the light incidence angle and acoustic frequency. Variation in acoustic frequency from 108 to 112 MHz rotates the polarization of the output optical beam by 90°. The acousto-optic control is accomplished entirely by electronic means and can be applied for implementation of fast polarization converters.     

Preparation and characterization of Y1−xPrxBa2Cu3O7−δ single crystals

We present a reliable method for growing single crystals of Y_1−xPr_xBa₂Cu₃O_7−δ high-T_c superconductors in ZrO₂ crucibles. This method results in crystals with greatly improved superconducting properties compared to crystals grown with the previously reported methods which use Al₂O₃ crucibles. We describe techniques for crystal growth in both Al₂O₃ and ZrO₂ crucibles using an excess of BaCo₃ and CuO as the flux. The crystals were characterized by means of DC magnetic-susceptibility measurements, electrical-resistivity measurements, and electron microprobe analysis. The effects of Al contamination on the conditions for crystal growth and on the superconducting properties of the crystals are found to be quite significant.     

Experimental characterization of temperature‐dependent electron transport in single‐wall multi‐tube carbon nanotube transistors

Current–voltage, radio‐frequency (RF) and noise characteristics of single‐wall multi‐tube carbon nanotube (CNT) transistors were measured at cryogenic temperatures. Compared to an ambient temperature (T_a) of 300 K, only a slight drain current increase at T_a = 77 K was observed. In addition, a weak dependence of the maximum value of the current gain cut‐off frequency (f_T) on T_a was obtained, indicating that f_T is rather limited by the device intrinsic quantum and extrinsic capacitances than by an improved mobility due to reduced optical phonon scattering at low T_a. A noise analysis of the devices at T_a = 10 K reveals that the noise factor (NF) improvement at very low temperatures is related to the reduced Nyquist noise of all resistive transistor noise contributors. Since the main noise source in CNTFETs is the shot noise, NF remains comparatively high even at T_a = 10 K.

     

Volatile compounds composition and antioxidant activity of bee pollen collected in Lithuania

Characterization of volatile compounds composition and evaluation of antioxidant properties of bee pollen collected in Lithuania is presented in the paper, which is the first study on pollen of Lithuanian origin to our knowledge. Three polyfloral pollen samples collected by honey bees were analyzed. Characterization of volatile compounds was performed using solid phase microextraction (SPME) and GC-MS. Styrene was predominant in all samples contributing 19.6–27.0 mass %. Sample A distinguished by a high amount of limonene, 9.0 mass %, sample B differed from the rest by a high content of hexanal, 9.3 mass %, and nonanal, 12.3 mass %, while sample C showed the highest content of 1-tridecene, 43.3 mass %. Screening of antioxidant properties was carried out by spectrophotometric methods and liquid chromatography coupled with a post-column 1,1-diphenyl-2-picrylhydrazyl (DPPH) reaction detector and electrochemical detector. Total phenolic and flavonoid contents together with radical scavenging activity in the free radical (DPPH) model system were evaluated in the tested samples. Total phenolic content varied from 24.4 mg g^?1 to 38.9 mg g^?1, total flavonoid content was in the range of 7.3–10.0 mg g^?1 and radical scavenging activity was found between 30.7 mg g^?1 and 34.9 mg g^?1, all data are expressed in rutin equivalents. To process the collected data statistically and classify the bee pollen samples to clusters according to their volatile composition and antioxidant activity, principal component analysis, hierarchical cluster analysis and non-linear discriminant analysis were applied.     

Nanometer-scale probing of optical and thermal near-fields with an apertureless NSOM

We have used a home-made apertureless near-field scanning optical microscope (ANSOM) for mapping nanometric steps between SiC and gold regions under visible (λ=655 nm) and infrared (λ=10.6 μm) illumination. The images, obtained with a signal demodulation at the tip oscillation frequency and at higher harmonics, clearly show optical contrasts with a subwavelength resolution of about 30 nm. Other images recorded in the visible on a YBa₂Cu₃O₇ crystal indicate that the tip used in our experiments is able to reveal polarization effects. We also present a near-field thermal optical microscope (NTOM) which operates without any external illumination. In this new kind of microscope, the laser source which is usually used to excite the evanescent waves, is replaced by a simple heating of the sample. The electromagnetic radiation locally scattered by the tip comes from the thermal radiation. Our results with this new technique prove a 200 nm lateral resolution.     

Chemometric analysis of volatiles of propolis from different regions using static headspace GC-MS

Six samples of propolis were analyzed in the paper: a sample from Brazil, Estonia, China and three samples from different locations of Uruguay. Static headspace technique coupled with gas chromatography-mass spectrometry analysis has been applied for the determination of the characteristic volatile profile with the aim to differentiate the propolis from different regions. Monoterpenes (α- and β-pinenes) were predominant in all samples, except the sample from China. This sample separated itself by the alcohols 3-methyl-3-buten-1-ol and 3-methyl-2-buten-1-ol, (40.33% and 11.57%, respectively) and ester 4-penten-1-yl acetate (9.04%). α-Pinene and β-pinene composed 64.59–77.56% of volatiles in Brazilian and Uruguayan propolis, and 29.43% in Estonian propolis. Brazilian propolis was distinguished by a high amount of β-methyl crotonaldehyde (10.11%), one of Uruguayan samples 3- by limonene (15.58%), and the Estonian sample — by eucalyptol (25.95%). Statistical investigation of the samples was made applying principal component, hierarchical cluster and K-Means cluster analyses. Various data pre-processing techniques were proposed and used to study and obtain the important volatile compounds contributed to the differentiation of the propolis samples from different regions to separate clusters.