Scaling of loop-erased walks in 2 to 4 dimensions

We simulate loop-erased random walks on simple (hyper-)cubic lattices of dimensions 2,3, and 4. These simulations were mainly motivated to test recent two loop renormalization group predictions for logarithmic corrections in $d=4$, simulations in lower dimensions were done for completeness and in order to test the algorithm. In $d=2$, we verify with high precision the prediction $D=5/4$, where the number of steps $n$ after erasure scales with the number $N$ of steps before erasure as $n\sim N^{D/2}$. In $d=3$ we again find a power law, but with an exponent different from the one found in the most precise previous simulations: $D = 1.6236\pm 0.0004$. Finally, we see clear deviations from the naive scaling $n\sim N$ in $d=4$. While they agree only qualitatively with the leading logarithmic corrections predicted by several authors, their agreement with the two-loop prediction is nearly perfect.Comment: 3 pages, including 3 figure

Some Aspects of the Quality of Corporate Governance in Digital Economy

The relevance of this article is due to technological changes that are constantly introducing new characteristics, both in the global economic system and in the economy of individual fields of activity. The newest digital economy is significantly different from the traditional economy. A modern business environment requires constant adaptation of an entrepreneur to dynamically changing conditions at a strategic and tactical level. The purpose of the article is to study aspects of the quality of corporate governance, taking into account the challenges of the digital economy. The objectives of the study are: to identify the key elements of corporate governance and environmental factors affecting them; to determine the conditions and factors of the formation of economic interests in the corporate governance system for the purpose of improving the quality of corporate governance in the digital economy

Genotype by yield × trait (GYT) biplot analysis for the identification of the superior winter and facultative barley breeding lines

Received: January 25th, 2023 ; Accepted: May 21st, 2023 ; Published: June 17th, 2023 ; Corresponding author e-mail: [email protected] the present study, in a panel of promising winter and facultative barley (Hordeum vulgare L.) breeding lines, the peculiarities of yield performance and its combination with resistance (tolerance) to the most common under conditions of the Ukrainian Forest-Steppe abiotic and biotic stresses have been determined. In 2016-17–2018-19 the breeding lines were differentiated based on grain yield, thousand kernel weight, frost resistance, leakage of electrolytes, relative drought tolerance, lodging resistance, and resistance to powdery mildew (caused by Blumeria graminis (DC.) E. O. Speer, f. sp. hordei emend. É. J. Marchal (anamorph Oidium monilioides Link)), spot blotch (caused by Cochliobolus sativus (anamorph Bipolaris sorokiniana [Sacc.] Shoem.)), and leaf rust (caused by Puccinia hordei Otth.). GYT (genotype by yield × trait) biplot model was used for comprehensive evaluation of the breeding lines by a combination of yield with a complex of traits. As a result, the winter breeding line ‘Pallidum 5096’ and facultative breeding line ‘Pallidum 5110’ superior to others in terms of yield × traits combinations have been identified. These breeding lines as new varieties ‘MIP Atlas’ and ‘MIP Yanus’ accordingly have been submitted to the Ukrainian Institute for Plant Variety Examination for further State Qualification Examination. The winter (‘Pallidum 5134’, ‘Pallidum 5097’, ‘Pallidum 5024’, ‘Pallidum 5090’, and ‘Pallidum 5130’) and facultative (‘Pallidum 5153’, ‘Pallidum 5102’, ‘Pallidum 5126’, and ‘Pallidum 5131’) breeding lines can be used as valuable genetic sources in breeding programs in Ukraine and some other Central a nd Eastern European countries

Light-induced sulfur transport inside single-walled carbon nanotubes

Filling of single-walled carbon nanotubes (SWCNTs) and extraction of the encapsulated species from their cavities are perspective treatments for tuning the functional properties of SWCNT-based materials. Here, we have investigated sulfur-modified SWCNTs synthesized by the ampoule method. The morphology and chemical states of carbon and sulfur were analyzed by transmission electron microscopy, Raman scattering, thermogravimetric analysis, X-ray photoelectron and near-edge X-ray absorption fine structure spectroscopies. Successful encapsulation of sulfur inside SWCNTs cavities was demonstrated. The peculiarities of interactions of SWCNTs with encapsulated and external sulfur species were analyzed in details. In particular, the donor-acceptor interaction between encapsulated sulfur and host SWCNT is experimentally demonstrated. The sulfur-filled SWCNTs were continuously irradiated in situ with polychromatic photon beam of high intensity. Comparison of X-ray spectra of the samples before and after the treatment revealed sulfur transport from the interior to the surface of SWCNTs bundles, in particular extraction of sulfur from the SWCNT cavity. These results show that the moderate heating of filled nanotubes could be used to de-encapsulate the guest species tuning the local composition, and hence, the functional properties of SWCNT-based materials

Field theory conjecture for loop-erased random walks

We give evidence that the functional renormalization group (FRG), developed to study disordered systems, may provide a field theoretic description for the loop-erased random walk (LERW), allowing to compute its fractal dimension in a systematic expansion in epsilon=4-d. Up to two loop, the FRG agrees with rigorous bounds, correctly reproduces the leading logarithmic corrections at the upper critical dimension d=4, and compares well with numerical studies. We obtain the universal subleading logarithmic correction in d=4, which can be used as a further test of the conjecture.Comment: 5 page

Analysis of variability of quantitave traits of Vaccinium corymbosum L. ex vitro under different lighting modes

The article presents the results of studies on the comparative analysis of bioproductional parameters of plant growth of Bluecrop and Elizabeth high-bush blueberry ex vitro under the conditions of fluorescent and LED lighting. Ensuring the optimal spectral composition of radiation, realized with the original LED light, led to a significant increase at 1.1–1.6 times in all of the analyzed growth parameters in high-bush blueberry ex vitro plants.Представлены результаты сравнительного анализа изменчивости биопродукционных параметров роста растений сортов Блюкроп и Элизабет голубики высокой ex vitro в условиях люминесцентного и светодиодного освещения. Обеспечение оптимального спектрального состава излучения, реализуемое с помощью оригинального светодиодного светильника, чаще приводит к достоверному (при p < 0,01 и p < 0,05) повышению в 1,1–1,6 раза показателей всех анализируемых признаков у адаптантов сортовой голубики высокой

Transformation of SiOx films into nanocomposite SiO₂(Si) films under thermal and laser annealing

Oxide-assisted growth of Si nanocrystals includes deposition of a siliconenriched SiOx film at the first stage and annealing at the second one. The ion-plasma sputtering method has been used for deposition of the SiOx film. The influence of thermal and laser annealing on SiOx film properties has been investigated. Formation of silicon nanoislands on oxide film surface has been observed by AFM both after thermal and laser annealing. The height and surface density of the nanoislands depends both on the silicon content in the initial SiOx film and temperature of thermal annealing. The higher annealing temperature causes formation of large nanoislands, but their surface density decreases. Comparison of nanoislands created at thermal and laser annealing shows that in case of laser annealing the nanoislands are higher and their surface density is lower. The intensity of laser irradiation influences on nanoisland parameters significantly. The growth of electrical conductivity with thermal annealing temperature has been observed. The influence of gas atmosphere during annealing is also significant in case of higher temperatures. In case of laser annealing at the beginning at low laser irradiation intensities, the SiOx film conductivity increases, but the following growth of intensity causes the decrease in electrical conductivity

The three-dimensional randomly dilute Ising model: Monte Carlo results

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining $\nu = 0.683(3)$, $\eta = 0.035(2)$, $\beta = 0.3535(17)$, and $\alpha = -0.049(9)$, in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio $R^+_\xi$ that expresses the universality of the free-energy density per correlation volume. We find $R^+_\xi = 0.2885(15)$.Comment: 34 pages, 7 figs, few correction

ИММУНОГЕНЕТИЧЕСКИЕ АСПЕКТЫ РАННЕГО РЕВМАТОИДНОГО АРТРИТА

The study is aimed to investigate the distribution of alleles of HLA-DRB1 gene in patients with early rheumatoid arthritis and healthy individuals in Russian population, and evaluate their significance as molecular genetic markers of rheumatoid arthritis predisposition and protection. The association between alleles of HLA-DRB1 genes, antibodies to cyclic citrullinated peptides and IgM rheumatoid factor was also studied. Low and high resolution HLA-DRB1 genotyping were compared. In the cohort of patients with early rheumatoid arthritis, the alleles of HLA-DRB1 gene were found to be markers of rheumatoid arthritis protection/risk, especially in the homozygous state. They determined production of antibodies to cyclic citrullinated peptides but were not associated with rheumatoid factor IgM levels. These findings support different autoimmune mechanisms of rheumatoid arthritis pathogenesis. Изучено распределение аллелей гена HLA-DRB1 у больных ранним ревматоидным артритом и здоровых лиц контрольной группы российской популяции и оценена их значимость в качестве молекулярно-генетических маркеров предрасположенности и протекции ревматоидного артрита. Определена сила ассоциативной связи аллелей гена HLA-DRB1 с продукцией антител к циклическим цитруллинированным пептидам и ревматоидному фактору класса М. В исследовании проведено сравнение методов высоко- и низкоразрешающего генотипирования аллелей HLA-DRB1. У больных ранним ревматоидным артритом обнаружены аллели гена HLA-DRB1, являющиеся маркерами риска и протекции ревматоидного артрита, детерминирующие продукцию антител к циклическим цитруллинированным пептидам, но не ассоциированные с антителами класса M к ревматоидному фактору. Полученные данные могут свидетельствовать о различных аутоиммунных механизмах патогенеза ревматоидного артрита. 

Relaxation phenomena at criticality

The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the thermodynamic control parameters. The non-equilibrium evolution following this change displays some of the features typically observed in glassy materials, such as ageing, and it can be monitored via dynamic susceptibilities and correlation functions of the order parameter, the scaling behaviour of which is characterized by universal exponents, scaling functions, and amplitude ratios. This universality allows one to calculate these quantities in suitable simplified models and field-theoretical methods are a natural and viable approach for this analysis. In addition, if a statistical system is spatially confined, universal Casimir-like forces acting on the confining surfaces emerge and they build up in time when the temperature of the system is tuned to its critical value. We review here some of the theoretical results that have been obtained in recent years for universal quantities, such as the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the Ising model with Glauber dynamics in the bulk. The non-equilibrium dynamics of the Casimir force acting in a film is discussed within the Gaussian model.Comment: Talk delivered at Statphys23, Genova, Italy, July 9-13, 2007. 8 pages, 7 figure