Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure

The mathematics of french fries

Although the act of cutting a single potato (Solanum tuberosum) into french fries may appear to be trivial, the questions concerning the efficiency of this process on an industrial scale are quite daunting. Therefore, many producers are looking for a rigorous method to evaluate the market potential of a given potato crop by predicting the number and parameters of the fries that can be cut from it. Applying the methods of geometry and numerical analysis our group was able to propose several algorithms that can be directly incorporated into the existing production process. Keywords: French fries, geometry, cutting, Finite Fry Method, simulations, histogram

Promising directions of laboratory diagnostics in spores and fitness

The article describes the main biomarkers for determining human adaptation to physical activity. Analyzed modern scientific publications on the criteria of individual tolerance of food products, studied promising directions of personalized correction of the diet. The authors have formed a group of valid (sports-specific) laboratory indicators, it is proposed to pay close attention to the reference values of laboratory equipment that have “their own” norms. A promising direction of laboratory diagnostic work is the formation of reliable and accessible complementary criteria that are at the “junction” of functional and instrumental diagnostic methods. Metabolomics is viewed as a young but highly effective science for detecting highly specific metabolic characteristics of human health. The authors proposed the main directions of scientific research in laboratory diagnostics in sports

Muon Spin Rotation Measurement of the Magnetic Field Penetration Depth in Ba(Fe0.93 Co0.07)2 As2 : Evidence for Multiple Superconducting Gaps

We have performed transverse field muon spin rotation measurements of single crystals of Ba(Fe$_{0.93}$Co$_{0.07})_2$As$_2$ with the applied magnetic field along the $\hat{c}$ direction. Fourier transforms of the measured spectra reveal an anisotropic lineshape characteristic of an Abrikosov vortex lattice. We have fit the $\mu$SRSR spectra to a microscopic model in terms of the penetration depth $\lambda$ and the Ginzburg-Landau parameter $\kappa$. We find that as a function of temperature, the penetration depth varies more rapidly than in standard weak coupled BCS theory. For this reason we first fit the temperature dependence to a power law where the power varies from 1.6 to 2.2 as the field changes from 200G to 1000G. Due to the surprisingly strong field dependence of the power and the superfluid density we proceeded to fit the temperature dependence to a two gap model, where the size of the two gaps is field independent. From this model, we obtained gaps of $2\Delta_1=3.7k_BT_c$ and $2\Delta_2=1.6k_BT_c$, corresponding to roughly 6 meV and 3 meV respectively

Oxygen transport and consumption in germinating seeds

Three mathematical models were formulated to describe the oxygen con-sumption of seeds during germination. These models were fitted to measure-ment data of oxygen consumption curves for individual germinating seeds of Savoy cabbage, barley and sugar beet provided by Fytagoras. The first model builds on a logistic growth model for the increasing population of mitochondria in the embryo during growth. The other two take the anatomy and physiologi-cal properties of the seed into account. One describes the oxygen uptake during the germination phase only. An extension of this model is capable of fitting the complete oxygen consumption curve, including the initial ‘repair’ phase in which the embryonic cells recover from their dormant state before extensive cell division and growth commences. Keywords: Modelling, seed germination, cellular respiration, oxygen transpor

Comparative analysis of the ICT development level in the CIS and the european Union

В статье для стран Евросоюза и СНГ с помощью метода главных компонент факторного анализа построен интегральный показатель уровня развития информационно-коммуникационных технологий (ИКТ). Построен и проанализирован рейтинг стран, выявлены показатели, в наибольшей степени влияющие на интегральный показатель уровня развития ИКТ. Использовалась система из 11 показателей. In the article for the countries of the European Union and the CIS, using the method of the principal components of factor analysis, an integral indicator of the level of development of information and communication technologies (ICT) is constructed. The rating of countries is built and analyzed; indicators are identified that have the greatest impact on the integral indicator of the level of ICT development. A system of 11 indicators was used

Analysis of the London penetration depth in Ni-doped CaKFe4As4

We report combined experimental and theoretical analysis of superconductivity in CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ (CaK1144) for $x=$0, 0.017 and 0.034. To obtain the superfluid density, $\rho=\left(1+\Delta \lambda_L(T)/\lambda_L(0) \right)^{-2}$, the temperature dependence of the London penetration depth, $\Delta \lambda_L (T)$, was measured by using tunnel-diode resonator (TDR) and the results agreed with the microwave coplanar resonator (MWR) with the small differences accounted for by considering a three orders of magnitude higher frequency of MWR. The absolute value of $\lambda_L (T \ll T_c) \approx \lambda_L(0)$ was measured by using MWR, $\lambda_L (\mathrm{5~K}) \approx 170 \pm 20$ nm, which agreed well with the NV-centers in diamond optical magnetometry that gave $\lambda_L (\mathrm{5~K}) \approx 196 \pm 12$ nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless s$_{\pm}$ order parameter and that upon Ni doping the interband interaction increases.Comment: 8 pages, 5 figure

Малая ГТФаза Rab3B: биологические свойства и возможная роль в канцерогенезе

Proteins of the superfamily of small guanosine triphosphate hydrolase (GTPase) perform various functions: from the control of cell proliferation to the regulation of vesicular transport. The superfamily of small GTPase Ras includes more than 150 proteins, devided to 5 major families (Arf, Ran, Rho, Ras and Rab), and plays an important role in carcinogenesis. Compared to the other families, the Rab family was investigated by relatively small number studies, which does not equally reflect their role in malignant transformation processes. In our review  we have focused on both the subfamily Rab3 and its poorly investigated member Rab3B. Recent findings allow to consider Rab3B not only  as a promising diagnostic or prognostic marker for several types of neoplasms, but also is a potential target for antitumor therapy. Our analysis of publicly available transcriptional databases revealed that kidney, lung and liver cancer patients with low Rab3B gene expression demonstrate a better overall five-year survival.Белки суперсемейства малых гуанозинтрифосфат гидролаз (ГТФаз) выполняют различные функции: от контроля клеточной пролиферации до регуляции везикулярного транспорта. Суперсемейство малых ГТФаз Ras включает более 150 белков, 5 основных семейств (Arf, Ran, Rho, Ras и Rab) и играет важную роль в канцерогенезе. По сравнению с остальными семействами малых ГТФаз, белкам семейства Rab посвящено относительно небольшое количество исследований, что не отражает их важную роль в процессах злокачественной трансформации. Помимо рассмотрения семейства Rab в целом, особое внимание в обзоре уделено подсемейству Rab3 и его малоизученному представителю Rab3B. Накопленные к настоящему времени данные позволяют рассматривать Rab3B не только как перспективный диагностический или прогностический маркер при целом ряде новообразований, но и как потенциальную мишень для противоопухолевой терапии. Проведенный нами анализ общедоступных транскриптомных баз данных показал, что пациенты с низкой экспрессией гена Rab3B демонстрируют лучшую общую 5-летнюю выживаемость при раке почки, легкого и печени