We consider a parabolic equation in one spatial variable with Dini continuous coefficients. For this equation, the existence of a classical fundamental solution is proved and estimates are given. The ...condition on the nature of the continuity of the leading coefficient of the equation for the existence of a fundamental solution is sharp.
We consider a parabolic equation with Dini continuous coefficients in the case of many spatial variables The existence of a regular fundamental solution to this equation is proved, and estimates for ...the solution are obtained. These results imply that the Dini condition for the principal coefficients of the equation is sharp.
The paper presents the development and investigation of a semiconductor power supply for metal atoms' active media excitation with a pulse repetition rate of up to 200 kHz in pulse-periodic mode. ...High voltage excitation pulses are formed by a source based on the LTD-generator concept (linear transformer driver) with a single-turn step-up transformer. The calculation and justification for the selection of power supply elements, based on typical excitation modes of the active medium in copper bromide vapor, are presented. The mean radiation power was equal to 650 mW under excitation condition: PRF was to 150 kHz and specific pulse energy input was 160 µJ/cm
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We continue to develop a new Superconductor Flux Logic (SFL) family based on nSQUID gates with fundamentally low energy dissipation and the ability to operate in irreversible and reversible modes. ...Prospective computers utilizing the new gates can keep conventional logically irreversible architectures. In this case the energy dissipation is limited by fundamental thermodynamic laws and could be as low as a few kBT s per logic operation. Highly exotic and less practical logically and physically reversible circuit architectures are more attractive for us because they enable a reduction of the specific energy dissipation well below the thermodynamic threshold kBT ln2. The reversible option is of interest to us because we can then experimentally demonstrate that all technical mechanisms of the energy dissipation could be cut below the fundamental thermodynamic limit. In other words, we like to set the energy dissipation record for all conventional digital technologies that (if measured in kBT ) is about one million times below the best figures achieved in commercially available semiconductor circuits. Besides, we believe that diving below the thermodynamic threshold would have impressive scientific and philosophical impacts. In the paper we introduce a new timing belt clocking scheme and present new circuits. While we still work with test circuits, some of them contain two 8-stage shift registers, one with direct and the other with inverted outputs. The energy dissipation per nSQUID gate per bit measured at 4 K temperature is already below the thermodynamic threshold. We are confident that we passed through the critical phase of the project and we simply need more time to make more sophisticated circuits. The extremely low energy dissipation converts our circuits into a natural candidate to support circuitry for any sensors operating at milli-Kelvin temperatures.
The development results of a small-size copper bromide vapor laser with pulsed charging of the storage capacitor are presented. A specific feature of the developed device is a high-frequency charging ...mode of the working capacitor (over 200 kHz). Moreover, the pulse repetition frequency (PRF) of laser emission can be varied from 12 to 36 kHz. The developed power supply was used to excite the active element. The length of the active element was 50 cm and its diameter was 2 cm. The emission power was 1.6 W at a PRF of 36 kHz. In this case, the consumption power of the power supply was 750 W.
Carbon nanoparticles attract attention of plant researchers as a possible means of improving crop yield and its quality. There are grounds to believe that the beneficial influence of polyhydroxy ...fullerene (PHF) on plants is due to its antioxidant activity, but the mechanism of its action on their growth and development remains unclear. Our study shows that PHF added to the nutrient medium accelerates barley roots elongation owing to the increase of their longitudinal extensibility in the growth zone. The impact of PHF on root growth was much more pronounced under the action of stressors inducing the accumulation of reactive oxygen species, such as UV-B radiation, salt stress and the excess of salicylic acid. Dichlorofluorescein assay showed that PHF prevented oxidative stress development and subapical root swelling after UV-B irradiation of roots. The conclusion is drawn that the important reason of root growth acceleration in the presence of PHF is its ability to serve as a scavenger of free radicals. That’s why it may be especially useful for the improvement of plant growth under environmental stress.
This paper is dedicated to the metrological aspects of clustering procedure. It is shown that taking into account the information on uncertainty of the data to be clustered allows easily making ...reasonable decisions that are metrologically supported. The paper presents that the problems that are usually difficult to solve in practice of the clustering become simpler: the proposed approach allows determining the number of maximum recognizable clusters and thus protects from the unreasonable conclusions and allows performing the preconditioning of data to be clustered simpler.
The design and main technical characteristics of the Zarnitsa‑D portable LED device for short-wave ultraviolet irradiation are described. The radiation source consists of LEDs with maximum power ...output at a wavelength of 272 nm and an emission spectrum half-width of ~12 nm. Electrical power is 10 W. Results obtained from in vitro microbiological studies of the device are presented. The device is shown to have a marked antimicrobial effect and has promise for use in systems for the operational disinfection of massively contaminated surfaces, potentially including wound surfaces.
The statistical theory based on the two-parameter Sharma–Mittal functional is a generalization of Gibbs, Renyi, and Tsallis statistics. This study focuses on the formalism of statistical mechanics ...based on the Sharma–Mittal entropy functional and proves the theorem on the energy equipartition over degrees of freedom for classical statistical systems. A generalized Maxwell distribution is derived for the corresponding statistics, and the characteristics of statistical systems described by this distribution are calculated, including the mean velocity magnitude, root mean square velocity, and the most probable velocity of gas particles. Additionally, a generalized Sackur–Tetrode formula is obtained.
The hybocrinid crinoid
Trecrinus schmidti
gen. et sp. nov. is described from the Middle Ordovician (Uhaku Regional Stage, Darriwilian) of the lower reaches of the Volkhov River. Three long arms in ...the A, D and C radii, and a low cup with a flattened base without a stem are the main characteristics of the new genus. Morphology of the new genus emphasizes the similarities and differences in the morphogenetic capabilities of the hybocrinid lineages, which simultaneously developed on the Baltica and Laurentia paleocontinents, separated from each other in Ordovician. In the pronounced tiering of the Valim benthic community, this new genus occupied the lowest bottom stage.
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