Об ограниченности длин периодов непрерывных дробей ключевых элементов гиперэллиптических полей над полем рациональных чисел

The problem of the periodicity of functional continued fractions of elements of a hyperelliptic field is closely related to the problem of finding and constructing fundamental S-units of a hyperelliptic field and the torsion problem in the Jacobian of the corresponding hyperelliptic curve. For elliptic curves over a field of rational numbers, the torsion problem was solved by B. Mazur in 1978. For hyperelliptic curves of genus 2 and higher over the field of rational numbers, the above three problems remain open.The theory of functional continued fractions has become a powerful arithmetic tool for studying these problems. In addition, tasks arising in the theory of functional continued fractions have their own interest. Sometimes these tasks have analogues in the numerical case, but tasks that are significantly different from the numerical case are especially interesting. One such problem is the problem of estimating from above the lengths of periods of functional continued fractions of elements of a hyperelliptic field over a field of rational numbers.In this article, we find upper bounds on the period lengths for key elements of a hyperelliptic field over a field of rational numbers. In the case when the hyperelliptic field is defined by an odd degree polynomial, the period length of the elements under consideration is either infinite or does not exceed twice the degree of the fundamental S-unit. A more interesting and complicated case is when a hyperelliptic field is defined by a polynomial of even degree.In 2019, V. P. Platonov and G. V. Fedorov for hyperelliptic fields$$L = \mathbb{Q}(x)(\sqrt{f}), \deg f = 2g + 2,$$ found the exact interval values$$s \in \mathbb{Z}$$ such that continued fractions of elements of the form$$\sqrt{f}/h^s \in L \setminus \mathbb{Q}(x)$$ are periodic.Using this result in this article, we find exact upper bounds on the period lengths of functional continued fractions of elements of a hyperelliptic field over a field of rational numbers, depending only on the genus of the hyperelliptic field and the order of the torsion group of the Jacobian of the corresponding hyperelliptic curve.Проблема периодичности функциональных непрерывных дробей элементов гиперэллиптического поля тесно связана с проблемой поиска и построения фундаментальных S-единиц гиперэллиптического поля и проблемой кручения в якобиане соответствующей гиперэллиптической кривой. Для эллиптических кривых над полем рациональных чисел проблема кручения была решена Б. Мазуром в 1978 году. Для гиперэллиптических кривых рода 2 и выше над полем рациональных чисел приведенные три проблемы остаются открытыми.Теория функциональных непрерывных дробей стала мощным арифметическим инструментом для исследования этих проблем. Кроме этого, возникающие в теория функциональных непрерывных дробей задачи имеют собственный интерес. Иногда эти задачи имеют аналоги в числовом случае, но особенно интересны задачи, которые значительно отличаются от числового случая. Одной из таких задач является задача об оценке сверху длин периодов функциональных непрерывных дробей элементов гиперэллиптического поля над полем рациональных чисел.В данной статье мы находим оценки сверху на длины периодов для ключевых элементов гиперэллиптического поля над полем рациональных чисел. В случае, когда гиперэллиптическое поле задается многочленом нечетной степени, длина периода рассматриваемых элементов либо бесконечна, либо не превосходит удвоенной степени фундаментальной S-единицы. Более интересный и сложный случай, когда гиперэллиптическое поле задается многочленом четной степени. В 2019 году В.~П.~Платоновым и Г.~В.~Федоровым для гиперэллиптических полей$$L = \mathbb{Q}(x)(\sqrt{f}), \deg f = 2g+2,$$ найден точный промежутокзначений $$s \in \mathbb{Z}$$ таких, что непрерывные дроби элементов вида$$\sqrt{f}/h^s \in L \setminus \mathbb{Q}(x)$$ периодические.Используя этот результат в данной статье найдены точные оценки сверху на длины периодов функциональных непрерывных дробей элементов гиперэллиптического поля над полем рациональных чисел, зависящие только от рода гиперэллиптического поля и порядка группы кручения якобиана соответствующей гиперэллиптической кривой

A TunaCan Water-Based Thruster for CubeSats: System Development and Qualification

Governments and industries developed an increasing interest towards CubeSats and Small Satellites for commercial and scientific missions, however the general absence of propulsion capabilities is limiting the market potential. Electric propulsion systems are generally associated with low thrust and high power requirements, while cold gas thrusters are inefficient because of the low Specific Impulse (lsp). SteamJet Space Systems has developed a very compact, low pressure, water powered electrothermal thruster able to provide a high level of thrust, using less than 20W of power and with a specific impulse in excess of 170 s

Kinemon: inductively shunted transmon artificial atom

We experimentally investigate inductively shunted transmon-type artificial atoms as an alternative to address the challenges of low anharmonicity and the need for strong charge dispersion in superconducting quantum systems. We characterize several devices with varying geometries and parameters (Josephson energies and capacitances), and find a good agreement with calculations. Our approach allows us to retain the benefits of transmon qubit engineering and fabrication technology and high coherence, while potentially increasing anharmonicity. The approach offers an alternative platform for the development of scalable multi-qubit systems in quantum computing.Comment: 10 pages, 7 figure

Quantum-inspired optimization for wavelength assignment

Problems related to wavelength assignment (WA) in optical communications networks involve allocating transmission wavelengths for known transmission paths between nodes that minimize a certain objective function, for example, the total number of wavelengths. Playing a central role in modern telecommunications, this problem belongs to NP-complete class for a general case so that obtaining optimal solutions for industry-relevant cases is exponentially hard. In this work, we propose and develop a quantum-inspired algorithm for solving the wavelength assignment problem. We propose an advanced embedding procedure to transform this problem into the quadratic unconstrained binary optimization (QUBO) form, having a improvement in the number of iterations with price-to-pay being a slight increase in the number of variables (“spins”). Then, we compare a quantum-inspired technique for solving the corresponding QUBO form against classical heuristic and industrial combinatorial solvers. The obtained numerical results indicate on an advantage of the quantum-inspired approach in a substantial number of test cases against the industrial combinatorial solver that works in the standard setting. Our results pave the way to the use of quantum-inspired algorithms for practical problems in telecommunications and open a perspective for further analysis of the use of quantum computing devices

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong

Studies and Proposals for an Automatic Crystal Control System

This document presents the status of the studies for an Automatic Crystal Control System ( ACCOS) performed since autumn 1995 for the CMS collaboration. Evaluation of a startstop method for light yield, light uniformity and decay time measurements of PbWO4 crystals is presented, as well as the first results obtained with a compact double-beam spectrophotometer for transverse transmission. Various overall schemes are proposed for an integrated set-up including crystal dimension measurement. The initial financial evaluationperformed is also given

Systematic Study of the PbWO4 Crystal Short Term Instalibity Under Irradiation

The effect of the irradiation on the lead tungstate ( PWO) scintillator properties has been studied at different irradiation facilities. Lead tungstate crystals grown with the tuning of oxides content in the melt to the stoichiometry of pure sheelite or sheelite-like type crystals and doped with heterovalent, trivalent and pentavalent impurities have been studied in order to optimize their resistance to irradiation. A combination of a selective cleaning of raw materials, a tuning of the melt from crystallization to crystallisation, and a destruction or compensation of the point structure defects has been used to minimize the short-term instability of PWO parameters under irradiation

DataSheet1_Quantum-inspired optimization for wavelength assignment.PDF

Problems related to wavelength assignment (WA) in optical communications networks involve allocating transmission wavelengths for known transmission paths between nodes that minimize a certain objective function, for example, the total number of wavelengths. Playing a central role in modern telecommunications, this problem belongs to NP-complete class for a general case so that obtaining optimal solutions for industry-relevant cases is exponentially hard. In this work, we propose and develop a quantum-inspired algorithm for solving the wavelength assignment problem. We propose an advanced embedding procedure to transform this problem into the quadratic unconstrained binary optimization (QUBO) form, having a improvement in the number of iterations with price-to-pay being a slight increase in the number of variables (“spins”). Then, we compare a quantum-inspired technique for solving the corresponding QUBO form against classical heuristic and industrial combinatorial solvers. The obtained numerical results indicate on an advantage of the quantum-inspired approach in a substantial number of test cases against the industrial combinatorial solver that works in the standard setting. Our results pave the way to the use of quantum-inspired algorithms for practical problems in telecommunications and open a perspective for further analysis of the use of quantum computing devices.</p

Green Lithography for Delicate Materials

Online Version of Record before inclusion in an issue 2101533 Funding Information: A.G. and A.B. contributed equally to this work. The authors thank Andrey Starkov for the help with illustrations and Dr. Ivan Shuklov for providing chemical reagents. A.G., K.M., V.D. thank the late Vsevolod Gantmakher for the inspiration and support provided at the beginning of this study. The development concept was designed under financial support by Russian Science Foundation under grant 19‐73‐10154. The experiments of the model developer investigation were supported by Russian Science Foundation under grant No. 18‐72‐10135. XPS was carried out with the support of the Research Facility Center at the Institute of Solid State Physics (RAS) (R.N.M. and A.M.I). This work was performed using equipment of MIPT Shared Facilities Center. F.S.F. acknowledges Russian Foundation for Basic Research grant no. 19‐07‐00300. V.P. acknowledges support from the National Science Foundation under the grant ECCS‐1806363. B.P.R. and J.T.D. acknowledge support from the National Science Foundation Award No. ECCS‐1709222. Section on the synthesis of chitosan acetate with various molecular weights was supported by Ministry of Science and Higher Education of the Russian Federation. A.I. expresses gratitude to the Russian Foundation for Basic Research (project no. 19‐29‐03021 mk) for supporting his work. A.K.G. acknowledge RFBR grant 19‐32‐90143. A.G.N. acknowledges the Russian Science Foundation (project No 17‐19‐01787‐synthesis of carbon nanotubes and project No 21‐72‐20050‐SWCNT transistor fabrication and characterisation). Publisher Copyright: © 2021 Wiley-VCH GmbH Copyright: Copyright 2021 Elsevier B.V., All rights reserved.A variety of unconventional materials, including biological nanostructures, organic and hybrid semiconductors, as well as monolayer, and other low-dimensional systems, are actively explored. They are usually incompatible with standard lithographic techniques that use harsh organic solvents and other detrimental processing. Here, a new class of green and gentle lithographic resists, compatible with delicate materials and capable of both top-down and bottom-up fabrication routines is developed. To demonstrate the excellence of this approach, devices with sub-micron features are fabricated on organic semiconductor crystals and individual animal's brain microtubules. Such structures are created for the first time, thanks to the genuinely water-based lithography, which opens an avenue for the thorough research of unconventional delicate materials at the nanoscale.Peer reviewe