Моноиды натуральных чисел в теоретико-числовом методе в приближенном анализе

For every monoid M of natural numbers defined a new class of periodic functions $$M_s^\alpha$$, which is a subclass of a known class of periodic functions Korobov $$E_s^\alpha$$. With respect to the norm $$\|f(\vec{x})\|_{E_s^\alpha}$$, the class $$M_s^\alpha$$ is an inseparable Banach subspace of class $$E_s^\alpha$$.It is established that the class $$M_s^\alpha$$ is closed with respect to the action of the Fredholm integral operator and the Fredholm integral equation of the second kind is solvable on this class.In this paper we obtain estimates of the image norm of the integral operator, which contain the kernel norm and the s-th degree of the Zeta function of the monoid M. Estimates are obtained for the parameter $$\lambda$$, in which the integral operator $$A_{\lambda,f}$$ is a compression. The theorem on the representation of the unique solution of Fredholm integral equation of the second kind in the form of Neumann series is proved.The paper deals with the problems of solving the partial differential equation with the differential operator $$Q\left(\frac{\partial }{\partial x_1},\ldots,\frac{\partial }{\partial x_s}\right)$$ in the space $$M^\alpha_{s}$$, which depends on the arithmetic properties of the spectrum of this operator.A paradoxical fact is found that for a monoid $$M_{q,1}$$ of numbers comparable to 1 modulo q, a quadrature formula with a parallelepiped grid for an admissible set of coefficients modulo q is exact on the class $$M_{q,1,s}^\alpha$$. Moreover, this statement remains true for the class $$M_{q,a,s}^\alpha$$ with 1 < a < q when q is a Prime number. Since the functions of class $$M_{q,a,s}^\alpha$$ with 1 < a < q do not have a zero Fourier coefficient $$C(\vec{0})$$, then for a simple q the sum of the function values at the nodes of the corresponding parallelepipedal grid will be zero.В работе для каждого моноида M натуральных чисел определён новый класс периодических функций $$M_s^\alpha$$, который является подклассом известного класса Коробова периодических функций $$E_s^\alpha$$. Относительно нормы $$\|f(\vec{x})\|_{E_s^\alpha}$$ класс $$M_s^\alpha$$ является несепарабельным банаховым подпространством класса $$E_s^\alpha$$.Установлено, что класс $$M_s^\alpha$$ замкнут относительно действия интегрального оператора Фредгольма и на этом классе разрешимо интегральное уравнение Фредгольма второго рода. В работе получены оценки нормы образа интегрального оператора, которые содержат норму ядра и s-ю степень дзета-функции моноида M. Получены оценки на параметр $$\lambda$$, при которых интегральный оператор $$A_{\lambda,f}$$ является сжатием. Доказана теорема о представлении единственного решения интегрального уравнения Фредгольма второго рода в виде ряда Неймана.В работе рассмотрены вопросы решения дифференциального уравнения с частными производными с дифференциальным оператором $$Q\left(\frac{\partial }{\partial x_1},\ldots,\frac{\partial }{\partial x_s}\right)$$ в пространстве $$M^\alpha_{s}$$, который зависит от арифметических свойств спектра этого оператора.В работе обнаружен парадоксальный факт, что для моноида $$M_{q,1}$$ чисел сравнимых с 1 по модулю q квадратурная формула с параллелепипедальной сеткой для допустимого набора коэффициентов по модулю q точна на классе $$M_{q,1,s}^\alpha$$. Более того, это утверждение остается верным и для класса $$M_{q,a,s}^\alpha$$ с 1 < a < q, когда q - простое число. Так как функции из класса $$M_{q,a,s}^\alpha$$ с 1 < a < q не имеют нулевого коэффициента Фурье $$C(\vec{0})$$, то при простом q сумма значений функции по узлам соответствующей параллелепипедальной сетки будет нулевой

Poa_ITS_OCHLOPOA

Alignment file of the ITS sequences (ITS1-5.8S rRNA gene-ITS2 region, nuclear genome

Data from: On polyphyly of the former section Ochlopoa Asch. et Graebn. and hybridogenic section Acroleucae Tzvelev et Prob. (Poa L., Poaceae): insights from the molecular phylogenetic analysis

In this study, sequence data of the nuclear region ITS1-5.8S rDNA-ITS2 and the chloroplast region trnL-F as well as few morphological characters were examined trying to elucidate the relationships among known annual bluegrasses. It was shown that all taxa from the aggregate P. annua distinguished by lemma characters and growth form are identical according to ITS and trnL-trnF data wherein all ITS sequences of P. annua aggr. are the same as P. supina and all trnL-trnF sequences are homologous with those of P. infirma. Also we haven’t found any differences between unusual samples of P. supina with short spinules on their panicle branches and typical plants according to the sequence data though Siberian samples have minor distinction in trnL-trnF region. Our analysis showed hybrid origin of Asian annual bluegrasses (see also Nosov et al. 2015, Soreng et al. 2017). Their maternal genome is close to the section Homalopoa, but their ITS sequences were different. ITS sequences of some annual Asian bluegrasses group with the section Stenopoa and for other species (close to previous from the morphological traits) they fall into clade with the section Malacanthae. The latter group is distant from the sect. Ochlopoa and is better to be treated as a separate section, Acroleucae. American annual bluegrasses are heterogeneous and also rather distant from the sect. Ochlopoa. P. chapmaniana, species with cleistogamic flowers, is nested with basal Subantarctic sections falling out of its previously described affinity group. It is closer to the sect. Ochlopoa than other annual American bluegrasses. Thus, studied annual species in fact belong to the four independent evolutionary lines (or six including genus Eremopoa and Turkish Poa jubata – Cabi et al. 2017) one of which, Acroleucae, also passed triple reticulation event. As in previous studies our analysis didn’t support the generic status of sect. Ochlopoa

An Indirect Method of Micromagnetic Structure Estimation in Microwires

The tunable magnetic properties of amorphous ferromagnetic glass-coated microwires make them suitable for a wide range of applications. Accurate knowledge of the micromagnetic structure is highly desirable since it affects almost all magnetic properties. To select an appropriate wire-sample for a specific application, a deeper understanding of the magnetization reversal process is required, because it determines the measurable response (such as induced voltage waveform and its spectrum). However, the experimental observation of micromagnetic structure of micro-scale amorphous objects has strict size limitations. In this work we proposed a novel experimental technique for evaluating the microstructural characteristics of glass-coated microwires. The cross-sectional permeability distribution in the sample was obtained from impedance measurements at different frequencies. This distribution enables estimation of the prevailing anisotropy in the local region of the wire cross-section. The results obtained were compared with the findings of magnetostatic measurements and remanent state analysis. The advantages and limitations of the methods were discussed

Environmental management and proposals to improve the wage system

In today’s global economy, the importance of environmental and social responsibility is constantly growing. There are thousands of environmental and social standards and guidelines around the world today. These guidelines and standards define requirements and objectives. However, the main problem is their practical implementation and implementation. The Environmental and Social Management System (ESMS) enables companies to integrate the requirements of these guidelines and standards into their operations by organizing a set of well- defined, iterative processes. One aspect of this system is the remuneration system. On the basis of content analysis and analysis of statistical data, the authors develop proposals for improving this system

Improving the sustainability of metal-producing industries in Russia

In recent years, the metal-producing industries face a range of economic and ecological problems. The authors use content-analysis and statistical methods for analyzing the recent data and make proposals for the development t of metallurgy. The metallurgical industry is in second place among all other industries in terms of atmospheric emissions. Ferrous and non-ferrous metallurgy enterprises are forced to use ore with a very low content of useful components in the extraction of metals. Thus, a huge volume of ore is supplied to beneficiation and smelting, and this, in turn, generates large quantities of waste gases from unused components. The current position of metallurgy companies in Russia does not contribute to the development of new industries for several reasons: lack of funds for the development of large plants; lack of forecast for short-term global demand for ferrous metallurgy products; a growing group of competition from foreign manufacturers for the products provided by the industry. To reduce the level of negative impact of metallurgy on the environment, it is necessary to develop and use new technologies that are safe for the environment. Unfortunately, not all enterprises use purification filters and facilities, although this is mandatory in the activities of every metallurgical enterprise

Substitution-induced internal strain and high disorder in weakly radiation damaged hydrothermal zircon from Mt. Malosa, Malawi

International audienc