A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

This paper contains the results collected so far on polynomial composites in terms of many basic algebraic properties. Since it is a polynomial structure, results for monoid domains come in here and there. The second part of the paper contains the results of the relationship between the theory of polynomial composites, the Galois theory and the theory of nilpotents. The third part of this paper shows us some crypto systems. We find generalizations of known ciphers taking into account the infinite alphabet and using simple algebraic methods. We also find two cryptosystems in which the structure of Dedekind rings resides, namely certain elements are equivalent to fractional ideals. Finally, we find the use of polynomial composites and monoid domains in cryptology.

CORRELATION BETWEEN ANTONYMS AND OTHER LEXICAL AND SEMANTIC CATEGORIES

The article argues that antonymous words are not isolated in the language but are part of the general scheme of thematic classification of the vocabulary, entering into close ties with representatives of synonymous and polysemantic groups. Proof of this position is the availability of antonymous-synonymous blocks and paradigms of meanings of antonymous words-polysemants in the language. This fact serves to understand the antonymy of lexical as a relationship between members of opposing dichotomous series, as well as expands the boundaries of closed binary structures, which are traditionally used to make antonymous connections. Antonymous relations are established to connect two opposites in pairs, as well as to combine several units into one polynomial structure. Words are found to have more antonyms than the corresponding number of meanings. This proves that some semes of one word are opposed by two or more synonymous antonyms. From the above-mentioned, it follows that the antonyms of polysemous words can be stated only within one family. Such a framework can be defined by limiting the range of antonymous units to a third common concept, under which two antonyms are summed up; establishing the antonyms of polysemous words through the contextual indicative minimum; distinguishing between the direct and figurative meaning of the word. The antonymous connections within the framework of the synonymous-antonymous paradigm are established to demonstrate a qualitatively heterogeneous character, differ in the strength of the manifestation of the relations of opposites and the frequency of practical implementation. The analysis of the manifestations of antonyms between the members of the dichotomous synonymous series allows distinguishing the following types: radial, linear, and cross radial. It is proved that the quantitative indicator of the formation of certain antonymous pairs from among the members of synonymous series depends on the volume of the synonymous series being compared, from the nature of semantic differences of the words of each series, from the emotional, evaluative, and stylistic characteristics of the members of the series, and the distribution of the words with relatively opposite meanings.

Modeling and simulating dynamics of lithium-ion batteries using block-oriented models with piecewise linear static nonlinearity

The article deals with the research of the efficiency of modelling the dynamics of voltage change in lithium-ion rechargeable batteries in charging/discharging modes using nonlinear block-oriented systems. Drawing on experimental data, a structural and parametric identification of the Hammerstein, Wiener and Hammerstein-Wiener models with a polynomial structure of the linear dynamic block and piecewise linear static nonlinearities was performed. It has been established that the best modelling accuracy was ensured by using the Hammerstein-Wiener system with a linear model having the 6th order of the numerator and denominator polynomials and an input delay of 3 samples. It showed 15.67% and 6.2% higher accuracy compared to the Wiener and Hammerstein systems, respectively. The application of those models in battery management systems will make it possible to improve the control quality for battery assemblies of solar and wind power plants in the context of the variable nature of the charging/discharging processes due to the variability of weather conditions and fluctuations in power consumption during a 24-hour period. This will ensure a wider introduction of renewable power generation into existing power systems, which is currently the leading way to ensure sustainable development of the energy sector.

Robust stabilization and tracking control schemes for disturbed multi-input multi-output Hammerstein model in presence of approximate polynomial nonlinearities

This article presents robust stabilization and tracking control problems for multi-input multi-output Hammerstein model with external disturbances. This model is characterized by static nonlinear elements followed by a linear dynamic block. Moreover, the unknown parameters of the identified mathematical model are estimated using the multivariable output error state space subspace algorithm. Unlike the general control strategy that used the nonlinearity inversion method, the nonlinearities are supposed not bijective. In this context, inverse nonlinear functions of polynomial structure are suggested in this article. Furthermore, the composition of the static nonlinear elements and their approximate inverses in series with the linear dynamic block are then decomposed into a set of linear parts using the Takagi–Sugeno fuzzy representation. Consequently, new sufficient stability conditions with decay rate and disturbance attenuation using the [Formula: see text] criterion and linear matrix inequality tools are discussed. Finally, simulation studies are provided to illustrate the merit of our purpose.

Growth rate for endomorphisms of finitely generated nilpotent groups

We prove that the growth rate of an endomorphism of a finitely generated nilpotent group is equal to the growth rate of the induced endomorphism on its abelianization, generalizing the corresponding result for an automorphism in [T. Koberda, Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups, In the Tradition of Ahlfors–Bers. VI, Contemp. Math. 590, American Mathematical Society, Providence 2013, 87–99].

Population Age Structure and Greenhouse Gas Emissions from Road Transportation: A Panel Cointegration Analysis of 21 OECD Countries

Using panel data from 21 Organization for Economic Cooperation and Development (OECD) countries collected between 2000 and 2016, this study analyzes the effect of age structure on greenhouse gas (GHG) emissions from road transportation. Previous studies have failed to reflect the driver’s behavior patterns, especially by age group. We apply the Fully-Modified Ordinary Least Squares (FMOLS) method, including the age structure effect by reorganizing 17 age groups into a polynomial structure. The age structure exhibits an asymmetric inverted U-shaped effect on GHG emissions. Initially, people emit more GHGs as they age, and reach peak emissions in their late 20s, after which emissions fall until around the age of 70, when GHG emissions remain constant because of minimum mobility demand. Factors, such as higher income, increased vehicle ownership, and raised transport volumes increase emission rates. On the other hand, fuel transition and increased fuel price, population density, urbanization rate, and fuel economy reduce GHG emissions. Furthermore, we perform a projection of GHG emissions until 2050, and conclude that the effect of age structure is limited because of the minimum mobility demand of the elderly. We conclude that various policy measures, such as increased fuel economy and urbanization, must be considered in order to achieve sustainable transport

The Development of Fast Algorithm for Continuous-Time Subsectional Polynomial E-Pulse Synthesis

This paper discusses the development in the E-pulse technique, also known as the method of extinction pulse, which is an aspect-independent approach to ultra-wideband radar target discrimination in which each target can be characterized by the set of its natural resonances. It is shown that subsectional polynomial E-pulse can be constructed without composing a linear problem and further solution of the underlying matrix equation set. The key concept of the proposed algorithm consists of several steps, where the first one is building a skeleton E-pulse of an especial waveform, the second step is its extension, and the final step is the series of integration. The polynomial structure of the pulse allows above listed steps to be performed over the coefficients of basic functions rather than the functions themselves. As a result, the proposed solution could perform up to a thousand times faster than one based on direct matrix solution. It also provides the coefficients of the polynomial E-pulse sections without solving a linear problem associated with ill-conditioned sparse matrix in its left-hand side. The E-pulse signals synthesized by means of the fast algorithm are proven to be exactly the same as one synthesized by the direct approach. The numerical example given in the paper exposures the main features of the E-pulse technique. The discrimination scheme where two aircraft scaled model targets are involved is simulated.It was shown that the E-pulse discrimination number provides the effective tool for measuring the energy of the late-time part of the convolution as a measure of the difference of two pole sets belonging to the responses under comparison.

Observer-Based Control for Uncertain Nonlinear Systems Applied to Continuous Biochemical Reactors

The purpose of this paper is to present an observer-based control design with application to continuous bioreactors. For this purpose, phenomenological bioreactor models were represented by identified linear models plus unknown modelling error terms. Therefore, an uncertainty-based observer with a polynomial structure capable of estimating the unknown modelling error of the reactor representation is coupled to a linear input-output controller. The proposed methodology was evaluated in a sulphate reduction bioprocess and an acetone-butanol-ethanol (ABE) fermentation process for butanol (biofuel) production, under continuous regimes. Experimentally validated mathematical models were considered for this purpose. A theoretical framework is presented to demonstrate the corresponding closed-loop stability of the systems, and numerical simulations were carried out to corroborate the satisfactory performance of the proposed methodology.