COMPUTER TOOLS FOR SOLVING MATHEMATICAL PROBLEMS: A REVIEW

The rapid development of digital computer hardware and software has had a dramatic influence on mathematics, and contrary. The advanced hardware and modern sophistical software such as computer visualization, symbolic computation, computerassisted proofs, multi-precision arithmetic and powerful libraries, have provided resolving many open problems, a huge very difficult mathematical problems, and discovering new patterns and relationships, far beyond a human capability. In the first part of the paper we give a short review of some typical mathematical problems solved by computer tools. In the second part we present some new original contributions, such as intriguing consequence of the presence of roundoff errors, distribution of zeros of random polynomials, dynamic study of zero-finding methods, a new three-point family of methods for solving nonlinear equations and two algorithms for the inclusion of a simple complex zero of a polynomial.

Metasurface virtual absorbers: unveiling operative conditions through equivalent lumped circuit model

Virtual absorption concept has been recently introduced as a new phenomenon observed in electromagnetics and optics consisting of theoretically unlimited accumulation of energy within a finite volume of material without dissipation. The anomalous behaviour is achieved by engaging the complex zero scattering eigenmodes of the virtual absorbing system by illuminating it with a proper complex frequency ω = ω r + jω i , whose value is strictly determined by the system characteristics. In this paper, we investigate on the position of the zero-pole scattering pairs in the complex frequency plane as a function of the input impedance of the metasurface-based lossless virtual absorber. We analytically derive the conditions under which a properly modulated monochromatic plane wave can be virtually absorbed by the system and stored within its volume. The analysis is developed by modelling the propagation of a normally impinging plane wave through its equivalent transmission line model terminated in an arbitrary reactive load, which in turn models the input impedance of the metasurface-based system under consideration. The study allows to determine a priori whether the metasurface-based system can support the virtual absorption or not by evaluating the time-constant from its equivalent circuit.

Metasurface virtual absorbers: unveiling operative conditions through equivalent lumped circuit model

Virtual absorption concept has been recently introduced as a new phenomenon observed in electromagnetics and optics consisting of an undefined energy accumulation within a finite volume of material without dissipation. The anomalous behaviour is achieved by engaging the complex zero scattering eigenmodes of the virtual absorbing system by illuminating it with a proper complex frequency, whose value is strictly determined by the system characteristics. In this paper, we investigate on the position of the zero-pole scattering pairs in the complex frequency plane as a function of the input impedance of the metasurface-based lossless virtual absorber. We analytically derive the conditions under which a properly modulated monochromatic plane wave can be virtually absorbed by the system and stored within its volume. The analysis is developed by modelling the propagation of a normally impinging plane wave though its equivalent transmission line model terminated on an arbitrary reactive load, which in turn models the input impedance of the metasurface-based system under consideration. The study allows to determine a priori whether the metasurface-based system can support the virtual absorption or not by evaluating the time-constant from its equivalent circuit.

Metasurface virtual absorbers: unveiling operative conditions through equivalent lumped circuit model

Virtual absorption concept has been recently introduced as a new phenomenon observed in electromagnetics and optics consisting of an undefined energy accumulation within a finite volume of material without dissipation. The anomalous behaviour is achieved by engaging the complex zero scattering eigenmodes of the virtual absorbing system by illuminating it with a proper complex frequency, whose value is strictly determined by the system characteristics. In this paper, we investigate on the position of the zero-pole scattering pairs in the complex frequency plane as a function of the input impedance of the metasurface-based lossless virtual absorber. We analytically derive the conditions under which a properly modulated monochromatic plane wave can be virtually absorbed by the system and stored within its volume. The analysis is developed by modelling the propagation of a normally impinging plane wave though its equivalent transmission line model terminated on an arbitrary reactive load, which in turn models the input impedance of the metasurface-based system under consideration. The study allows to determine a priori whether the metasurface-based system can support the virtual absorption or not by evaluating the time-constant from its equivalent circuit.

Utilising Deep Learning Techniques for Effective Zero-Day Attack Detection

Machine Learning (ML) and Deep Learning (DL) have been used for building Intrusion Detection Systems (IDS). The increase in both the number and sheer variety of new cyber-attacks poses a tremendous challenge for IDS solutions that rely on a database of historical attack signatures. Therefore, the industrial pull for robust IDSs that are capable of flagging zero-day attacks is growing. Current outlier-based zero-day detection research suffers from high false-negative rates, thus limiting their practical use and performance. This paper proposes an autoencoder implementation for detecting zero-day attacks. The aim is to build an IDS model with high recall while keeping the miss rate (false-negatives) to an acceptable minimum. Two well-known IDS datasets are used for evaluation—CICIDS2017 and NSL-KDD. In order to demonstrate the efficacy of our model, we compare its results against a One-Class Support Vector Machine (SVM). The manuscript highlights the performance of a One-Class SVM when zero-day attacks are distinctive from normal behaviour. The proposed model benefits greatly from autoencoders encoding-decoding capabilities. The results show that autoencoders are well-suited at detecting complex zero-day attacks. The results demonstrate a zero-day detection accuracy of 89–99% for the NSL-KDD dataset and 75–98% for the CICIDS2017 dataset. Finally, the paper outlines the observed trade-off between recall and fallout.

НЕМОТИВОВАНІ СКЛАДНОНУЛЬСУФІКСАЛЬНІ АД’ЄКТИВИ З ДРУГИМ НЕСОМАТИЧНИМ КОМПОНЕНТОМ НА ОЗНАЧЕННЯ ЛЮДИНИ

The article outlines the derivational, structural-semantic and functional properties of usual and individual-authorial adjectival composites with a materially non-marked suffix with the first adjectival and the second substantive component, denoting a characteristic of a person and having basically non-somatic notion of anthroponymic and non-anthroponymic character. Adjectival composites with the first adjectival and the second substantive component occupy a noticeable place among adjectival derivatives formed with the participation of a zero-suffix formant. So far, composites of the investigated word-formative type in general and complex-zero-suffixal adjectives with a materially non-marked formant in particular have never been the subject of a special study, which determines the relevancy of the chosen topic. The purpose of the article is to define the word-usage frequency of the corresponding complex-zero-suffixal adjectival derivatives, to find out their place, role, specificity of functioning in the modern Ukrainian language, to elucidate their derivational, structural-semantic and functional properties. The achievement of the stated goal involves solving of the following tasks: to determine the peculiar properties of the motivation of the derivatives under study, to analyze the external valency, as well as to find out their pragmatic potential. The conducted analysis of the complex-zero-suffixal adjectival derivatives has revealed the following tendencies: among the composites of the lexical-semantic group being studied, only opaque (non-motivated) composites function actively, while we have not noticed motivated and semi-motivated lexical items among them. Complex-zero-suffixal adjectives have broad co-occurrence and extensively implement their figurative (allegoric) meanings. On the whole, the corresponding composites, entering into distribution with the nouns denoting a person, gain pejorative meaning, becoming the markers of negative evaluation and disparagement. Sometimes it happens that the units under study come into distribution with the nouns denoting the phenomena of nature, realizing a new figurative idiomatic meaning – “the revival” of the nonliving, thus replenishing the corpus of epithets and contributing to the enrichment of the poetic language imagery.

Vibration Antiresonance Design for a Spacecraft Multifunctional Structure

Spacecraft must withstand rigorous mechanical environment experiences such as acceleration, noise, vibration, and shock during the process of launching, satellite-vehicle separation, and so on. In this paper, a new spacecraft multifunctional structure concept designed by us is introduced. The multifunctional structure has the functions of not only load bearing, but also vibration reduction, energy source, thermal control, and so on, and we adopt a series of viscoelastic parts as connections between substructures. Especially in this paper, a vibration antiresonance design method is proposed to realize the vibration reduction. The complex zero-point equations of the vibration system are firstly established, and then the vibration antiresonance design for the system is achieved. For solving the difficulties due to viscoelastic characteristics of the connecting parts, we present the determining formulas to obtain the structural parameters, so that the complex zero-point equations can be satisfied. Numerical simulation and ground experiment demonstrate the correctness and effectiveness of the proposed method. This method can solve the structural vibration control problem under the function constraints of load bearing and energy supplying and will expand the performance of spacecraft functional modules.