## Abstract

The parafree Lie algebras are an extraordinary class of Lie algebras which shares many properties with a free Lie algebra. In this work, we turn our attention to soluble product of parafree Lie algebras. We show that soluble product of parafree Lie algebras is parafree. Furthermore, we investigate some residual properties of that product.

## Abstract

In this paper, we adopt the model of [12] by including fuzzy initial values to study the interaction of a monoclonal brain tumor and the macrophages for a condition of extinction of GB(Glioblastoma) by using Allee threshold. Numerical simulations will give detailed information on the behavior of the model at the end of the paper. We perform all the computations in this study with the help of the Maple software.

## Abstract

Different types of number theories such as elementary number theory, algebraic number theory and computational number theory; algebra; cryptology; security and also other scientific fields like artificial intelligence use applications of quadratic fields. Quadratic fields can be separated into two parts such as imaginary quadratic fields and real quadratic fields. To work or determine the structure of real quadratic fields is more difficult than the imaginary one.

The Dirichlet class number formula is defined as a special case of a more general class number formula satisfying any types of number field. It includes regulator, 𝓛-function, Dedekind zeta function and discriminant for the field. The Dirichlet’s class number *h*(*d*) formula in real quadratic fields claims that we have

for positive *d* > 0 and the fundamental unit *ε _{d}* of ℚ(

*ε*are significant and necessary tools for determining the structure of real quadratic fields.

_{d}The focus of this paper is to determine structure of some special real quadratic fields for *d* > 0 and *d* ≡ 2, 3 (*mod* 4). In this paper, we provide a handy technique so as to calculate particular continued fraction expansion of integral basis element *w _{d}*, fundamental unit

*ε*, and so on for such real quadratic number fields. In this paper, we get fascinating results in the development of real quadratic fields.

_{d}## Abstract

In the paper, we present EVALD applications (Evaluator of Discourse) for automated essay scoring. EVALD is the first tool of this type for Czech. It evaluates texts written by both native and non-native speakers of Czech. We describe first the history and the present in the automatic essay scoring, which is illustrated by examples of systems for other languages, mainly for English. Then we focus on the methodology of creating the EVALD applications and describe datasets used for testing as well as supervised training that EVALD builds on. Furthermore, we analyze in detail a sample of newly acquired language data – texts written by non-native speakers reaching the threshold level of the Czech language acquisition required e.g. for the permanent residence in the Czech Republic – and we focus on linguistic differences between the available text levels. We present the feature set used by EVALD and – based on the analysis – we extend it with new spelling features. Finally, we evaluate the overall performance of various variants of EVALD and provide the analysis of collected results.

## Abstract

This paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under linear growth generator, we prove existence and uniqueness of solution.

## Abstract

Recent developments in machine translation experiment with the idea that a model can improve the translation quality by performing multiple tasks, e.g., translating from source to target and also labeling each source word with syntactic information. The intuition is that the network would generalize knowledge over the multiple tasks, improving the translation performance, especially in low resource conditions. We devised an experiment that casts doubt on this intuition. We perform similar experiments in both multi-decoder and interleaving setups that label each target word either with a syntactic tag or a completely random tag. Surprisingly, we show that the model performs nearly as well on uncorrelated random tags as on true syntactic tags. We hint some possible explanations of this behavior.

The main message from our article is that experimental results with deep neural networks should always be complemented with trivial baselines to document that the observed gain is not due to some unrelated properties of the system or training effects. True confidence in where the gains come from will probably remain problematic anyway.

## Abstract

In QSAR/QSPR study, topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we study the QSPR analysis of selected distance and degree-distance based topological indices. Our study reveals some important results which help us to characterize the useful topological indices based on their predicting power.

## Abstract

The purpose of this study is to apply the distribution function formalism to the problem of electronic transport in open systems, and to numerically solve the kinetic equation with a dissipation term. This term is modeled within the relaxation time approximation and contains two parts, corresponding to elastic or inelastic processes. The collision operator is approximated as a sum of the semi-classical energy dissipation term and the momentum relaxation term, which randomizes the momentum but does not change the energy. As a result, the distribution of charge carriers changes due to the dissipation processes, which has a profound impact on the electronic transport through the simulated region discussed in terms of the current–voltage characteristics and their modification caused by the scattering. Measurements of the current–voltage characteristics for titanium dioxide thin layers are also presented, and compared with the results of numerical calculations.

## Abstract

Extracting useful information from astronomical observations represents one of the most challenging tasks of data exploration. This is largely due to the volume of the data acquired using advanced observational tools. While other challenges typical for the class of big data problems (like data variety) are also present, the size of datasets represents the most significant obstacle in visualization and subsequent analysis. This paper studies an efficient data condensation algorithm aimed at providing its compact representation. It is based on fast nearest neighbor calculation using tree structures and parallel processing. In addition to that, the possibility of using approximate identification of neighbors, to even further improve the algorithm time performance, is also evaluated. The properties of the proposed approach, both in terms of performance and condensation quality, are experimentally assessed on astronomical datasets related to the GAIA mission. It is concluded that the introduced technique might serve as a scalable method of alleviating the problem of the dataset size.

## Abstract

This paper proposes a new method for the analysis of continuous and periodic event-based state-feedback plus static feed-forward controllers that regulate linear time invariant systems with time delays. Measurable disturbances are used in both the control law and triggering condition to provide better disturbance attenuation. Asymptotic stability and *L*2-gain disturbance rejection problems are addressed by means of Lyapunov–Krasovskii functionals, leading to performance conditions that are expressed in terms of linear matrix inequalities. The proposed controller offers better disturbance rejection and a reduction in the number of transmissions with respect to other robust event-triggered controllers in the literature.