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Fully discrete convergence analysis of non-linear hyperbolic equations based on finite element analysis

Abstract

With the development of modern partial differential equation (PDE) theory, the theory of linear PDE is becoming more and more perfect, . Non-linear PDE has become a research hotspot of many mathematicians. In fact, when describing practical physical problems with PDEs, non-linear problems tend to be more general than linear problems, which are close to real problems and have practical physical significance. Hyperbolic PDEs are a kind of important PDEs describing the phenomena of vibration or wave motion. The solution of hyperbolic PDE can be decomposed into the form of multiplication of vibration and vibration or of exponential function and exponential function. Generally, the energy is infinite. A full discrete convergence analysis method for non-linear hyperbolic equation based on finite element analysis is proposed. Taking second-order and fourth-order non-linear hyperbolic equation as examples, the full discrete convergence of non-linear hyperbolic equation is analysed by finite element method and the super-convergence results are obtained.

Open access
Investigation of A Fuzzy Problem by the Fuzzy Laplace Transform

Abstract

This paper is on the solutions of a fuzzy problem with triangular fuzzy number initial values by fuzzy Laplace transform. In this paper, the properties of fuzzy Laplace transform, generalized differentiability and fuzzy arithmetic are used. The example is solved in relation to the studied problem. Conclusions are given.

Open access
A New Approach For Weighted Hardy’s Operator In VELS

Abstract

A considerable number of research has been carried out on the generalized Lebesgue spaces L p(x) and boundedness of different integral operators therein. In this study, a new approach for weighted increasing near the origin and decreasing near infinity exponent function that provides a boundedness of the Hardy’s operator in variable exponent space is given.

Open access
Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

Abstract

A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

Open access
EVALD – a Pioneer Application for Automated Essay Scoring in Czech

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.

Open access
Multidimensional BSDE with Poisson jumps of Osgood type

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.

Open access
Replacing Linguists with Dummies: A Serious Need for Trivial Baselines in Multi-Task Neural Machine Translation

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.

Open access
QSPR Analysis of certain Distance Based Topological Indices

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.

Open access
The Effect of Elastic and Inelastic Scattering on Electronic Transport in Open Systems

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.

Open access
Efficient Astronomical Data Condensation Using Approximate Nearest Neighbors

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.

Open access