Resolvent convergence of Sturm-Liouville operators with singular potentials

In this paper we consider the Sturm-Liuoville operator in the Hilbert space $L_2$ with the singular complex potential of $W^{-1}_2$ and two-point boundary conditions. For this operator we give sufficient conditions for norm resolvent approximation by the operators of the same class.Comment: 6 pages, to appear in Math. Note

Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Web quest method in online teaching Ukrainian as a foreign language in higher educational institutions

Introduction. The research is topical due to the need to find effective methods of teaching Ukrainian to foreign students. The development of information technology urged the development of communicative competencies in foreign students. So, the web quest method is becoming increasingly popular in the study of foreign languages in higher educational institutions around the world. This method is an effective tool that allows a full involvement of foreign students in learning Ukrainian as a foreign language. Methods: testing students for the level of proficiency in Ukrainian as a foreign language, statistical and mathematical processing of results using Pearson’s formulas. Results: The results of the study showed the high efficiency of the web quest method in the experimental group in comparison with traditional teaching methods. According to all the criteria studied, the students of the experimental group showed higher results than the students of the control group, which proves the effectiveness of this method. Namely, the indicator of lexical skills of the experimental group with the excellent grade exceeds the indicator of the control group by 10.2%. The indicator of grammar skills of the experimental group with the excellent grade exceeds the indicator if the control group by 7.7%. And the indicator of phonetic skills of the experimental group with the excellent grade exceeds the indicator of the control group by 8.4%. There were 55.74% of foreign students who showed a high level of information search and analysis skills. Conclusion: The study notes the high efficiency of using the web quest method in the development of various communicative competencies in foreign students. Therefore, the expediency of using the web quest method in teaching Ukrainian as a foreign language to foreign students has been established. Prospects: further research will be aimed at studying the effectiveness of web quests for the development of professional communicative competencies for other subjects

Sampling Plans for Control-Inspection Schemes Under Independent and Dependent Sampling Designs With Applications to Photovoltaics

The evaluation of produced items at the time of delivery is, in practice, usually amended by at least one inspection at later time points. We extend the methodology of acceptance sampling for variables for arbitrary unknown distributions when additional sampling infor- mation is available to such settings. Based on appropriate approximations of the operating characteristic, we derive new acceptance sampling plans that control the overall operating characteristic. The results cover the case of independent sampling as well as the case of dependent sampling. In particular, we study a modified panel sampling design and the case of spatial batch sampling. The latter is advisable in photovoltaic field monitoring studies, since it allows to detect and analyze local clusters of degraded or damaged modules. Some finite sample properties are examined by a simulation study, focusing on the accuracy of estimation