298 research outputs found
Resolvent convergence of Sturm-Liouville operators with singular potentials
In this paper we consider the Sturm-Liuoville operator in the Hilbert space
with the singular complex potential of 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
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