Papers by Natalija Sergejeva
We consider solving linear ill-posed problems by conjugate gradient type methods. Typically only ... more We consider solving linear ill-posed problems by conjugate gradient type methods. Typically only noisy data are available. It is important to stop iterations at the right moment, choosing the stopping index properly according to the noise level. For finding stopping index we formulate the monotone error rule and another rule which works well also for approximately given noise level. Numerical comparison with known rules shows that the new rules are competitive.
Communications in Applied Analysis
In this article we consider the equation x ′′ = -µf (x + ) + λg(x -), where x + = max{x, 0}, x -=... more In this article we consider the equation x ′′ = -µf (x + ) + λg(x -), where x + = max{x, 0}, x -= max{-x, 0}, together with the boundary conditions We give description of a set of (µ, λ) such that the problem has a nontrivial solution.
21st International Scientific Conference Engineering for Rural Development Proceedings
COVID-19 has changed the pedagogical work of university lecturers. All lecturers have been forced... more COVID-19 has changed the pedagogical work of university lecturers. All lecturers have been forced to learn quickly and to find new educational solutions for distance learning. The biggest challenges were in organizing and conducting laboratory work remotely and in motivating students to participate actively in the learning process. During the online teaching period, university lecturers have gained new knowledge, skills and tried various pedagogical solutions. These include the use of different software applications, creation of short video lectures, the use of pre-prepared video and audio instructions, and many more. In this paper, a qualitative content analysis was used to study the case of teaching with technologies to engineering students at universities in Latvia and Lithuania. The study discloses the challenges faced by university lecturers in preparing video materials, organizing laboratory work, and assessing student performance. Recommendations based on the research findings have been provided. These recommendations could be useful not only for university lecturers who teach engineering subjects but also for science, technology, engineering, arts, and mathematics pedagogues and vocational education trainers and educators.
We construct the spectra for some second order boundary value problem of Fucik type. This spectru... more We construct the spectra for some second order boundary value problem of Fucik type. This spectrum differs essentially from the known Fucik spectra.
Abstract. We construct the spectra for some second order boundary value problem of Fučík type. Th... more Abstract. We construct the spectra for some second order boundary value problem of Fučík type. This spectrum differs essentially from the known Fučík spectra. 1. Introduction. In
20th International Scientific Conference Engineering for Rural Development, ERD 2021, 2021
Innovation is needed for the 21st century education around the world. Nowadays, traditional class... more Innovation is needed for the 21st century education around the world. Nowadays, traditional classroom teaching methods, in which the learners passively participate and the teacher controls everything, are no longer relevant. The impact of information and technological change is also visible in the field of education. The meaning of such concepts as education, teachers, learner, learning process is changing. Therefore, it is necessary to diversify learning models. Key components such as face-to-face teaching, effective learning strategies, and the use of learning technologies are common to all practices. Given today's needs and the profile of 'learners', it is obvious that different teaching methods are needed than traditional ones. This is the time of digital students, and if teachers want to teach the younger generation, they should redesign their methods and materials according to the learning style of the learners. This article was designed to assess the impact of COV...
19th International Scientific Conference Engineering for Rural Development Proceedings
Statistical data in recent years show stable interest in engineering sciences at higher schools i... more Statistical data in recent years show stable interest in engineering sciences at higher schools in Latvia. In the present academic year, in the programs of engineering sciences and natural sciences in total about 7 thousand first year students have been enrolled, which is approximately the same as last year. At the same time, every year also large numbers of students leave the studies already in the first year. The teachers working with the first year students (including the teachers of Higher mathematics and Physics) often meet with the problem that the new students do not have equal level of preliminary knowledge. It is due to the different number of lessons in Mathematics and Physics at the secondary schools in different education programs. Qualitative engineering studies are not possible without profound preparation in mathematics. In turn, the course in Physics is like a bridge between Mathematics and Engineering science. Analysing the results of the tests of the first year LLU students, which were performed at the beginning of studies after finishing the secondary school, and the achievements of the students in the courses of Mathematics and Physics after the first semester, it was concluded that, if there is a wish to maintain the number of students in engineering sciences, there must be a repetition course in Mathematics, as well as in Physics.
The basic mathematical skills are acquired in elementary school. This research compares basic mat... more The basic mathematical skills are acquired in elementary school. This research compares basic mathematical knowledge of three groups -elementary school graduates, students from four different specialties (future engineers) with varied levels of higher mathematics and future teachers of mathematics. The study concludes that students from elementary school have better knowledge in comparison with students from university. The possible reason for that is resent acquirement of the study material and examination at finishing elementary school. It is also observed that several students had taken gap years between school and university, but the current educational system in Latvia does not require entrance examinations. Modern engineering education is founded on good basics of mathematics that are acquired in elementary school. The experience shows that acquisition of the course of mathematics at elementary school is the determinant factor for further successful acquisition of the course of higher mathematics.
Nonlinear Analysis: Modelling and Control
We construct the Fučik spectrum for some second order boundary value problem with nonlocal bounda... more We construct the Fučik spectrum for some second order boundary value problem with nonlocal boundary condition. This spectrum differs essentially from the known Fučik spectra. We apply this result to the second order differential equation x'' + g(x) = f(t, x, x') with the conditions x(a) = 0, ∫ab x(s)ds = 0.
Engineering for Rural Development
It is a well known fact that a large number of students leave their studies already during the fi... more It is a well known fact that a large number of students leave their studies already during the first year. Some of them understand that it is not the right specialty for them; some students mention their inability to acquire definite study subjects, for instance, the course of higher mathematics, as the reason for leaving studies. It should be noted that often the problems do not arise due to the acquisition of higher mathematics, but due to the lack in the basic knowledge in mathematics. The results of testing the first year students in the knowledge of mathematics of the elementary school level show that about 60 % of them have unsatisfactory knowledge. These are the students, who potentially will not be able to acquire the course in higher mathematics of full value. The problem arises how to help them, as they may become (or already are) good specialists in their branch of specialty. This year, in cooperation of the teachers of the Department of Higher Mathematics and the Faculty of Food Engineering, a study course "Elementary Mathematics" (1CP) was organised. The students, whose test results were unsatisfactory, were especially invited to attend this course. Finishing the course, the students were tested once more. The results of this test showed that the students' knowledge in elementary mathematics has essentially improved. The offered solution is not universal, as it helps only fill the gaps in knowledge, but it cannot help acquire all knowledge and skills of elementary mathematics within several hours.
Nonlinear Analysis: Modelling and Control
The Fučík equation x' '= -μ x+λ x- with two types of nonlocal boundary value conditions a... more The Fučík equation x' '= -μ x+λ x- with two types of nonlocal boundary value conditions are considered. The Fučík type spectrum for both problems are constructed. The visualization of the spectrum for some values of parameter γ is provided.
Proceedings of The 10'th Colloquium on the Qualitative Theory of Differential Equations (July 1–4, 2015, Szeged, Hungary) edited by: T. Krisztin
The Fučík equation
AIP Conference Proceedings, 2009
We consider two types of Fučík like spectra, which have somewhat peculiar features. The first one... more We consider two types of Fučík like spectra, which have somewhat peculiar features. The first one stretches along the bysectrix of the plane of parameters, the second one may contain separated components. Both spectra are significant for existence of solutions to nonlinear boundary value problems with nonlinearities having asymmetric asymptotics.
Nonlinear Analysis: Modelling and Control, 2014
Boundary value problem of the form x
Mathematical Modelling and Analysis, 2008
We consider a second order nonlinear differential equation with nonlocal (integral) condition. Th... more We consider a second order nonlinear differential equation with nonlocal (integral) condition. The spectrum of it differs essentially from the known ones.
Mathematical Modelling and Analysis, 2014
The solvability results are established for the boundary value problem with a damping term
Mathematical Modelling and Analysis, 2007
We construct the Fučik spectrum for some third order nonlinear boundary value problems. This spec... more We construct the Fučik spectrum for some third order nonlinear boundary value problems. This spectrum differs essentially from the known Fučik spectra.
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Papers by Natalija Sergejeva