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- ItemConcentration of solutions for non-autonomous double-phase problems with lack of compactness(Springer Nature, 2024-07-20) zhang, Weiqiang; Zuo, Jiabin; Radulescu, VicentiuThe present paper is devoted to the study of the following double-phase equation (Formula presented.) where N2, 1
- ItemInquiry-Based Linear Algebra Teaching and Learning in a Flipped Classroom Framework: A Case Study(Taylor & Francis, 2024-07-17) Fredriksen, Helge; Rebenda, Josef; Rensaa, Ragnhild Johanne; Pettersen, PetterFlipped Classroom (FC) approaches, which utilize video distribution via modern internet platforms, have recently gained interest as a pedagogical framework. Inquiry Based Mathematics Education (IBME) has proven to be a valid form of task design to motivate active learning and enhance classroom interactivity. This article presents a practical combination of introductory videos and inquiry-based class activities adoptable in a basic linear algebra course for stimulating students’ exploration of the underlying mathematics. Teachers’ and students’ work addressed in the article was realized in two case studies in engineering programs in Norway and the Czech Republic. The learning objective was to connect different interpretations of the matrix equation Ax=b, which is often perceived as challenging for engineering students. Feedback from classroom sessions, interviews, and questionnaires encourage further research and inspired us as teachers to closely examine the mathematics behind the task design.
- ItemBounded solutions of delay dynamic equations on time scales(Springer Nature, 2012-10-24) Diblík, Josef; Vítovec, JiříIn this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where $f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$ is a delay function and $\mathbb{T}$ is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example.
- ItemThe role of Campylobacter spp. in chronic enteropathy in dogs(2019-10-31) Vávra, Miloš; Bořilová, Gabriela; Fusek, Michal; Gabriel, Vojtěch; Ceplecha, Václav; Skoric, Misa; Crha, MichalThe aim of the study is to identify Campylobacter species in a group of patients with chronic gastrointestinal problems and to investigate the relationship between the presence of Campylobacter spp. in stool samples and as well as the severity of chronic enteropathy. Twenty-six dogs with chronic gastrointestinal problems were included in the prospective study. Each research subject had their stomach, duodenum, ileum, and colon examined endoscopically. A histopathological examination of the obtained biopsy samples was then performed afterwards, other potential diseases were excluded. Stool samples were collected and then examined for the presence of Campylobacter spp. To evaluate the relationship between Campylobacter spp. occurrence and the intensity of chronic enteropathy, patients were divided into two groups; animals in the first group presented with no to mild inflammation whereas research subjects in the second group suffered from moderate to severe inflammation. Subsequently, the patients were divided based on positive or negative test results for Campylobacter spp. cultures. No statistically significant relationship between the presence of Campylobacter spp. in stool samples and chronic enteropathy was found. In contrast to other previously published papers, our study showed a lower occurrence of Campylobacter upsaliensis.
- ItemVanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point(De Gruyter, 2024-02-05) Diblík, Josef; Růžičková, MiroslavaA singular nonlinear differential equation z(sigma) dw/dz = aw + zwf(z , w), where sigma > 1, is considered in a neighbourhood of the point z = 0 z=0 located either in the complex plane C if sigma is a natural number, in a Riemann surface of a rational function if sigma is a rational number, or in the Riemann surface of logarithmic function if sigma is an irrational number. It is assumed that w = w ( z ) w=w\left(z) , a is an element of C { 0 } a, and that the function f f is analytic in a neighbourhood of the origin in C x C . Considering sigma to be an integer, a rational, or an irrational number, for each of the above-mentioned cases, the existence is proved of analytic solutions w = w (z ) w=w(z) in a domain that is part of a neighbourhood of the point z = 0 z=0 in C or in the Riemann surface of either a rational or a logarithmic function. Within this domain, the property lim z -> 0 w (z) = 0 is proved and an asymptotic behaviour of w (z) s established. Several examples and figures illustrate the results derived. The blow-up phenomenon is discussed as well.