Perturbed generalized half-linear Riemann-Weber equation - further oscillation results

We establish new oscillation and nonoscillation criteria for the perturbed generalized Riemann-Weber half-linear equation with critical coefficients (Phi (x'))' + (gamma p/t(p) + Sigma(n)(j=1) mu(p)/t(p)Log(j)(2)t + (c) over tilde (t))Phi(x) = 0 in terms of the expression 1/log(n + 1) t integral(t)(c) over tilde (s) s(p-1) Log(n)s log(n+1)(2) s ds. The obtained criteria complement results of [O. Dosly, Electron. J. Qual. Theory Differ. Equ., Proc. 10'th Coll. Qualitative Theory of Diff. Equ. 2016, No. 10, 1-14]

Nonoscillatory solutions of half-linear Euler-type equation with n terms

We consider the half-linear Euler-type equation with n terms (Phi(x '))'+(gamma(p)/t(p) + Sigma(n-1)(j=1) mu(p)/t(p)Log(j)(2)t +mu/t(p)Log(n)(2)t)Phi(x)=0, Phi(x)=|x|(p-1)sgnx in the subcritical case when 01. The solutions of this nonoscillatory equation cannot be found in an explicit form and can be studied only asymptotically. In this paper, with the use of the perturbation principle, modified Riccati technique, and the fixed point theorem, we establish an asymptotic formula for one of its solutions

Asymptotic formulas for solutions of half-linear Euler-Weber equation

We establish improved asymptotic formulas for nonoscillatory solutions of the half-linear Euler-Weber type differential equation $$(\Phi(x'))'+\left[\frac{\gamma_p}{t^p}+\frac{\mu_p}{t^p\log^2 t}\right]\Phi(x)=0, \quad \Phi(x):=|x|^{p-2}x,\quad p>1$$ with critical coefficients $$\gamma_p=\left(\frac{p-1}{p}\right)^p, \quad \mu_p= \frac{1}{2}\left(\frac{p-1}{p}\right)^{p-1},$$ where this equation is viewed as a perturbation of the half-linear Euler equation

Hille-Wintner type comparison kriteria for half-linear second order differential equations

summary:We establish Hille-Wintner type comparison criteria for the half-linear second order differential equation $$\left(r(t)\Phi (x^{\prime })\right)^{\prime }+c(t)\Phi (x)=0,\quad \Phi (x)=|x|^{p-2}x\,,\ p>1\,,$$ where this equation is viewed as a perturbation of another equation of the same form

Integral comparison criteria for half-linear differential equations seen as a perturbation

In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation). © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Hille-Nehari type criteria and conditionally oscillatory half-linear differential equations

We study perturbations of the generalized conditionally oscillatory half-linear equation of the Riemann-Weber type. We formulate new oscillation and nonoscillation criteria for this equation and find a perturbation such that the perturbed Riemann-Weber type equation is conditionally oscillatory

A comparative study of Tarski's fixed point theorems with the stress on commutative sets of L-fuzzy isotone maps with respect to transitivities

The paper deals mainly with a fuzzification of the classical Tarski's theorem for commutative sets of isotone maps (the so-called generalized theorem) in a sufficiently rich fuzzy setting on general structures called L-complete propelattices. Our concept enables a consistent analysis of the validity of single statements of the generalized Tarski's theorem in dependence on assumptions of relevant versions of transitivity (weak or strong). The notion of the L-complete propelattice was introduced in connection with the fuzzified more famous variant of Tarski's theorem for a single L-fuzzy isotone map, whose main part holds even without the assumption of any version of transitivity. These results are here extended also to the concept of the so-called L-fuzzy relatively isotone maps and then additionally compared to the results, which are achieved for the generalized theorem and which always need a relevant version of transitivity. Wherever it is possible, facts and differences between both the theorems are demonstrated by appropriate examples or counterexamples. © 2018 Elsevier B.V

Use of the modified riccati technique for neutral half-linear differential equations

We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equation is ensured by the divergence of a certain integral. The second one provides the condition of the oscillation in the case where the relevant integral converges, and it can be seen as a Hille–Nehari-type criterion. The use of the results is shown in several examples, in which the Euler-type equation and its perturbations are considered. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Fractional viscoelastic models of porcine skin and its gelatin-based surrogates

Viscoelasticity of porcine skin and its material substitute, modelled by variously concentrated bovine gelatin, was determined in static (creep test) and dynamic (oscillatory test) mode by the means of rotational rheometry to obtain creep compliance and complex shear modulus. Mechanical properties characterization was also supplemented with large deformation compression test in order to determine and correlate shear and compression moduli of gelatin with its concentration dependence. Obtained data was fitted with fractional viscoelastic models (Poynting-Thomson, Maxwell) in order to quantify in detail gelatin's transition from viscous-like behavior towards solid-like state with increasing gelatin concentration and hence crosslinking density. Potential of gelatin as biomaterial for skin surrogate was identified as well as a concentration region in which gelatin exhibits closest viscoelastic behavior to native porcine skin used. © 2023 The AuthorsMinisterstvo Školství, Mládeže a Tělovýchovy, MŠMT; Grantová Agentura České Republiky, GA ČR: 23-07244

Capacity Building in Mathematics and Statistics Learning Support in Norway and the Czech Republic (MSLS Net)

This report describes the final meeting of the project "Capacity Building in Mathematics and Statistics Learning Support in Norway and the Czech Republic (MSLS Net)" held at the Tomas Bata University in Zlín, Czech Republic (June 12-14, 2023). Provision of mathematics and statistics learning support (MSLS) is developing rapidly in many parts of the world and activity in Norway and the Czech Republic has been accelerated significantly through this EEA Grants funded project. Representatives of each of the five partner institutions worked on creating a summary of good practices in tutor training, designing learning resources, and in delivering, monitoring and evaluation of mathematics and statistics support. Provision varied considerably across the institutions and the centres represented demonstrated diverse and innovative ways in which mathematics support is evolving. Outputs from the project include a Handbook on good practice and a booklet concerned with mathematics support centre tutor training, including pedagogic training and learning resources for the development of the tutors as described below. Finally, consideration turned to the value of establishing a professional network to continue this important work. The report will be relevant to other international groups interested in working in university level mathematics and statistics support