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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.

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 supple-mented 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 to-wards 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.

The aim of this paper is to extend an oscillation criterion for the half-linear second order differential equations with delay to a more general form and to discuss relationship between these two variants and the link to the perturbation principle. The proving technique employs the Riccati transformation. © 2022 American Institute of Physics Inc.. All rights reserved.

Nonlinear differential equations are considered to be an important tool for describing a number of phenomena in engineering and the natural sciences, and their study is thus subject to contemporary research. The purpose of the paper is to show applications of the differential transform to second-order half-linear Euler equations with and without delay. The case of proportional delay is considered. Finding a numerical solution to an initial value problem is reduced to solving recurrence relations. The outputs of the recurrence relations are coefficients of the Taylor series of the solution. Validity of the presented algorithm is demonstrated on concrete examples of initial value problems. Numerical results are compared with solutions produced by Matlab function "ddesd".

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.

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.

An algorithm using the differential transformation which is convenient for finding numerical solutions to initial value problems for functional differential equations is proposed in this paper. We focus on retarded equations with delays which in general are functions of the independent variable. The delayed differential equation is turned into an ordinary differential equation using the method of steps. The ordinary differential equation is transformed into a recurrence relation in one variable using the differential transformation. Approximate solution has the form of a Taylor polynomial whose coefficients are determined by solving the recurrence relation. Practical implementation of the presented algorithm is demonstrated in an example of the initial value problem for a differential equation with nonlinear nonconstant delay. A two-dimensional neutral system of higher complexity with constant, nonconstant, and proportional delays has been chosen to show numerical performance of the algorithm. Results are compared against Matlab function DDENSD.

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.

The aim of this paper is to present a survey of already known results on asymptotics of nonoscillatory solutions of Riemann-Weber type half-linear differential equation and to sketch some ideas which could lead to further results in this field. © 2019 Author(s).

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.

Recently several authors have started to examine qualitative properties of fractional equations and among them, some have devoted their attention to equations with the so called modified Riemann-Liouville derivative, which was established by Jumarie. Their results utilize nice properties of Jumarie operator and in fact convert statements from integer order differential equations to those with Jumarie derivative. The aim of this paper is to give a survey of existing results and comment on the possibility of getting similar results when converting from half-linear criteria. © 2018 Author(s).

Digital Video Broadcast - Terrestrial (DVB-T) can be seen as a complex system with many concrete features and aspects. This paper presents a simplified model and the first insight into this system from point of view of formal modelling methods. Using Event-B a start-up model concerning relations between signals, multiplexes and channels is introduced. As a background the standards for DVB-T in the Czech Republic are taken. © 2017 Author(s).

For the case of classical Tarski's theorem on fixed points of isotone maps we show that embedding of this statement into fuzzy logical environment leads to surprising results, which cannot be easily seen and awaited in classical logical environment. © 2017 Author(s).

We establish Hartman-Wintner type criteria for the half -linear second order differential equation (r(t)Phi 1.(x'))' + c(t)Phi(x) = 0, Phi(x) =vertical bar x vertical bar P(-2)x, p > 1, where this equation is viewed as a perturbation of another equation of the same form.

We establish Hille-Wintner type comparison criteria for the half-linear second order differential equation r(t)Φ(x′ ) + c(t)Φ(x) = 0, Φ(x) = |x|p−2 x , p > 1 , where this equation is viewed as a perturbation of another equation of the same form.