Bi-continuous semigroups for flows in infinite networks

We study transport processes on infinite metric graphs with non-constant velocities and matrix boundary conditions in the $\mathrm{L}^{\infty}$-setting. We apply the theory of bi-continuous operator semigroups to obtain well-posedness of the problem under different assumptions on the velocities and for general stochastic matrices appearing in the boundary conditions.Comment: 12 page

Equal-area method for scalar conservation laws

We study one-dimensional conservation law. We develop a simple numerical method for computing the unique entropy admissible weak solution to the initial problem. The method basis on the equal-area principle and gives the solution for given time directly.Comment: 10 pages, 7 figure

Diffusion in networks with time-dependent transmission conditions

We study diffusion in a network which is governed by non-autonomous Kirchhoff conditions at the vertices of the graph. Also the diffusion coefficients may depend on time. We prove at first a result on existence and uniqueness using form methods. Our main results concern the long-term behavior of the solution. In the case when the conductivity and the diffusion coefficients match (so that mass is conserved) we show that the solution converges exponentially fast to an equilibrium. We also show convergence to a special solution in some other cases.Comment: corrected typos, references removed, revised Lemma A.3. Appl. Math. Optim. (2013

Dynamic Transmission Conditions for Linear Hyperbolic Systems on Networks

We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in \cite{KraMugNic20} by discussing well-posedness under rather general transmission conditions that might be either of stationary or dynamic type - or a combination of both. Our results rely upon semigroup theory and elementary linear algebra. We also discuss qualitative properties of solutions

INCIDENCE OF ACHILLES TENDINITIS IN FENCING

Namen diplomskega dela je bil preučiti pojavnost ahilarne tendinopatije pri sabljačih in predstaviti ugotovitve različnih raziskav o pogostosti in vzrokih za njen pojav, saj gre za eno pogostejših poškodb v športnem sabljanju. Uporabljena je bila deskriptivna metoda dela. Pri delu smo si pomagali z analizo domačih in tujih virov s tega področja in nato poiskali zaključke, ter napisali ugotovitve. V pomoč pa so bile tudi lastne izkušnje. Predstavljene so anatomske, biomehanske, ter strukturne lastnosti Ahilove tetive. Opredeljen je tudi pojem in vzročni dejavniki za pojavnost ahilarne tendinopatije, ter kakšen vpliv ima sabljaško gibanje na omenjeno poškodboThe aim of this thesis was to study incidence of achilles tendinitis in fencing and present findings of different studies about frequency and causes of this injury because it is one of most common injuries in fencing. With the help of literature and personal experience we described our findings. Anatomical, biomechanical and structural characteristics of achilles tendon are presented in this thesis. There is Ahiles tendinitis defined as well as causes of injury and influence of fencing movement