This paper presents an analytical solution for an orthotropic circular cross section bar with a magnetic coating weakened by multiple arbitrary oriented cracks under Saint-Venant torsion by means of the distributed dislocation technique. At first, the solution of the orthotropic bar with a magnetic coating weakened by a Volterra-type screw dislocation is achieved with the aid of the finite Four...

We prove a limit theorem on convergence of mathematical expectations functionals sums independent random variables to Cauchy problem solution for an evolution equation $$ \frac{\partial u}{\partial t}={\left(-1\right)}^m{\mathcal{A}}_{\mu }, where {\mathcal{A}}_m is convolution operator with generalized function |x|−2m − 2, m ∈ N.