We study the class of the free relativistic covariant equations generated by the fractional powers of the d′Alembertian operator $\left({\square }^{1/n}\right)$. The equations corresponding to $n=1$ and $2$ (Klein-Gordon and Dirac equations) are local in their nature, but the multicomponent equations for arbitrary $n>2$ are nonlocal. We show the representation of the generalized algebra of Pauli and Dirac matrices and how these matrices are related to the algebra of $\text{SU}\left(n\right)$ group. The corresponding representations of the Poincaré group and further symmetry transformations on the obtained equations are discussed. The construction of the related Green functions is suggested.

The network flow optimization approach is offered for restoration of gray-scale and color images corrupted by noise. The Ising models are used as a statistical background of the proposed method. We present the new multiresolution network flow minimum cut algorithm, which is especially efficient in identification of the maximum a posteriori (MAP) estimates of corrupted images. The algorithm is able to compute the MAP estimates of large-size images and can be used in a concurrent mode. We also consider the problem of integer minimization of two functions, $U_1\left(\mathbf{x}\right)=\lambda {\sum }_i\left|y_i-x_i\right|+{\sum }_{i,j}{\beta }_{i,j}\left|x_i-x_j\right|$ and $U_2\left(\mathbf{x}\right)={\sum }_i{\lambda }_i{\left(y_i-x_i\right)}^2+{\sum }_{i,j}{\beta }_{i,j}{\left(x_i-x_j\right)}^2$, with parameters $\lambda ,{\lambda }_i,{\beta }_{i,j}>0$ and vectors $\mathbf{x}=\left(x_1,\dots ,x_n\right)$, $\mathbf{y}=\left(y_1,\dots ,y_n\right)\in {\left\{0,\dots ,L-1\right\}}^n$. Those functions constitute the energy ones for the Ising model of color and gray-scale images. In the case $L=2$, they coincide, determining the energy function of the Ising model of binary images, and their minimization becomes equivalent to the network flow minimum cut problem. The efficient integer minimization of $U_1\left(\mathbf{x}\right),U_2\left(\mathbf{x}\right)$ by the network flow algorithms is described.