Distributions of partons at small $x$ values

New data on diffraction and inelastic scattering processes obtained at the Large Hadron Collider (LHC) have been analyzed. The properties of interactions at very high energies have been studied. In this case, the behavior of cross sections and distributions of secondary particles are determined by distributions of partons (constituents of the initial proton) carrying only a small fraction $x$ of the momentum of the initial protons. It has been shown that not only the radius of the interaction but also characteristic transverse momenta of particles $k_t$ increase with the energy. A model has been developed for the simultaneous description of soft (with low $k_t$ values) and hard (with the production of jets of particles with high $k_t$ values) interactions; this model provides a continuous smooth transition between them. The possibility of the measurement of the parton density for very small $x$ values at the LHC has been considered. A method has been proposed for the determination and variation of a factorization scale specifying the dimension of the spatial region in which partons are detected in these measurements.