Solovay reducibility and continuity

The objective of this study is a better understandingof the relationships between reduction and continuity. Solovay reduction is a variation of Turing reduction based on the distance of two real numbers. We characterize Solovay reduction by the existence of a certain real function that is computable (in the sense of computable analysis) and Lipschitz continuous. We ask whether thereexists a reducibility concept that corresponds to H¨older continuity. The answer is affirmative. We introduce quasi Solovay reduction and characterize this new reduction via H¨older continuity. In addition, we separate it from Solovay reduction and Turing reduction and investigate the relationships between complete sets and partial randomness.

Probabilistic and dynamic colloid equations

We obtained two equations that characterize the structure of the colloid: the equation of the Schrodinger type that specifies the redistribution of heat and potential energy in the colloid and material equation – the diffusion equation with the operator of Liesegang associated directly with a substance that allows you to find the discontinuities of the structures caused by the vibrations of electrically charged particles. This procedure based on the assumption of the instability of the colloidal state, caused by the movement of charged particles. The reality is not collected in parts from the particles of matter in the course of evolution from the past to the future, and is all at once from the past to the future for a given pattern, that is, for specific PATTERNS, as defined by quantum theory. Without going deep into the theory of Kulakov, we will accept its fundamental provisions as a certain given. The forms of this structural data were obtained experimentally and mathematically confirmed. Let there be a certain angle of the skeleton, where due to the unevenness and partial randomness of the structure of the core grids forms "defects" – that is, electrical or magnetic moments of a particular order. Then small mobile clusters are attracted to it by electrostatic or electromagnetic forces, which are then adsorbed and somehow arranged on the "defects" in accordance with their dipole moments. This circumstance can be determined by "magic numbers", that is, as the number of clusters "stuck" to the defect of the core structure, with the formation of chemical bonds in the future. We can assume that the spanning structure of Coxeter can form small clusters form regular polyhedrons, and may occur or other structure having more complicated form.