Science for Education

These lectures were delivered to the high school students at the School – seminar «Nonlinear Days for Youth in Saratov – 2012» in October 2012. They present the two ways of historical investigation of symmetry. The first way is self-similarity, i.e. invariance at dimension scale changing. In a more general way the term «scaling» is used, meaning the existence of power-law correlation between some variable and variables x1, ...xn: y = Ax₁^α1...x_n^αn, where A, α₁,...α_n – are constant.

Built in a cell synthetic gene regulatory elements may function rather independently on the original natural system. Experimental and theoretical studies of small synthetic networks allow for a better understanding of fundamental dynamical mechanisms of gene regulation. This paper gives an introduction to the modern mathematical approaches and methods in this field, primarily in the framework of nonlinear dynamics.

In the two lectures read at school for senior pupils «Nonlinear days in Saratov for youth» the basic definitions of the theory of dimension and similarity are stated, and also some special ways for concrete problems decision, in particular, use Pi-theorem and additions of Huntley are presented. The solutions of problems from different areas of physics are shown.

This article was prepared on the basis of a lecture for higher forms students on school-conference «Nonlinear days in Saratov for youth – 2011». The lecture discusses about the results of the experimental work on the use of gold plasmon-resonance particles in cytological studies of undergraduate and graduate students of the basic Chair of biophysics of DNP SSU and Laboratory of nanobiotechnology of IBPPM RAS. Some of the optical properties of gold nanoparticles are discussed to ensure their use for diagnostics and therapy of malignant tumors (cancer cells).