As is clearly illustrated in the 1992 volume by I. Stewart and M. Golubitsky, starting from this point of view a general theory of symmetry breaking can be developed by tackling such questions as "which subgroups can occur?", "when does a given subgroup occur?" Symmetry breaking was first explicitly studied in physics with respect to physical objects and phenomena.
Random matrices studied in physics have statistical properties similar to the statistical properties of randomly chosen sequences of numbers, but no explanation was available until Okounkov showed an underlying unity between branches of physics, the probabilistic behaviour of numbers, and algebraic geometry based on the concept of random surfaces.
Open quantum maps have been studied in physics and mathematics.
Processes with such a character arise naturally and often, especially in phenomena studied in physics, chemical technology, population dynamics, biotechnology, and economics.
Processes with such characteristics arise naturally and often; for example, phenomena studied in physics, chemical technology, population dynamics, biotechnology and economics.
Composite materials making use of dispersed and elongated particles in a continuous liquid medium are fundamental for understanding many types of flow studied in physics, biology and engineering.
In recent years, impulsive differential equations have become more important tools in some mathematical models of real processes and phenomena studied in physics, biotechnology, chemical technology, population dynamics and economics; see [1 5].
The time scales calculus has a tremendous potential for applications in some mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, social sciences (see [11]).
The time scales calculus has a tremendous potential for applications in some mathematical problems and some mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology, economics, neural networks, and social sciences [17, 18].
Impulsive differential equations have become more important in recent years in some mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology and economics.
