15 research outputs found
Interpolation of Power Mappings
Let and
be increasing sequences satisfying some mild rate of growth conditions. We
prove that there is an entire function
whose behavior in the large annuli is given by a perturbed
rescaling of , such that the only singular values of are
rescalings of . We describe several applications to the dynamics
of entire functions
Prescribing the Postsingular Dynamics of Meromorphic Functions
We show that any dynamics on any discrete planar sequence can be realized
by the postsingular dynamics of some transcendental meromorphic function,
provided we allow for small perturbations of . This work was influenced by
an analogous result of DeMarco, Koch and McMullen for finite in the
rational setting. The proof contains a method for constructing meromorphic
functions with good control over both the postsingular set of and the
geometry of , using the Folding Theorem of Bishop and a classical fixpoint
theorem of Tychonoff
Zero forcing number, maximum nullity, and path cover number of subdivided graphs
The zero forcing number, maximum nullity and path cover number of a (simple, undirected) graph are parameters that are important in the study of minimum rank problems. We investigate the effects on these graph parameters when an edge is subdivided to obtain a so-called edge subdivision graph. An open question raised by Barrett et al. in “Minimum rank of edge subdivisions of graphs, ” Electronic Journal of Linear Algebra (2009) 18: 530–563, is answered in the negative, and we provide additional evidence for an affirmative answer to another open question in that paper. It is shown that there is an independent relationship between the change in maximum nullity and zero forcing number caused by subdividing an edge once. Bounds on the effect of a single edge subdivision on the path cover number are presented, conditions under which the path cover number is preserved are given, and it is shown that the path cover number and the zero forcing number of a complete subdivision graph need not be equal
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Approximation Theory and Complex Dynamics
Data management plan for the grant, "Approximation Theory and Complex Dynamics." This project involves the study of approximation theory in the setting of complex functions, with applications to complex dynamics. Approximation theory seeks to understand the extent to which the behavior of a general function can be effectively modeled by that of functions drawn from a more restricted class. Efficient approximation of functions is of relevance for numerical calculation. Since the only calculations that can be carried out numerically are the elementary operations of addition, subtraction, multiplication, and division, in practical terms it is of importance to understand when the values of general functions are well approximated by the values of either polynomial or rational functions. In many situations, the values of the approximant resemble those of the general function only for a sampling of input values. What can be said about values of the approximant for other choices of input? This is the main question studied in this project, with the following application in mind: when a general function is iterated to produce a dynamical system, to what extent does the dynamical behavior of an approximant resemble the dynamical behavior of the original function? The project will also contribute to the development of human resources through educational outreach at the high school level as well as mentoring and training at the undergraduate and graduate levels, and will facilitate the interaction of different fields of mathematics through the organization of conferences and seminars
Regulace tlaku předlohy koksárenské baterie
Import 20/04/2006Prezenční výpůjčkaVŠB - Technická univerzita Ostrava. Fakulta elektrotechniky a informatiky. Katedra (455) měřící a řídící technik