c]/N is called the critical exponent (loosely speaking, [alpha] is the "first non zero exponent" appearing in the series, and if [z.

Theorem 2 (Q is the set of critical exponents) For every rational number [alpha] that is not a positive integer there exists an algebraic power series with positive integer coefficients for which its Puiseux expansion at the radius ofconvergence has exactly the critical exponent [alpha].

For example, is it the case that for any radius of convergence, any critical exponent is possible?

Theorem 3 (First main result: dyadic critical exponents for N-algebraic function) The critical exponent of an N-algebraic (or even [R.

can be used to describe the viscosity as a function of temperature and extent of reaction by using a temperature and conversion dependent critical exponent.

Although the percolation model was initially established to describe properties near the gel point through a constant critical exponent, the chemoviscosity law is able to follow the behavior shown by the experimental data from the beginning of the crosslinking reaction up to the gelation time.

In fact, it seems that this temperature dependence is included in the formation of the modified percolation law through the critical exponent (a, b) that can be related to temperature.

This last year has brought new breakthroughs: the jamming

critical exponents can be computed with the theory, which suggests a precise test in a lab.

2000, The role of

critical exponents in blow-up theorems, The sequel, J.

4:00 EXISTENCE THEOREM OF ELLIPTIC SYSTEMS WITH SINGULARITIES INVOLVING SOBOLEV OR SOBOLEV-HARDY CRITICAL EXPONENTS

In this research, we study the existence of positive solutions of the system of nonlinear elliptic equations with sigularities involving Sobolev or Sobolev-Hardy critical exponents.

Next I will explore links to non-equilibrium phase transitions in other areas of science by determining the

critical exponents and the universality class of the onset of shear flow turbulence.