Explicit Burgess bound for composite moduli

We prove an explicit version of Burgess’ bound on character sums for composite moduli.

Extended Bounds of Beatty Sequence Associated with Primes

This paper discusses on the estimation of character sums with respect to non-homogeneous Beatty sequences, over prime where , and is irrational. In particular, the bounds is found by extending several properties of character sums associated with composite moduli over prime. As a result, the bound of is deduced.

Rheological Characterization of Agarose and Poloxamer 407 (P407) Based Hydrogels

ABSTRACTPoloxamer 407 (P407) is a biocompatible thermo-setting polymer, while agarose is a biocompatible thermo-softening material. It is interesting to mix them to examine any possible synergy in thermomechanical properties. In this study, rotational rheometer was adopted to study rheological properties of the mixtures of agarose/P407 gels with different concentrations at various frequencies, strain rates and temperatures. It has revealed that the addition of P407 decreased the gel stiffness by an order of magnitude. For the given combinations in this study, the increase in agarose concentration would increase both the storage modulus and loss modulus of the gel mixtures. The variation in P407 concentration (2.5%-10%) minimally changes the composite moduli. These agarose/P407 gel mixtures also exhibited shear thinning behavior. However, the addition of P407 (2.5%-10%) to agarose gel only has very small effect on thermomechanical properties of agarose gels. The overall transition temperature for these gel mixtures is governed by P407 melting point where the phase change starts around 55°C and the gels completely collapse at the melting temperature of agarose.