In this paper a class of quartic trigonometric Bézier curve, called QT Bézier curve, with two shape parameters is presented. These curves not only inherit most properties of the usual quartic Bézier curves in the polynomial space, but also enjoy some other advantageous properties for shape modelling. The shape of the curve can be adjusted by altering the values of shape parameters while the con...

We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one another. More specifically, let K0 be an arbitrary prime field and let r > 1 and s > 1 be integers that are coprime to one another. We show that one can find a finite extension K of K0, a degree-r extension L of K, a degr...

This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of Seiberg-Witten curves in terms of corresponding integrable models.

Manjul Bhargava and I have recently proved a result on the average order of the 2-Selmer groups of the Jacobians of hyperelliptic curves of a fixed genus n ≥ 1 over Q, with a rational Weierstrass point [2, Thm 1]. A surprising fact which emerges is that the average order of this finite group is equal to 3, independent of the genus n. This gives us a uniform upper bound of 3 2 on the average ran...

The arithmetic of quaternions is recalled from a constructive point of view. A Hecke module is introduced, defined as a free abelian group on right ideal classes of a quaternion order, together with a natural action of Hecke operators. An equivalent construction in terms of Shimura curves is then introduced, and the quaternion construction is applied to the analysis of specific modular and Shim...

Microbial induced calcite precipitation (MICP) offers a host of interesting features, from both theoretical and practical standpoints. This process was firstly investigated as geo-biological mechanism involved in carbonate mineral formation rocks soil. The interest its use has significantly increased recent years, MICP been used different fields, such oil recovery, the improvement soil geotechn...

The mechanical and durability properties of recycled aggregate concrete (RAC) are generally inferior to conventional due the old mortar attached surface original aggregate, which induces more complicated interfacial transition zones (ITZs) in RAC. microbial induced carbonate precipitation (MICP) modification is a novel environmentally-friendly method improve ITZs In this study, physical coarse ...

A simple and parsimonious model which originated from the Weibull frequency distribution was proposed to describe nonlinear survival curves of spores. This model was suitable for downward concavity curves (Bacillus cereus and Bacillus pumilus), as well as for upward concavity curves (Clostridium botulinum). It was shown that traditional F values calculated from this new model were no longer add...

By combining experiments with simple model calculations, we obtain new insight in spin transport through hybrid, CoFeB/Al2O3(1.5 nm)/tris(8-hydroxyquinoline)aluminium (Alq3)/Co spin valves. We have measured the characteristic changes in the I-V behavior as well as the intrinsic loss of magnetoresistance at the onset of multiple-step tunneling. In the regime of multiple-step tunneling, under the...