Multipole Moments of Fractal Distribution of Charges

In this paper we consider the electric multipole moments of fractal distribution of charges. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. In the paper we compute the electric multipole moments for homogeneous fractal distribution of charges.Comment: LaTeX, 11 page

Phytoplankton Community and Algal Toxicity at a Recurring Bloom in Sullivan Bay, Kabetogama Lake, Minnesota, USA

Kabetogama Lake in Voyageurs National Park, Minnesota, USA suffers from recurring late summer algal blooms that often contain toxin-producing cyanobacteria. Previous research identified the toxin microcystin in blooms, but we wanted to better understand how the algal and cyanobacterial community changed throughout an open water season and how changes in community structure were related to toxin production. Therefore, we sampled one recurring bloom location throughout the entire open water season. The uniqueness of this study is the absence of urban and agricultural nutrient sources, the remote location, and the collection of samples before any visible blooms were present. Through quantitative polymerase chain reaction (qPCR), we discovered that toxin-forming cyanobacteria were present before visible blooms and toxins not previously detected in this region (anatoxin-a and saxitoxin) were present, indicating that sampling for additional toxins and sampling earlier in the season may be necessary to assess ecosystems and human health risk

Electromagnetic field of fractal distribution of charged particles

Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of integral Maxwell equation, the simple examples of the fields of homogeneous fractal distribution are considered. The electric dipole and quadrupole moments for fractal distribution are derived.Comment: RevTex, 21 pages, 2 picture

On the Grothendieck Theorem for jointly completely bounded bilinear forms

We show how the proof of the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras by Haagerup and Musat can be modified in such a way that the method of proof is essentially C*-algebraic. To this purpose, we use Cuntz algebras rather than type III factors. Furthermore, we show that the best constant in Blecher's inequality is strictly greater than one.Comment: 9 pages, minor change