Hamartoma Breast, Chondromatous Type.

This case report describes an exceedingly rare case of hamartoma of breast with predominantly chondroid stroma. A 45 year old lady presented with a mobile lump in the upper outer quadrant of left breast, clinically diagnosed as fibroadenoma. Mammography and FNAC were not done. She underwent lumpectomy and we received the specimen measuring 7x5x3cm. Cut surface of which revealed grey white nodule with glistening surface. Histopathologically we found a circumscribed lesion with predominantly mature hyaline cartilage separated by fibrocollagenous bands

A completely entangled subspace of maximal dimension

A completely entangled subspace of a tensor product of Hilbert spaces is a subspace with no non-trivial product vector. K. R. Parthasarathy determined the maximum dimension possible for such a subspace. Here we present a simple explicit example of one such space. We determine the set of product vectors in its orthogonal complement and see that it spans whole of the orthogonal complement. This way we are able to determine the minimum dimension possible for an unextendible product basis (UPB) consisting of product vectors which are linearly independent but not necessarily mutually orthogonal.Comment: 8 page

Pure Semigroups of Isometries on Hilbert C*-Modules

We show that pure strongly continuous semigroups of adjointable isometries on a Hilbert C*-module are standard right shifts. By counter examples, we illustrate that the analogy of this result with the classical result on Hilbert spaces by Sz.-Nagy, cannot be improved further to understand arbitrary isometry semigroups of isometries in the classical way.Comment: 18 pages; correction of an awful lot of typos; avoiding in some places a conflict with the known terminology 'reducing subspace

Nilpotent Completely Positive Maps

We study the structure of nilpotent completely positive maps in terms of Choi-Kraus coefficients. We prove several inequalities, including certain majorization type inequalities for dimensions of kernels of powers of nilpotent completely positive maps.Comment: 10 page

Mycotoxin food safety risk in developing countries

"Mycotoxins are produced by fungi, commonly known as mold. These toxins can develop during production, harvesting, or storage of grains, nuts, and other crops. Mycotoxins are among the most potent mutagenic and carcinogenic substances known. They pose chronic health risks: prolonged exposure through diet has been linked to cancer and kidney, liver, and immune-system disease. Because mycotoxins occur more frequently under tropical conditions and diets in many developing countries are more heavily concentrated in crops susceptible to mycotoxins, these chronic health risks are particularly prevalent in developing countries." from TextFood safety ,food security ,Public health ,

Standard noncommuting and commuting dilations of commuting tuples

We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly there is the minimal isometric dilation consisting of isometries with orthogonal ranges and hence it is a noncommuting tuple. There is also a commuting dilation related with a standard commuting tuple on Boson Fock space. We show that this commuting dilation is the maximal commuting piece of the minimal isometric dilation. We use this result to classify all representations of Cuntz algebra O_n coming from dilations of commuting tuples.Comment: 18 pages, Latex, 1 commuting diagra