2. (T) Let CPn be complex projective n-space. (a) Describe the cohomology ring H∗(CPn,Z) and, using the Kunneth formula, the cohomology ring H∗(CPn × CPn,Z). (b) Let ∆ ⊂ CPn×CPn be the diagonal, and δ = i∗[∆] ∈ H2n(CP×CP,Z) the image of the fundamental class of ∆ under the inclusion i : ∆ → CPn × CPn. In terms of your description of H∗(CPn × CPn,Z) above, find the Poincaré dual δ∗ ∈ H2n(CPn × C...

1. (a) Prove that the Galois group G of the polynomial X6 + 3 over Q is of order 6. (b) Show that in fact G is isomorphic to the symmetric group S3. (c) Is there a prime number p such that X6 + 3 is irreducible over the finite field of order p? Solution. We initially work over any field k in which the polynomial X6 + 3 is irreducible. Clearly k cannot have characteristic 2 or 3. Let α be a root...

A digital rectal examination is a highly important procedure carried out on infants and children during visits to the gastroenterology clinic, but is often accompanied with physiologic and psychologic trauma in patients, along with being diagnostically inaccurate in the results obtained from it. In order to avoid causing discomfort to the patients, and to improve the accuracy of the results obt...

In this paper many of the principal struc­ture of the Moral Lung were studied with the help of Electron Microscopy. Detailed descrip­tion was given of Granular Pneumocytes, Membranous Pneumocytes, Macrophages, and Alveolar Capillaries. A discussion followed on the form and function of Granular Pneumo­cytes.  Acknowledgements  I am grateful to the Reza Shah Pahlavi Foundation for its generou...

With respect to the important role of clinical examination in breast lesion diagnosis, training of Clinical Breast Examination (CBE) to medical students are very critical. Despite the various method of physical examination, the current methods like using patients especially about breast aren’t accepted because of various reasons. Until now, any review studies about the optimum method of CBE hav...

When research on repatriation has shown that repatriates quit within one year of return from a foreign assignment, this study attempts to find what makes some repatriates stay committed and loyal to their companies when their colleagues are quitting and joining their immediate competitors? The research further extends to explore - factors determining repatriates loyalty, repatriates’ most desir...