The Fermat-Weber problem consists in finding a point in R that minimizes the weighted sum of distances from m points in R that are not collinear. An application that motivated this problem is the optimal location of industries in the 2-dimensional case. The Weber problem is a generalization of the well-known Fermat problem. An usual method to solve the Weber problem, proposed by Weiszfeld in 19...

We say that a group is almost abelian if every commutator is central and squares to the identity. Now let G be the Galois group of the algebraic closure of the field Q of rational numbers in the field C of complex numbers. Let Gab+ be the quotient of G universal for continuous homomorphisms to almost abelian profinite groups, and let Qab+ /Q be the corresponding Galois extension. We prove that ...

The patient was a 21-year-old man with a lifelong history of skin lesions (well-defined port wine stains) on the right thigh, which had exhibited progressive growth, accompanied by pain and ulceration. Physical examination revealed hypertrophy of the right lower extremity and venous varicosities, with an ischemic ulcer in the medial malleolus. There was a palpable thrill and audible murmur in t...

A fourteen month old infant was admitted for evaluation because of continuous high fever and an indurated nodular lesion at the left thigh of one month course. After admittance painful inflammatory subcutaneous nodules appeared in the face and trunk, these were accompanied by enlarged cervical lymph nodes and hepatomegaly. Histological evaluation of the skin biopsy showed destruction of subcuta...

Assignment: Each of you should write a couple of pages, identifying important comparisons between the two theorists. The comparisons should concern important analytical themes or styles of theorizing--the kinds of issues discussed in the "handouts" meant to guide your group papers and those raised in class. You may focus on one comparison or identify several. For each, try to state the issue, i...

A generalisedWeber function is wN (z) = η(z/N)/η(z) where η(z) is the Dedekind function and N is any integer (the original function corresponds to N = 2). We give the complete classification of cases where some power w N evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a ...

the sturge-weber syndrome or encephalotrigeminal angiomatosis is a rare neurological and congenital disorder with a frequency of 1 in 50,000 births. this syndrome is a nonhereditary developmental condition and is characterized by the presence of congenital capillary malformation and a hamartomatous vascular proliferation involving the face (port-wine stain or facial birthmark), sometimes skull ...

The objective of this research is to develop an accurate numerical method to be used in showing the deformation of a liquid fuel droplet in a convective field. To simultaneously solve the internal liquid droplet flow field as well as the external gas phase flow field, a nonstaggered rectangular grid system without any coordinate transformation is used. Transition from the gas field to the liqui...

The internal flow circulation dynamics of a liquid drop moving in a co- or counter-flowing gas stream has been numerically studied. The present work is concerned with the time accurate numerical solution of the two phase flow field at the low Mach number limit with an appropriate volume tracking method to capture motion and deformation of a liquid drop. It is shown that relative velocity betwee...