fall & winter 2013

Fall Winter 2005

There is far greater theoretical coherence and clinical value in the concepts of the personal (person-to-person) and the new relationship than in the earlier concept of the “real” relationship. To develop this thesis, the author traces the historical evolution of the concept of the “real” relationship, elucidates its meaning(s), and considers its problematic features in the light of a relationa...

fall & winter 2011

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Algebra Prelim Fall 2013

First we will prove a small lemma. Lemma 1. Let P be a p-Sylow subgroup of G. Let N be a normal subgroup of G such that P ⊂ N . Then all p-Sylow subgroups are in N . Proof. Let P̃ be a p-Sylow subgroup that is not P . Then by the Sylow Theorems, we know that gPg−1 = P̃ for some g ∈ G. Since P ⊂ N , and N is normal, we know that gPg−1 ⊂ N and hence P̃ ⊂ N . Thus all p-Sylow subgroups are in N . Now...

Inside IAQ, Fall/Winter 1998

Inside IAQ is distributed twice a year and highlights indoor air quality (IAQ) research conducted by EPA’s National Risk Management Research Laboratory’s (NRMRL’s) Indoor Environment Management Branch (IEMB) and other parts of EPA’s Office of Research and Development. If you would like to be added to or removed from the mailing list, please mail, fax, or e-mail your name and address to; Inside ...

Honors A: Fall 2013

Proof. We prove the statement by induction on n. n = 1 case can be easily verified. Let’s assume the theorem is true for n − 1. We take an orthonormal basis [e1, · · · , en] for W and write Lei = ∑n j=1 ajiej. Since L is symmetric, we have aji = aij or A = [aij] is a symmetric matrix. From the lemma, any root of the characteristic polynomial of A is real. Take λ1 to be a root, then A−λ1I is sin...

Algebra Fall 2013