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We relate the Weyr structure of a square matrix B to that of the t × t block upper triangular matrix C that has B down the main diagonal and first superdiagonal, and zeros elsewhere. Of special interest is the case t = 2 and where C is the nth Sierpinski matrix B n , which is defined inductively by B 0 = 1 and B n = [ B n − 1 B n − 1 0 B n − 1 ] . This yields an easy derivation of the Weyr structure of B n as the binomial coefficients arranged in decreasing order. Earlier proofs of the Jordan analogue of this had often relied on deep theorems from such areas as algebraic geometry. The result has interesting consequences for commutative, finite-dimensional algebras.

Although second-generation antipsychotics (SGAs) are characterized by fewer prolactin (PRL)-related side effects compared with first-generation antipsychotics, the detailed effects of SGAs on the plasma PRL levels still remain unclear. We examined the differences in plasma PRL levels among 268 patients treated for schizophrenia with olanzapine (OLZ), risperidone (RIS), aripiprazole (ARP), quetiapine (QTP), or perospirone (PER). The participants had received antipsychotic monotherapy with stable doses of OLZ, RIS, ARP, QTP, or PER for ≥ 3 weeks, and fasting blood samples were drawn to examine plasma PRL levels. The differences in median plasma PRL levels in all (P

We investigated the association between remission of depressive symptoms in fluvoxamine treatment and catechol- O -methyltransferase (COMT) gene. Sixteen SNPs in the COMT gene were investigated in 123 outpatients with major depression. Three single nucleotide polymorphisms located in the 5′ region were associated with remission in fluvoxamine-treated outpatients with moderate to severe depression.

Let B be the Boolean lattice on an n-set with B=@?B"i the rank decomposition. Let M(n,i) be the incidence matrix between B"i and B"n"-"i. We obtain a recursive formula for the determinant of the matrix M(n,i).

Let A = bigoplus_{i >= 0} A_i be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element ell of degree 1 such that the multiplication times ell : A_i --> A_{i+1} has maximal rank, for every i, and A has the Strong Lefschetz property if times ell^d : A_i --> A_{i+d} has maximal rank for every i and d. The main results obtained in this paper are the following. 1) EVERY height three complete intersection has the Weak Lefschetz property. (Our method, surprisingly, uses rank two vector bundles on P^2 and the Grauert-Mulich theorem.) 2) We give a complete characterization (including a concrete construction) of the Hilbert functions that can occur for K-algebras with the Weak or Strong Lefschetz property (and the characterization is the same one). 3) We give a sharp bound on the graded Betti numbers (achieved by our construction) of Artinian K-algebras with the Weak or Strong Lefschetz property and fixed Hilbert function. This bound is again the same for both properties. Some Hilbert functions in fact FORCE the algebra to have the maximal Betti numbers. 4) EVERY Artinian ideal in K[x,y] possesses the Strong Lefschetz property. This is false in higher codimension., To appear in J. Algebra