An n × n sign pattern A is spectrally arbitrary if given any self-conjugate spectrum there exists a matrix realization of A with that spectrum. If replacing any nonzero entry (or entries) of A by zero destroys this property, then A is a minimal spectrally arbitrary sign pattern. For n ≥ 3, several families of n × n spectrally arbitrary sign patterns are presented, and their minimal spectrally a...

(i) E xperim en ts have been m ade on th e incidence and tim e of onset of decom pression sickness in m ice exposed in single or repeated exposures to raised pressures of n itrogen or helium . I f a first (conditioning) exposure to pressure is followed 5 m in la te r by a second (test) exposure, th e incidence of sickness is considerably higher th a n th a t for e ither exposure alone, or for a...

We prove that for a generic hypersurface in P of degree at least 2 + 2/n, the n-th Picard number is one. The proof is algebraic in nature and follows from certain coherent cohomology vanishing.

(i) E xperim en ts have been m ade on th e incidence and tim e of onset of decom pression sickness in m ice exposed in single or repeated exposures to raised pressures of n itrogen or helium . I f a first (conditioning) exposure to pressure is followed 5 m in la te r by a second (test) exposure, th e incidence of sickness is considerably higher th a n th a t for e ither exposure alone, or for a...

We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the polynomial equations. Our algorithm works in time polynomial in the number of equations and the logarithm of the size of the field, whenever the degree of the pol...

We consider the supersymmetric WZNW model gauged in a manifestly supersymmetric way. We find the BRST charge and the necessary condition for nilpotency. In the BRST framework the model proves to be a Lagrangian formulation of the supersymmetric coset construction, known as the N=1 Kazama-Suzuki coset construction.

We give a classification of two-generator p-groups of nilpotency class 2. Using this classification, we give a formula for the number of such groups of order p in terms of the partitions of n of length 3, and find formulas for the number and size of their conjugacy classes.

A given number of n applicants are to be interviewed for a position of secretary. They present themselves one-by-one in random order, all n! permutations being equally likely. Two players I and II jointly interview the i-th applicant and observe that his (or her) relative rank is y for I and z for II, relative to i − 1 applicants that have already seen (rank 1 is for the best). Each player choo...