If E is a subset of Z then the n-th characteristic ideal of the algebra of rational polynomials taking integer values on E, Int(E, Z), is the fractional ideal consisting of 0 and the leading coefficients of elements of Int(E, Z) of degree no more than n. For p a prime the characteristic sequence of Int(E, Z) is the sequence of negatives of the p-adic values of these ideals. We give recursive fo...

Let Z be a fat point scheme in P supported on general points. Here we prove that if the multiplicities are at most 3 and the length of Z is sufficiently high then the number of generators of the homogeneous ideal IZ in each degree is as small as numerically possible. Since it is known that Z has maximal Hilbert function, this implies that Z has the expected minimal free resolution.

A bijection is proved between Sl( n, Z)-conjugacy classes of hyperbolic matrices with eigenvalues {A,,_A,,} which are units in an n-degree number field, and narrow ideal classes of the ring Rk = Z[A,]. A bijection between Gl(«,Z)-conjugacy classes and the wide ideal classes, which had been known, is repeated with a different proof. In 1980, Peter Sarnak was able to obtain an estimate of the gro...

by proposing a predictive method with no adjustable parameter and by using infinite dilution activity coefficients of components in binary mixtures obtained from unifac model, the binary interaction parameters (k12) in van der waals mixing rule (vdwmr) and orbey-sandler mixing rule (osmr) have been evaluated. the predicted binary interaction parameters are used in peng-robinson-stryjek-vera equ...