Histidine pK(a) values were measured in charge-reversal (K78E, K97E, K127E, and K97E/K127E) and charge-neutralization (E10A, E101A, and R35A) mutants of staphylococcal nuclease (SNase) by (1)H-NMR spectroscopy. Energies of interaction between pairs of charges (DeltaG(ij)) were obtained from the shifts in pK(a) values relative to wild-type values. The data describe the distance dependence and sa...

For each n, let $$A_n=(\sigma _{ij})$$ be an $$n\times n$$ deterministic matrix and $$X_n=(X_{ij})$$ random with i.i.d. centered entries of unit variance. In the companion article (Cook et al. in Electron J Probab 23:Paper No. 110, 61, 2018), we considered empirical spectral distribution $$\mu _n^Y$$ rescaled entry-wise product $$\begin{aligned} Y_n = \frac{1}{\sqrt{n}} A_n\odot X_n \left( \sig...

We consider the free non-commutative analogue , introduced by D. Voiculescu, of the concept of Fisher information for random variables. We determine the minimal possible value of (a; a), if a is a non-commutative random variable subject to the constraint that the distribution of a a is prescribed. More generally, we obtain the minimal possible value of (fa ij ; a ij g 1i;jd), if fa ij g 1i;jd i...

A sign pattern is a matrix with entries in {+, −, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also be used to construct potentially nilpotent sign patterns that are not full, as well as potentiall...

— A characterization oj decreasing rational transductions is given, We show that x is a decreasing rational transduction jrom X* into Y* if and only ij there exist an alphabet Z, two alphabetic morphisms h:Z* -> X*,g:Z* -» Y*t with h e-jree and a regular language R o Z* such that x = go(nR)oh~. Résumé. — Nous proposons une caracterisation des transductions rationnelles décroissantes. Nous montr...

in this paper we will generalize  some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .

we shall also denote by P [∂ x ] the differential operator P (∂ x) = P The transposition that interchanges x i and x j will be denoted s ij. It is easily shown that for any P ∈ R and 1 ≤ i < j ≤ n we have the factorization (1 − s ij)P (x) = (x i − x j) 1+2r P ij (x) I .1 with r ≥ 0, P ij (x) prime with (x i − x j) and symmetric in x i , x j. This given, a polynomial P (x) ∈ Q[X n ] is said to b...

It is interesting to ask how the invariants of the maps i, such as the ideal Ij(bi) generated by the j x j minors of q, reflect the properties of M. For example, it is not hard to show (see Buchsbaum-Eisenbud [4]) that if the grade of M is g (that is, g is the length of a maximal regular sequence contained in J) and r is the rank of the map b (that is, the size of the largest nonvanishing minor...