An important predictor of historical sound change, functional load, fails to capture insights from speech perception. Building on ideal observer models of word recognition, we devise a new definition of functional load that incorporates both a priori expectedness and perceptual information. We explore this new measure with a simple model and find that it outperforms tra-

We define the notion of a power stable ideal in a polynomial ring R[X] over an integral domain R. It is proved that a maximal ideal χ M in R[X] is power stable if and only if P t is P primary for all t ≥ 1 for the prime ideal P = M ∩ R. Using this we prove that for a Hilbert domain R any radical ideal in R[X] which is a finite intersection G-ideals is power stable. Further, we prove that if R i...

Proposition 1. Assume that r = n − m > 1 and that the first nonvanishing Fitting ideal of M has grade r + 1. Then the following conditions are equivalent. (1) There is a χ ∈ M∗ = HomR(M,R) such that the ideal Imχ has grade r + 1. (2) There exists a submodule U of M with the following properties: (i) rankU = r − 1; (ii) U is reflexive, orientable, and Up is a free direct summand of Mp for all pr...

Let R be a polynomial ring over a field of dimension n. Let m be the maximal homogeneous ideal of R. Let I be a complete intersection homogeneous ideal of R minimally generated by polynomials of degrees d1, d2, . . . , dn. F. S. Macaulay showed that for all integers i = 0, 1, . . . , δ + 1, I : m = I + m where δ = d1 + d2 + . . .+ dn − n. We provide a modern proof of a generalization of this re...

Problem 1. Let R be a ring and let M be a left R-module. (a) Let I be a right ideal in R and let IM be the abelian subgroup of M generated by the elements rm, r ∈ I, m ∈M . Then R/I ⊗RM ∼= M/IM as an abelian group. (b) If I is a two-sided ideal, then the isomorphism in (a) is that of left R-modules. (c) Let R be commutative, I, J ⊂ R be ideals. Then R/I ⊗R R/J ∼= R/(I + J) as an R-module. (d) L...

We consider the Rosenfeld-Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F , let M(F ) be the sum of maximal orders of differential indeterminates occurring in F . We propose a modification of the Rosenfeld-Gröbner algorithm, in whi...

‎Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$‎. ‎Let $I$ be an ideal of $R$ with $grade(I,M)=c$‎. ‎In this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎The main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎Tor^{R}_c(k,H^c_I(M))to kotim...

If K is a eld, let the ring R 0 consist of nite sums of homogeneous elements in R = Kx 1 ; x 2 ; x 3 ; : : : ]]. Then, R 0 contains M, the free semi-group on the countable set of variables fx 1 ; x 2 ; x 3 ; : : :g. In this paper, we generalize the notion of admissible order from nitely generated sub-monoids of M to M itself; assume that > is such an admissible order on M. We show that we can d...

We consider the Rosenfeld-Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F , let M(F ) be the sum of maximal orders of differential indeterminates occurring in F . We propose a modification of the Rosenfeld-Gröbner algorithm, in whi...

Let J (M) denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of J (M) is bigger than the covering number of the ideal of the meager subsets of ω. We also show that Martin’s Axiom implies that the additivity of J (M) is 2. Finally we prove that there are no analytic infinite maximal antichains in any finite pro...