To determine what is lost or gained by using fewer age classes in a Leslie matrix model, I develop a novel method to reduce a Leslie matrix model to a …
To determine what is lost or gained by using fewer age classes in a Leslie matrix model, I develop a novel method to reduce a Leslie matrix model to a smaller one. An aggregated (“reduced”) Leslie matrix model inherits important properties of the original model. To illustrate the influence of aggregation on asymptotic and transient dynamics, I apply the aggregator to 10 Leslie matrices for populations drawn from a diverse set of species.
We give a very short proof of the Theorem: Suppose that $f(x) = a_1x + a_2x^2 + \cdots$ is a formal power series with coefficients in an integral domain, and …
We give a very short proof of the Theorem: Suppose that $f(x) = a_1x + a_2x^2 + \cdots$ is a formal power series with coefficients in an integral domain, and $a_1$ is a primitive $n^{\mathrm {th}}$ root of unity $(n \in {\Bbb N})$. If the $n^{\mathrm {th}}$ iterate $f^{(n)}(x) \equiv f\big (f(\cdots f\big (f(x)\big )\cdots \big )$ satisfies $f^{(n)}(x) = x + b_mx^m + b_{m + 1}x^{m + 1} + \cdots$, with $b_m \neq 0$ and $m > 1$, then $m \equiv 1 \pmod {n}$.
Abstract We prove that every ultraproduct of p -adics is inp-minimal (i.e., of burden 1). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselian valued …
Abstract We prove that every ultraproduct of p -adics is inp-minimal (i.e., of burden 1). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselian valued fields of equicharacteristic 0 in the RV language.
We prove a couple of results on NTP2 theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by 2. …
We prove a couple of results on NTP2 theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by 2. This improves previous work of Ben Yaacov and Chernikov. We propose a line of investigation of NTP2 theories based on S1 ideals with amalgamation and ask some questions. We then define and study a class of groups with generically simple generics, generalizing NIP groups with generically stable generics.
We prove that every ultraproduct of $p$-adics is inp-minimal (i.e., of burden $1$). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselian valued fields of …
We prove that every ultraproduct of $p$-adics is inp-minimal (i.e., of burden $1$). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselian valued fields of equicharacteristic $0$ in the RV language.
Abstract We prove that in a group without the independence property a nilpotent subgroup is always contained in a definable nilpotent subgroup of the same nilpotency class. The analogue for …
Abstract We prove that in a group without the independence property a nilpotent subgroup is always contained in a definable nilpotent subgroup of the same nilpotency class. The analogue for the soluble case is also shown when the subgroup is normal in the ambient group.
The Fitting subgroup of a type-definable group in a simple theory is relatively definable and nilpotent. Moreover, the Fitting subgroup of a supersimple hyperdefinable group has a normal hyperdefinable nilpotent …
The Fitting subgroup of a type-definable group in a simple theory is relatively definable and nilpotent. Moreover, the Fitting subgroup of a supersimple hyperdefinable group has a normal hyperdefinable nilpotent subgroup of bounded index, and is itself of bounded index in a hyperdefinable subgroup.
The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of …
The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having infinite index in its predecessor stabilizes after finitely many steps. The Fitting subgroup of such groups is shown to be nilpotent and a theorem of Hall for nilpotent groups is generalized to ind-definable almost nilpotent subgroups of $\widetilde{\mathfrak M}\_c$-groups.
Abstract Indispensability arguments are introduced and their connection to scientific realism is discussed. The Quine–Putnam indispensability argument for mathematical realism is then outlined. In particular, the argument's dependence on the …
Abstract Indispensability arguments are introduced and their connection to scientific realism is discussed. The Quine–Putnam indispensability argument for mathematical realism is then outlined. In particular, the argument's dependence on the doctrines of naturalism and holism is established.
A group is small if it has countably many complete $n$-types over the empty set for each natural number n. More generally, a group $G$ is weakly small if it …
A group is small if it has countably many complete $n$-types over the empty set for each natural number n. More generally, a group $G$ is weakly small if it has countably many complete 1-types over every finite subset of G. We show here that in a weakly small group, subgroups which are definable with parameters lying in a finitely generated algebraic closure satisfy the descending chain conditions for their traces in any finitely generated algebraic closure. An infinite weakly small group has an infinite abelian subgroup, which may not be definable. A small nilpotent group is the central product of a definable divisible group with a definable one of bounded exponent. In a group with simple theory, any set of pairwise commuting elements is contained in a definable finite-by-abelian subgroup. First corollary : a weakly small group with simple theory has an infinite definable finite-by-abelian subgoup. Secondly, in a group with simple theory, a normal solvable group A of derived length n is contained in an A-definable almost solvable group of class n.