The basic properties of distributivity and deletion of pure and o-substitution are investigated. The obtained results are applied to show preservation of recognizability in a number of surprising cases. It is proved that linear and recognizable tree series are closed under o-substitution provided that the underlying semiring is commutative, continuous, and additively idempotent. It is known tha...

Using the Frobenius map, we introduce a new invariant for a pair (R, a) of a ring R and an ideal a ⊂ R, which we call the F-pure threshold c(a) of a, and study its properties. We see that the F-pure threshold characterizes several ring theoretic properties. By virtue of Hara and Yoshida’s result [HY], the F-pure threshold c(a) in characteristic zero corresponds to the log canonical threshold lc...

In the pure spinor formalism for the superstring and supermembrane, supersymmet-ric invariants are constructed by integrating over five θ's in d=10 and over nine θ's in d=11. This pure spinor superspace is easily explained using the superform (or " ecto-plasm ") method developed by Gates and collaborators, and generalizes the standard chiral superspace in d=4. The ectoplasm method is also usefu...

The philosophy of mathematics provides a severe test for a materialist explanation of science. This is because mathematics is mostly abstract and mathematical theory is rarely tested directly in practice. All the main schools of the philosophy of mathematics | platonism, logicism, intuitionism, formalism | are varieties of idealism. Nevertheless all human ideas, including mathematical ideas, or...

A mathematical model is proposed for ventricular parasystole. In this model, there are two separate rhythms, a sinus rhythm and a ventricular ectopic rhythm. An ectopic beat will occur if the ectopic depolarization falls during a time interval when the ventricles are not refractory. Following an ectopic beat there is a compensatory pause. Analysis of this model, utilizing numerical simulation a...

We present an efficient algorithm that checks the satisfiability of pure dominance constraints, which is a tree description language contained in several constraint languages studied in computational linguistics. Pure dominance constraints partially describe unlabeled rooted trees. For arbitrary pairs of nodes they specify sets of admissible relative positions in a tree. The task is to find a t...

Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations. We describe the relation in terms of pointed modules. We present methods for producing superdecomposable pure-injectives and give some details of recent work of Harland doing this in the context of tubular algebras. 2010 Mathematics Subject Classification. Primary 16G...

Ossified lipoma or osteolipoma are rarely reported. It is defined as a histologic variant of lipoma that has undergone osseous metaplasia. Osteolipoma presents with a dominant osseous component within a lipoma. We report a case of a histologically confirmed osteolipoma on the nuchal ligament independent of bone. The patient was a 51-year-old female who presented with a 5-year history of a painl...

A pure state f of a von Neumann algebra M is called classically normal if f is normal on any von Neumann subalgebra of M on which f is multiplicative. Assuming the continuum hypothesis, a separably represented von Neumann algebra M has classically normal, singular pure states iff there is a central projection p ∈ M such that pMp is a factor of type I∞, II, or III. DEFINITION: A pure state f of ...

Aphemia, also called anarthria or severe apraxia of speech, is a rare disorder of speech production usually resulting from vascular lesions affecting the inferior premotor cortex of the left hemisphere. A patient presenting with aphemia as the sole manifestation of primary progressive aphasia (PPA) is reported.