Graded change of ring

We investigate scalar restriction, scalar extension, and scalar coextension functors for graded modules, including their interplay with coarsening functors, graded tensor products, and graded Hom functors. This leads to several characterisations of epimorphisms of graded rings.Comment: To appear in Quaestiones Mathematica

Quasicoherent sheaves on toric schemes

Let X be the toric scheme over a ring R associated with a fan Sigma. It is shown that there are a group B, a B-graded R-algebra S and a graded ideal I of S such that there is an essentially surjective, exact functor ~ from the category of B-graded S-modules to the category of quasicoherent O_X-modules that vanishes on I-torsion modules and that induces for every B-graded S-module F a surjection Xi_F from the set of I-saturated graded sub-S-modules of F onto the set of quasicoherent sub-O_X-modules of ~F. If Sigma is simplicial, the above data can be chosen such that ~ vanishes precisely on I-torsion modules and that Xi_F is bijective for every F. In case R is noetherian, a toric version of the Serre-Grothendieck correspondence is proven, relating sheaf cohomology on X with B-graded local cohomology with support in I.Comment: To appear in Expositiones Mathematicae; corrected typo

Graded integral closures

It is investigated how graded variants of integral and complete integral closures behave under coarsening functors and under formation of group algebras.Comment: to appear in Beitr\"age Algebra Geom.; typos correcte

Apraxia in progressive nonfluent aphasia

The clinical and neuroanatomical correlates of specific apraxias in neurodegenerative disease are not well understood. Here we addressed this issue in progressive nonfluent aphasia (PNFA), a canonical subtype of frontotemporal lobar degeneration that has been consistently associated with apraxia of speech (AOS) and in some cases orofacial apraxia, limb apraxia and/or parkinsonism. Sixteen patients with PNFA according to current consensus criteria were studied. Three patients had a corticobasal syndrome (CBS) and two a progressive supranuclear palsy (PSP) syndrome. Speech, orofacial and limb praxis functions were assessed using the Apraxia Battery for Adults-2 and a voxel-based morphometry (VBM) analysis was conducted on brain MRI scans from the patient cohort in order to identify neuroanatomical correlates. All patients had AOS based on reduced diadochokinetic rate, 69% of cases had an abnormal orofacial apraxia score and 44% of cases (including the three CBS cases and one case with PSP) had an abnormal limb apraxia score. Severity of orofacial apraxia (but not AOS or limb apraxia) correlated with estimated clinical disease duration. The VBM analysis identified distinct neuroanatomical bases for each form of apraxia: the severity of AOS correlated with left posterior inferior frontal lobe atrophy; orofacial apraxia with left middle frontal, premotor and supplementary motor cortical atrophy; and limb apraxia with left inferior parietal lobe atrophy. Our findings show that apraxia of various kinds can be a clinical issue in PNFA and demonstrate that specific apraxias are clinically and anatomically dissociable within this population of patients

The Enforcement of Ohio's Litter Control Laws

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