Let G = (V,E) be a 2-connected plane graph on n vertices with outer face C such that every 2-vertex cut of G contains at least one vertex of C. Let PG(q) denote the chromatic polynomial of G. We show that (−1)nPG(q) > 0 for all 1 < q ≤ 1.2040.... This result is a corollary of a more general result that (−1)ZG(q,w) > 0 for all 1 < q ≤ 1.2040..., where ZG(q,w) is the multivariate Tutte polynomial...

The cohomology of a group G with coefficients in a left G–module M is denoted H .GIM /. We are primarily interested in the case where M is the group ring, ZG . Since ZG is a G–bimodule, H .GIZG/ inherits the structure of a right G– module. When G is discrete and acts properly and cocompactly on a contractible CW complex , there is a natural topological interpretation for this cohomology group:...

By the gauge group bundle of a principal bundle P(B,G) we mean the Lie group bundle associated to P(B, G) through the conjugacy action of G on itself. Given only B and a Lie group bundle M on B, we ask if there exists P(B, G) with gauge group bundle isomorphic to M and, if so, how they can be described. Using a form of Whitehead’s concept of crossed module, in place of the idea of an ‘abstract ...

Racket’s syntax parameters support the hygienic implementation of syntactic forms that would otherwise introduce implicit identifiers unhygienically.

It is well known that every uniquely clean ring is strongly clean. In this paper, we investigate the question of when this result holds element-wise. We first construct an example showing that uniquely clean elements need not be strongly clean. However, in case every corner ring is clean the uniquely clean elements are strongly clean. Further, we classify the set of uniquely clean elements for ...

The STAR collaboration presents jet substructure measurements related to both the momentum fraction and opening angle within jets in \pp \AuAu collisions at \sqrtsn $= 200$ GeV. observables include SoftDrop groomed (\zg), radius (\rg), subjet (\zsj) (\tsj). latter observable is introduced for first time. Fully corrected are presented compared leading order Monte Carlo models. \tsj~distributions...

We show that an ambiguity in setting the primitives of the matching with contracts model by Hatfield and Milgrom (2005) has serious implications for the model. Of the two ways to clear the ambiguity, the first (and what we consider more “clean”) remedy renders several of the results of the paper invalid in the absence of an additional irrelevance of removed contracts condition implicitly assume...

We describe new combinatorial methods for constructing explicit free resolutions of Z by ZG-modules when G is a group of fractions of a monoid where enough least common multiples exist (“locally Gaussian monoid”), and, therefore, for computing the homology of G. Our constructions apply in particular to all Artin–Tits groups of finite Coxeter type. Technically, the proofs rely on the properties ...

Aldosterone-producing adenomas (APAs) vary in phenotype and genotype. Zona glomerulosa (ZG)-like APAs frequently have mutations of an L-type calcium channel (LTCC) CaV1.3. Using a novel antagonist of CaV1.3, compound 8, we investigated the role of CaV1.3 on steroidogenesis in the human adrenocortical cell line, H295R, and in primary human adrenal cells. This investigational drug was compared wi...

G. Navarro raised the question whether the ordinary character table X(G) of a finite group G determines the Sylow numbers of G. In this note we show that this is the case when G is nilpotent-by-nilpotent, quasinilpotent, Frobenius group or a 2-Frobenius group. In particular Sylow numbers of supersoluble groups are determined by their ordinary character table. If G and H are finite groups with i...