The goal of the present paper is study some algebraic invariants Stanley–Reisner rings Cohen–Macaulay simplicial complexes dimension d−1. We prove that inequality d≤reg(Δ)⋅type(Δ) holds for any (d−1)-dimensional complex Δ satisfying Δ=core(Δ), where reg(Δ) (resp. type(Δ)) denotes Castelnuovo–Mumford regularity type) ring k[Δ]. Moreover, given integers d,r,t r,t≥2 and r≤d≤rt, we construct a Δ(G)...

Semi-artificial photoelectrochemistry combines semiconductors with biocatalysts for selective chemical synthesis powered by sunlight, but the overall energy conversion efficiency of these hybrid systems has remained limited to date. In their Communication on page 26303, Erwin Reisner and co-workers report control local environment a formate dehydrogenase integrated in hierarchical porous TiO2 s...

Exploiting the analogy between exemplar models and population coding schemes, we characterize, by means of information theoretic tools, the efficiency of a large but finite population of cells coding for a discrete set of categories (e.g. vowels). The optimal code is shown to typically allocate more cells to class boundaries than to regions further apart. We then discuss the predicted perceptua...

We consider the problem of designing reliable and confidential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for finite lattice constellations a finite sum of inverse of algebraic norms, in fact the analogous for finite sums of the known criterion for infinite constellations, which motivates us to study totally real number fields w...

Pregnancy and delivery is one of the main causes in the female body weight alteration, especially with obesity. This alteration in body weight has a significant effect not only for a femine beauty standpoint, but also for more important reproductive functions in postpartum. For the actual condition of the maternal body weight alteration and its clinical significance, we made the various analysi...

A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring R/IΛ and the inverse system algebra R/I∆. We give a careful study of both of these algebras. Our main results are a full description of the graded Betti numbers of both algebras in the more general setting of linear spaces (giv...

We discuss simple partitioning phenomena for intersection rings of certain toric varieties, and apply this to prove the following results. ̋ We generalize a result of Gräbe, proving that Stanley–Reisner rings of homology spheres are Gorenstein. ̋ We give a new and direct proof of a theorem of the authors due to which the cohomology rings of matroids are Poincare duality algebras. ̋ We prove a conj...

References 1. Keller C, Brimacombe J, Lirk P, Pühringer F. Failed obstetric tracheal intubation and postoperative respiratory support with the ProSealTM laryngeal mask airway. Anesth Analg 2004;98:1467–70. 2. Reisner LS, Benumof JL, Cooper SD. The difficult airway: risk, prophylaxis and management. In: Chestnut DH, ed. Obstetric anesthesia principles and practice. St. Louis: Mosby, 1999:590–620...

In this paper, we give an algebra–combinatorics formula of the Möbius transform for an abstract simplicial complex K on [m] = {1, ...,m} in terms of the Betti numbers of the Stanley–Reisner face ring of K. Furthermore, we employ a way of compressing K to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex...