Standard graded vertex cover algebras, cycles and leaves

The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals defining these algebras. It turns out that such simplicial complexes are closely related to a range of hypergraphs which generalize bipartite graphs and trees. These relationships allow us to obtain very general results on standard graded vertex cover algebras which cover previous major results on Rees algebras of squarefree monomial ideals.

     

Extremal Betti numbers of edge ideals

Archiv der Mathematik - Let A be an algebra over a field F of characteristic zero. For every $$n\ge 1$$ , let $$\delta _n(A)$$ be the number of linearly independent multilinear proper central...     

Kinetic study of the thermal inactivation of glucose oxidase in the presence of denaturant and stabilizer by means of bioelectrocatalysis method

The thermal inactivation of glucose oxidase (GOD) in aqueous solution has been studied by the electrochemical method to follow the bioelectrocatalytic current due to the oxidation of glucose by GOD. Exponential time-dependent decrease in bioelectrocatalytic current, that is, the decrease in the enzymatic activity of GOD, was observed at given temperatures to determine the rate constant (k) of a simple inactivation process: GOD (active) → GOD (inactive). The ln[k] vs. T(-1) plots gave straight lines with all solution conditions tested, so that the resulting Arrhenius activation parameters including ΔH(?) and ΔS(?) can be compared with each other. In the 50 mmol/L phosphate buffer at 70°C, k was determined to be (6.6 ± 1.6)× 10(-4) s(-1), and ΔH(?) and ΔS(?) were calculated to be 202 ± 13 kJ mol(-1) and 282 ± 39 J K(-1) mol(-1), respectively. By addition of 3 mol/L guanidine hydrochloride, the k was increased to (4.7 ± 0.6)× 10(-3) s(-1), indicating that the denaturant accelerates the thermal inactivation. In this case, ΔH(?) was significantly reduced. By addition of 1 g/L ε-poly-L-lysine, which may adsorb onto the GOD surface to reduce the local disorder, k was decreased to (1.8 ± 0.6)× 10(-4) s(-1). In this case, ΔS(?) was reduced but ΔH(?) was not decreased much. This can be used as an important indication for selection of the enzyme stabilizer in solution.     

A new analytical formula to compute the step length of Padé approximants in the ANM: Application to buckling structures

In this paper, we propose a new analytical formula to define the next branch in the Asymptotic Numerical Method (ANM) using the Padé approximants. The proposed formula is based on the computation of the relative error of two consecutive Padé approximants. This formula is obtained by developing the relative error with respect to the path parameter. An appropriate matrix formulation is adopted for the computation of this relative error. A comparison between the analytical formula proposed in this paper and the classical continuation Padé approximants using the step length computed numerically using dichotomy method is presented for examples of buckling structures.     

Unimodular Triangulations and Coverings of Configurations Arising from Root Systems

Existence of a regular unimodular triangulation of the configuration , where ⁺ is the collection of the positive roots of a root system and where (0, 0,...,0 ) is the origin of , will be shown for = B _n , C _n , D _n and BC _n . Moreover, existence of a unimodular covering of a certain subconfiguration of the configuration A _n+1 ⁺ will be studied.     

Gorenstein simplices with a given δ-polynomial

To classify the lattice polytopes with a given $\delta$-polynomial is an important open problem in Ehrhart theory. A complete classification of the Gorenstein simplices whose normalized volumes are prime integers is known. In particular, their $\delta$-polynomials are of the form $1+t^k+?+t^{(v?1)k}$, where $k$ and $v$ are positive integers. In the present paper, a complete classification of the Gorenstein simplices with the above $\delta$-polynomials will be performed, when $v$ is either $p^2$ or $pq$, where $p$ and $q$ are prime integers with $p\ne q$. Moreover, we consider the number of Gorenstein simplices, up to unimodular equivalence, with the expected $\delta$-polynomial.     

The relevance of Freiman’s theorem for combinatorial commutative algebra

Mathematische Zeitschrift - Freiman’s theorem gives a lower bound for the cardinality of the doubling of a finite set in $${\mathbb R}^n$$ . In this paper we give an interpretation of his...     

Finite lattices and Gröbner bases

Gröbner bases of binomial ideals arising from finite lattices will be studied. In terms of Gröbner bases and initial ideals, a characterization of finite distributive lattices as well as planar distributive lattices will be given.     

Non-very ample configurations arising from contingency tables

In this paper, it is proved that, if a toric ideal possesses a fundamental binomial none of whose monomials is squarefree, then the corresponding semigroup ring is not very ample. Moreover, very ample semigroup rings of Lawrence type are discussed. As an application, we study very ampleness of configurations arising from contingency tables.