Search results for "arithmetic"

On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces

2017

We study the arithmetically Cohen-Macaulay (ACM) property for finite sets of points in multiprojective spaces, especially ( P 1 ) n (\mathbb P^1)^n . A combinatorial characterization, the ( ⋆ ) (\star ) -property, is known in P 1 × P 1 \mathbb P^1 \times \mathbb P^1 . We propose a combinatorial property, ( ⋆ s ) (\star _s) with 2 ≤ s ≤ n 2\leq s\leq n , that directly generalizes the ( ⋆ ) (\star ) -property to ( P 1 ) n (\mathbb P^1)^n for larger n n . We show that X X is ACM if and only if it satisfies the ( ⋆ n ) (\star _n) -property. The main tool for several of our results is an extension to the multiprojective setting of certain liaison methods in projective space.

Assessment Tests in the Mathematics Teaching Guides in Spain. Analysis of the Content Blocks and the Treatment of Arithmetic Word Problems

2021

The teaching guides that complement textbooks have key importance in the assessment of competence in problem solving, because these materials contain the assessment tools that teachers frequently use to quantify the achievements of their students. In this paper, we set two aims: to analyze which curriculum contents are given priority in the assessment tests of the teaching guides

Special arrangements of lines: Codimension 2 ACM varieties in P 1 × P 1 × P 1

2019

In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.

Multiprojective spaces and the arithmetically Cohen-Macaulay property

2019

AbstractIn this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for ℙ1× ℙ1and, more recently, in (ℙ1)r. In ℙ1× ℙ1the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in ℙm× ℙn. In such an ambient space it is equivalent to the so-called (⋆)-property. Moreover, we start an investigation of the ACM property in ℙ1× ℙn. We give a new construction that highlights how different the behavior of the ACM property is in this setting.

Abelian Gradings on Upper Block Triangular Matrices

2012

AbstractLet G be an arbitrary finite abelian group. We describe all possible G-gradings on upper block triangular matrix algebras over an algebraically closed field of characteristic zero.

Divisible designs and groups

1992

We study (s, k, λ1, λ2)-translation divisible designs with λ1≠0 in the singular and semi-regular case. Precisely, we describe singular (s, k, λ1, λ2)-TDD's by quasi-partitions of suitable quotient groups or subgroups of their translation groups. For semi-regular (s, k, λ1, λ2)-TDD's (and, more general, for the case λ2>λ1) we prove that their translation groups are either Frobenius groups or p-groups of exponent p. Some examples are given for the singular, semi-regular and regular case.

PRINZIPIELLE BEMERKUNGEN ZU THEORIE UND PRAXIS DER METHODE DER ZWEITEN ABLEITUNG BEI DER INTERPRETATION GRAVIMETRISCHER MESSERGEBNISSE

1957

The first part of the paper deals with theoretical considerations concerning the arithmetic mean of gravity values and its use with regard to the derivation of approximation formulae for the second derivative. In order to calculate the second derivative in practice the arithmetic mean. ḡ(r) of a continuum of gravity values on a circle of radius r is approximated by a Taylor polynomial and then replaced by the arithmetic mean gn(r) of n discrete gravity values. Because of the invariance of ġ(r) with regard to rotations of the coordinate system in the horizontal datum plane there exists a lower limit for the number n; this lower limit depends on the degree of the Taylor polynomial used in the…

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

2009

Doubly nonlinear periodic problems with unbounded operators

2004

Abstract The solvability of the evolution system v ′( t )+ B ( t ) u ( t )∋ f ( t ), v ( t )∈ A ( t ) u ( t ), 0 t T , with the periodic condition v (0)= v ( T ) is investigated in the case where A (t) are bounded, possibly degenerate, subdifferentials and B (t) are unbounded subdifferentials.

Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space

2020

This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains …