Computing J-multiplicity
نویسندگان
چکیده
The j-multiplicity is an invariant that can be defined for any ideal in a Noetherian local ring (R, m). It is equal to the Hilbert-Samuel multiplicity if the ideal is m-primary. In this paper we explore the computability of the j-multiplicity, giving another proof for the length formula and the additive formula.
منابع مشابه
Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.
متن کاملStatistical Exploration of Fragmentation Phase Space and Source Sizes in Nuclear Multifragmentation
The multiplicity distributions for individual fragment Z values in nuclear multifragmentation are binomial. The extracted maximum value of the multiplicity, mZ , is found to depend on Z according to mZ = Z0/Z, where Z0 is the source size. This is shown to be a strong indication of statistical coverage of fragmentation phase space. The inferred source sizes coincide with those extracted from the...
متن کاملCOMPUTING WIENER INDEX OF HAC5C7[p, q] NANOTUBES BY GAP PROGRAM
The Wiener index of a graph Gis defined as W(G) =1/2[Sum(d(i,j)] over all pair of elements of V(G), where V (G) is the set of vertices of G and d(i, j) is the distance between vertices i and j. In this paper, we give an algorithm by GAP program that can be compute the Wiener index for any graph also we compute the Wiener index of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes by this program.
متن کاملA numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set
Let F1, F2, . . . , Ft be multivariate polynomials (with complex coefficients) in the variables z1, z2, . . . , zn. The common zero locus of these polynomials, V (F1, F2, . . . , Ft) = {p ∈ C|Fi(p) = 0 for 1 ≤ i ≤ t}, determines an algebraic set. This algebraic set decomposes into a union of simpler, irreducible components. The set of polynomials imposes on each component a positive integer kno...
متن کاملA Framework for the Complexity of High-Multiplicity Scheduling Problems
The purpose of this note is to propose a complexity framework for the analysis of high multiplicity scheduling problems. Part of this framework relies on earlier work aiming at the definition of outputsensitive complexity measures for the analysis of algorithms which produce “large” outputs. However, different classes emerge according as we look at schedules as sets of starting times, or as rel...
متن کامل