Displaying similar documents to “An edge-minimization problem for regular polygons.”

An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form

Peter Szabó (2013)

Kybernetika

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The paper presents an iterative algorithm for computing the maximum cycle mean (or eigenvalue) of n × n triangular Toeplitz matrix in max-plus algebra. The problem is solved by an iterative algorithm which is applied to special cycles. These cycles of triangular Toeplitz matrices are characterized by sub-partitions of n - 1 .

Polynomial cycles in certain local domains

T. Pezda (1994)

Acta Arithmetica

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1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple x ₀ , x ₁ , . . . , x k - 1 of distinct elements of R is called a cycle of f if f ( x i ) = x i + 1 for i=0,1,...,k-2 and f ( x k - 1 ) = x ₀ . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number 7 7 · 2 N , depending only on the degree N of K. In this...

Routh’s, Menelaus’ and Generalized Ceva’s Theorems

Boris A. Shminke (2012)

Formalized Mathematics

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The goal of this article is to formalize Ceva’s theorem that is in the [8] on the web. Alongside with it formalizations of Routh’s, Menelaus’ and generalized form of Ceva’s theorem itself are provided.

Even partition functions.

Ben Saïd, F., Nicolas, J.-L. (2002)

Séminaire Lotharingien de Combinatoire [electronic only]

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An arithmetic formula of Liouville

Erin McAfee, Kenneth S. Williams (2006)

Journal de Théorie des Nombres de Bordeaux

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An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.

Classification of discrete derived categories

Grzegorz Bobiński, Christof Geiß, Andrzej Skowroński (2004)

Open Mathematics

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The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.