We study variational mesh adaptation for axially symmetric solutions to twodimensional problems. The study is focused on the relationship between the mesh density distribution and the monitor function and is carried out for a traditional functional that includes several widely used variational methods as special cases and a recently proposed functional that allows for a weighting between mesh i...

Recently Logvinenko introduced a new objectcolor space, establishing a complete color atlas that is invariant to illumination [2]. However, the existing implementation for calculating the proposed color descriptors is computationally expensive and does not work for all types of illuminants. A new algorithm is presented that allows for an efficient calculation of Logvinenko’s color descriptors f...

A non-vanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system, however no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ε = E/N , the energy per degree of freedom. The fu...

Solution : Throughout the solution we will use the fact that λ2 = λ1 × λ1 whence we obtain the action of λ2 on rectangles: λ2(A1 × A2) = λ1(A1)λ1(A2). Also, for J1, J2 ⊆ R two intervals, let TJ1,J2 be any triangle with two sides equal to J1 (parallel to the first axis) and J2 (equal to the second axis). from the addittivity of λ2 it follows immediately that λ2(TJ1,J2) = |J1| · |J2|/2. (We use h...

If G is a simple graph (a non-oriented graph without loops or multiple edges), its (0, 1)-adjacency matrix A is symmetric and roots of the characteristic polynomial PG (λ) = det (λI −A) (the eigenvalues of G, making up its spectrum) are all real numbers, for which we assume their non-increasing order: λ1 ≥ λ2 ≥ · · · ≥ λn. In a connected graph for the largest eigenvalue λ1 (the index of the gra...

— We consider the Neumann Laplacian with constant magnetic field on a regular domain in R2. Let B be the strength of the magnetic field and let λ1(B) be the first eigenvalue of this Laplacian. It is proved that B 7→ λ1(B) is monotone increasing for large B. Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 supercon...

Recurrences are developed to enumerate any family of nonnegative integer sequences λ = (λ1, . . . , λn) satisfying the constraints: λ1 a1 ≥ λ2 a2 ≥ · · · ≥ λn−1 an−1 ≥ λn an ≥ 0, for a given constraint sequence a = [a1, . . . , an] of positive integers. They are applied to derive new counting formulas, to reveal new relationships between families, and to give simple proofs of the truncated lect...

In this paper we prove that if two self-similar tiling systems, with respective stretching factors λ1 and λ2, have a common factor which is a non periodic tiling system, then λ1 and λ2 are multiplicatively dependent.

Let G be a connected non-regular graph with n vertices, maximum degree ∆ and minimum degree δ, and let λ1 be the greatest eigenvalue of the adjacency matrix of G. In this paper, by studying the Perron vector of G, it is shown that type-I-a graphs and type-I-b (resp. type-II-a) graphs with some specified properties are not λ1-extremal graphs. Moreover, for each connected non-regular graph some l...