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[en] For a fixed rotation number we compute the Hausdorff dimension of the set of well approximable numbers. We use this result and an inhomogeneous version of Jarnik's theorem to demonstrate strong recurrence properties of the billiard flow in certain polygons
[en] In the study of enumeration polynomials of signed permutations of rank n, which is known as a Coxeter group of type B, Chow and Ma found that alternating runs of up signed permutations are closely related to peaks and valleys of these permutations. Notice that even-singed permutations of rank n, which is also called a Coxeter group of type D, forms a subgroup of signed permutations of index 2, we study the number of type D permutations according to alternating runs and consider how alternating runs connect with peaks and valleys. We find in this paper that the generating function of alternating runs of up even-signed permutations can be expressed as those generating functions of peaks and valleys of up even-signed permutations, which partially provide an affirmative answer to a conjecture by Chow and Ma. Additionally, we establish a recurrence for the generating function of alternating runs and an identity on alternating runs of type D permutations.
[en] The general phenomenon of jet production and their properties are presented. A semi-classical model and a recursive model are studied
[fr]Le phenomene general de production de jets est presente ainsi que leurs proprietes. On etudie pour cela un modele semi-classique puis un modele recursif
[en] Motivated by the our recent work in Tan et al., 2016, related to the bi-periodic Fibonacci quaternions, here we introduce the bi-periodic Lucas quaternions that gives the Lucas quaternions as a special case. We give the generating function and the Binet formula for these quaternions. Also, we give the relationships between bi-periodic Fibonacci quaternions and bi-periodic Lucas quaternions.
[en] We consider the recurrence time to the r-neighbourhood for interval exchange maps. For almost every interval exchange map we show that the logarithm of the recurrence time normalized by −log r goes to 1. A similar result of the hitting time also holds for almost every interval exchange map
[en] A combinatorial algorithm is presented for computing dimensions of irreducible representations of all nine types of simple Lie algebras over complexes. It was implemented on a programmable desk calculator. In conclusion some physical applications are discussed. (Auth.)
[en] This paper deals with a special class of functions called generalized Voigt functions H(n)(x,a) and G(n)(x,a) and their partial derivatives, which are useful in the theory of polarized spectral line formation in stochastic media. For n=0 they reduce to the usual Voigt and Faraday-Voigt functions H(x,a) and G(x,a). A detailed study is made of these new functions. Simple recurrence relations are established and employed for the calculation of the functions themselves and of their partial derivatives. Asymptotic expansions are given for large values of x and a. They are used to examine the range of applicability of the recurrence relations and to construct a numerical algorithm for the calculation of the generalized Voigt functions and of their derivatives valid in a large (x,a) domain. It is also shown that the partial derivatives of the usual H(x,a) and G(x,a) can be expressed in terms of H(n)(x,a) and G(n)(x,a)
[en] It is well known that the eigenvalues of tridiagonal matrices can be identified with the zeros of polynomials satisfying three-term recursion relations and being therefore members of an orthogonal set. A class of such polynomials is identified some of which feature zeros given by simple formulae involving integer numbers. In the process certain neat formulae are also obtained, which perhaps deserve to be included in standard compilations, since they involve classical polynomials such as the Jacobi polynomials and other 'named' polynomials