Several loop transformations techniques have been designed to extract parallelism from nested loop structures. We rst review two important approaches, known as Generalized Cycle Shrinking presented by Shang, O'Keefe and Fortes and the Index Shift Method introduced by Liu, Ho and Sheu. The main result of the paper is a new methodology that permits to combine cycle shrinking techniques with the i...

In 1989, Bai and Demmel proposed the multishift QR algorithm for eigenvalue problems. Although the global convergence property of the algorithm (i.e., the convergence from any initial matrix) still remains an open question for general nonsymmetric matrices, in 1992 Jiang focused on symmetric tridiagonal case and gave a global convergence proof for the generalized Rayleigh quotient shifts. In th...

The goal of our report is to compare a number of algorithms for computing a large number of eigenvectors of the generalized eigenvalue problem arising from a modal analysis of elastic structures using preconditioned iterative methods. The shift-invert Lanczos algorithm has emerged as the workhorse for the solution of this generalized eigenvalue problem; however a sparse direct method is require...

We give an exact formula for the L2 discrepancy of a class of generalized two-dimensional Hammersley point sets in base b, namely generalized Zaremba point sets. These point sets are digitally shifted Hammersley point sets with an arbitrary number of different digital shifts in base b. The Zaremba point set introduced by White in 1975 is the special case where the b shifts are taken repeatedly ...

Picosecond time-resolved x-ray spectroscopy is used to measure the spectral line shift of the 1s2p-1s^{2} transition in He-like Al ions as a function of the instantaneous plasma conditions. The plasma temperature and density are inferred from the Al He_{α} complex using a nonlocal-thermodynamic-equilibrium atomic physics model. The experimental spectra show a linearly increasing redshift for el...

Theory of Newtonian dynamical systems admitting normal shift of hypersurfaces was first developed for the case of Riemannian manifolds. Recently it was generalized for manifolds geometric equipment of which is given by some regular Lagrangian or, equivalently, by some regular Hamiltonian dynamical system. In present paper we consider further generalization of this theory for the case, when geom...

This paper is devoted to an in-depth study of cellular automaton rule 180 under the framework of symbolic dynamics. Rule 180, a member of Wolfram’s class IV and Chua’s hyper Bernoulli shift rules, defines infinite number of generalized sub-shifts. An effective method of constructing the shift invariant sets of the rule’s global map is proposed. It is noted that this method is also applicable to...

The Hopf algebra of Feynman diagrams, analyzed by A.Connes and D.Kreimer, is considered from the perspective of the theory of effective actions and generalized τ-functions, which describes the action of diffeomorphism and shift groups in the moduli space of coupling constants. These considerations provide additional evidence of the hidden group (integrable) structure behind the standard formali...

in this paper, a new class of multifunctions, called generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions, has been dened and studied. some characterizations and severalproperties concerning generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions are obtained. the re-lationships between generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions and some known con-ce...

The Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions using the ”long wave limit” procedure of Ablowitz and Satsuma, and appropriate ”gauge” transformations. Their properties are also discussed and it is shown that these solutions interact elastically with...