Saccades made between targets at optical infinity require both eyes to rotate by the same angle. Nevertheless, these saccades are consistently accompanied by transient vergence eye movements. Here we have investigated whether the dynamics of these vergence movements depend on the trajectory of the coincident conjugate movement, and whether moving the head during eye-head gaze shifts modifies ve...

This paper describes preconditioned conjugate gradient methods for solving sparse symmetric and positive definite systems of linear equations. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Elemen...

The conjugate gradient boundary iteration (CGBI) is a domain decomposition method for symmetric elliptic problems on domains with large aspect ratio. High efficiency is reached by the construction of preconditioners that are acting only on the subdomain interfaces. The theoretical derivation of the method and some numerical results revealing a convergence rate of 0.04–0.1 per iteration step are...

This paper provides a preconditioned iterative technique for the solution of saddle point problems. These problems typically arise in the numerical approximation of partial differential equations by Lagrange multiplier techniques and/or mixed methods. The saddle point problem is reformulated as a symmetric positive definite system, which is then solved by conjugate gradient iteration. Applicati...

We introduce a new technique to study pattern avoidance in dynamical systems, namely the use of a commuter function between non-conjugate dynamical systems. We investigate the properties of such a commuter function, specifically h : [0, 1]→ [0, 1] satisfying T1 ◦ h = h ◦ Tμ, where Tμ denotes a symmetric tent map of height μ. We make use of this commuter function to prove strict inclusion of the...

In this study, we give a characterization of all torsion units which are in the unit group of ZS3 integral group ring of symmetric group S3, and classify conjugate classes of these units. We used the group of all doubly stochastic matrices in GL(3,Z) in this classification. The investigation of torsion units is not restricted with this study, and the classification of torsion units of bigger or...

We summarize the field-theory/matrix model correspondence for a chiral N = 1 model with matter in the adjoint, antisymmetric and conjugate symmetric representations as well as eight fundamentals to cancel the chiral anomaly. The associated holomorphic matrix model is consistent only for two fundamental fields, which requires a modification of the original Dijkgraaf-Vafa conjecture. The modified...

We present in this work a new and shorter proof of the generalized λ-Newton inequalities for elementary symmetric functions defined on a self-conjugate set which lies essentially in the open right half-plane. We also point out some interesting consequences of the generalized λ-Newton inequalities. In particular, we establish an improved complex version of the arithmetic mean-geometric mean ineq...

Let F be a number field with adele ring AF , and let π, π ′ be cuspidal automorphic representations of GL2(AF ), say with the same central character. If the symmetric squares of π and π are isomorphic, we know that π will need to be an abelian, in fact quadratic, twist of π, which amounts to a multiplicity one statement for SL(2) ([Ram1]). It is of interest to ask if the situation is the same f...