This paper extends some results for the weighted Moore–Penrose inverse A+M,N in Hilbert space to the so-called weighted Minkowski inverse A⊕M,N of an arbitrary rectangular matrix A ∈ Mm,n in Minkowski spaces μ. Four methods are also used for approximating the weighted Minkowski Inverse A⊕M,N . These methods are: Borel summable, Euler–Knopp summable, Newton–Raphson and Tikhonov’s methods. c © 20...

A NEW multigrid relaxation scheme is developed for the steady-state solution of the Euler and Navier-Stokes equations. The lower-upper Symmetric-Gauss-Seidel method (LUSGS) does not require flux splitting for approximate Newton iteration. The present method, which is vectorizable and unconditionally stable, needs only scalar diagonal inversions. Application to transonic flow shows that the new ...

We consider a continuous family (fs), s ∈ [0, 1] of complex polynomials in two variables with isolated singularities, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber is constant. We firstly prove that the set of critical values at infinity depends continuously on s, and secondly that the degree of the fs is constant (up to an algebraic automorphism of...

We give an expression, in terms of the so-called Hermitian intrinsic volumes, for the measure of the set of complex r-planes intersecting a regular domain in any complex space form. Moreover, we obtain two different expressions for the Gauss-BonnetChern formula in complex space forms. One of them expresses the Gauss curvature integral in terms of the Euler characteristic and some Hermitian intr...

We study a formulation of the incompressible Euler equations in terms of the inverse Lagrangian map. In this formulation the equations become a first order advective nonlinear system of partial differential equations.

Several different hybrid Vlasov-fluid systems are formulated as Euler-Poincaré systems and compared in the same framework. In particular, the discussion focuses on three major hybrid MHD models. These are the current-coupling scheme and two different variants of the pressurecoupling scheme. The Kelvin-Noether theorem is presented explicitly for each scheme, together with the Poincaré invariants...

Previous work in haptics surface tracing for virtual prototyping and surface design applications has used a point model for virtual finger-surface interaction. We extend this tracing method for surface-to-surface interactions. A straightforward extension of the point-surface formulation to surface-surface can yield extraneous, undesirable solutions, although we rework the formulation to yield m...

Newton-Krylov methods, primarily using the Jacobian-Free Newton-Krylov (JFNK) approximation, are examined as an alternative to the traditional power iteration method for the calculation of the fundamental eigenmode in reactor analysis applications based on diffusion theory. One JFNK approach can be considered an acceleration technique for the standard power iteration as it is “wrapped around” t...

A model for the active deformation of cardiac tissue considering orthotropic constitutive laws is introduced and studied. In particular, the passive mechanical properties of the myocardium are described by the Holzapfel-Ogden relation, whereas the activation model is based on the concept of active strain. There, an incompatible intermediate configuration is considered, which entails a multiplic...