We construct projections from HΛk(Ω), the space of differential k forms on Ω which belong to L2(Ω) and whose exterior derivative also belongs to L2(Ω), to finite dimensional subspaces of HΛk(Ω) consisting of piecewise polynomial differential forms defined on a simplicial mesh of Ω. Thus, their definition requires less smoothness than assumed for the definition of the canonical interpolants base...

The fundamental quantities of classical dynamics, such as position, velocity and acceleration, are expressed in terms of the Cartan tetrad, and the first Cartan structure equation is used to develop classical dynamics. The velocity is defined as the covariant exterior derivative of the position, and the acceleration as the exterior covariant derivative of the velocity. The resulting terms are a...

whenever this limit exists. Here Σk(r) ≡ ∂Bn r (0)/Γk denotes the Euclidean sphere of radius r in the k-th conical end of M , all suband superscripts refer to the standard Euclidean coordinates on Rn, ν is the Euclidean exterior unit normal to Σk(r), and dA is the Euclidean area measure. Bartnik [1] and Chruściel [2] discovered sharp conditions on the decay rate of Φ∗g − g0 ensuring that the li...

For a semistable reflexive sheaf E of rank r and c1 = a on P n and an integer d such that r|ad, we give sufficient conditions so that the restriction of E on a generic rational curve of degree d is balanced, i.e. a twist of the trivial bundle (for instance, if E has balanced restriction on a generic line, or r = 2 or E is an exterior power of the tangent bundle). Assuming this, we give a formul...

This paper concerns with boundary value problems as { L u+a0u = f in Ω, < ∇u, γ > +c0|u|m−1u = g on ∂Ω, where L is an elliptic possibly degenerate second order operator, a0, c0 are positive function, γ is an oblique exterior vector and m 1 . By means of some arguments close to the Dynamics Programming we prove that the viscosity solution admits a representation formula that can be considered as...

The mathematics models of Reliability-based Structural Optimization (RBSO) were presented in this paper, then how to handle the constraint become sixty-four-dollar question of establishing the fitness function. Based on exterior penalty function method, penalty gene is made adaptively according to population’s evolution, then the fitness function is established, which is mapping formula of obje...

We deduce the structure of the Dirac field on the lattice from the discrete version of differential geometry and from the representation of the integral Lorentz transformations. The analysis of the induced representations of the Poincaré group on the lattice reveals that they are reducible, a result that can be considered a group theoretical approach to the problem of fermion doubling. 1. DISCR...

Starting from a high-order local nonreflecting boundary condition (NBC) for single scattering [25], we derive a local NBC for time-dependent multiple scattering problems, which is completely local both in space and time. To do so, we first develop an exterior evaluation formula for a purely outgoing wave field, given its values and those of certain auxiliary functions needed for the local NBC a...

A classical technique to construct polynomial preserving extensions of scalar functions defined on the boundary an n n simplex interior is us...

Let X = G=K be an odd-dimensional semisimple Riemannian symmetric space of the noncompact type, and suppose that all Cartan subgroups of G are conjugate. Let u be a real-valued classical solution of the modiied wave equation u tt = ((+ k)u on R X, the Cauchy data of which are supported in a closed metric ball of radius a at time t = 0. Here t is the coordinate on R, is the (nonpositive deenite)...