Let Γ be a discrete finitely generated group. Let M̂ → T be a Γ-equivariant fibration, with fibers diffeomorphic to a fixed even dimensional manifold with boundary Z. We assume that Γ → M̂ → M̂/Γ is a Galois covering of a compact manifold with boundary. Let (D(θ))θ∈T be a Γ-equivariant family of Dirac-type operators. Under the assumption that the boundary family is L-invertible , we define an inde...

Let M be a complete connected Riemannian manifold with boundary ∂M , Q a bounded continuous function on ∂M , and L = ∆+Z for a C1-vector field Z on M . By using the reflecting diffusion process generated by L and its local time on the boundary, a probabilistic formula is presented for the semigroup generated by L on M with Robin boundary condition 〈N,∇f〉+ Qf = 0, where N is the inward unit norm...

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

this paper deals with the boundary value problem involving the differential equationbegin{equation*}    ell y:=-y''+qy=lambda y, end{equation*} subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$ begin{equation*}    y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0),end{equation*}where $q(x),  a_1 , a_2$ are  real, $qin l...

In this paper, we derive a general accuracy-preserving boundary flux quadrature formula for the secondand third-order node-centered edge-based finite-volume discretizations on triangular and tetrahedral grids. It is demonstrated that the general formula reduces to some well-known formulas for the second-order scheme in the case of linear fluxes. Some special boundary grids are also examined. In...

We construct rigidly supersymmetric bulk-plus-boundary actions, both in x-space and in superspace. For each standard supersymmetric bulk action a minimal supersymmetric bulk-plus-boundary action follows from an extended F or D-term formula. Additional separately supersymmetric boundary actions can be systematically constructed using co-dimension one multiplets (boundary superfields). We also di...

nowadays, combination of gps heights with orthometric heights, derived from precise leveling, is broadly used to obtain point-wise solutions of the geoid, which is called “gps/leveling geoid”. the “gps/leveling geoid” is commonly used to constrain the gravimetric geoid solutions in a least squares surface fitting process. in this paper, unlike the usual application, the “gps/leveling geoid” is ...

where / i s the boundary function for jpand da is Lebesgue measure on the sphere. When m = 1, (1) easily transforms into the Cauchy integral formula. In dimension m9 the formula extends to be defined on all / in L , always yielding holomorphic functions. If we identify holomorphic functions with their boundary values, the extended operator can be regarded as the orthogonal projection from L to ...

For a general differential operator with smooth matrix-valued coefficients in a bounded domain with smooth boundary we consider the boundary properties of functions from the domain of definition of a maximal extension in L2(Ω) and we study the properties of extensions and boundary-value problems corresponding to them. The investigations are based on Green’s formula.

In homogenous space Sol we study compact surfaces with constant mean curvature and with non-empty boundary. We ask how the geometry of the boundary curve imposes restrictions over all possible configurations that the surface can adopt. We obtain a flux formula and we establish results that assert that, under some restrictions, the symmetry of the boundary is inherited into the surface. MSC: 53A10