The R package bvpSolve for the numerical solution of Boundary Value Problems (BVPs) is presented. This package is free software which is distributed under the GNU General Public License, as part of the R open source software project. It includes some well known codes to solve boundary value problems of ordinary differential equations (ODEs) and differential algebraic equations (DAEs). In additi...

We construct a smooth axially symmetric solution to the classical one phase free boundary problem in R, n ≥ 3. Its free boundary is of “catenoid” type. This is a higher dimensional analogy of the HauswirthHelein-Pacard solution [18] in R. The existence of such solution is conjectured in [18, Remark 2.4]. This is the first nontrivial smooth solution to the one phase free boundary problem in high...

Self-adjoint extensions of D correspond to Lagrangian subspaces of V and, moreover, the kernel of D determines such a Lagrangian subspace whenever D has a closed range. IfD is a symmetric differential operator on a manifold with boundary then, by partial integration, the form ω is given by an integral over the boundary. For example, if D is the Hessian of the symplectic action functional on pat...

In this article we study the behaviour near the boundary for weak solutions of the system u 00 ? u ? (+)r((x) div u) = h ; with u(x; t) = 0 on the boundary of a domain 2 R n , and u(x; 0) = u 0 , u 0 (x; 0) = u 1 in. We show that the Sobolev norm of the solution in an "-neighbourhood of the boundary can be estimated independently of ".

In this note we consider boundary perturbations in the A-Series unitary minimal models by φr,r+2 fields on superpositions of boundaries. In particular, we consider perturbations by boundary condition changing operators. Within conformal perturbation theory we explicitly map out the space of perturbative renormalisation group flows for the example φ13 and find that this sheds light on more gener...

jurassic deposits are well exposed in the bazehowz area, south west of mashhad city, east alborz, iran. it contains plant macrofossilsbelonging to eighteen species of eleven genera of various orders such as equisetales, filicales, bennettitales, cycadales,corystospermales, caytoniales, ginkgoales and pinales. two biozones were recognized in the type section of bazehowz formation.biozone i is an...

Thermal instabilities can cause a radiative shock to oscillate, thereby modulating the emission from the post-shock region. The mode frequencies are approximately quantised in analogy to those of a vibrating pipe. The stability properties depend on the cooling processes, the electron-ion energy exchange and the boundary conditions. This paper considers the effects of the lower boundary conditio...

In this paper, the effect of different boundary conditions on the free vibration analysis response of a sandwich plate is presented using the higher order shear deformation theory. The face sheets are orthotropic laminated composites that follow the first order shear deformation theory (FSDT) based on the Rissners-Mindlin (RM) kinematics field. The motion equations are derived considering the c...

Let K ⊂ R be a regular convex cone, let e1, . . . , en ∈ ∂K be linearly independent points on the boundary of a compact affine section of the cone, and let x∗ ∈ K be a point in the relative interior of this section. For k = 1, . . . , n, let lk be the line through the points ek and x ∗, let yk be the intersection point of lk with ∂K opposite to ek, and let zk be the intersection point of lk wit...