We use the notion of boundary points to study resolution proofs. Given a CNF formula F , an l(x)-boundary point is a complete assignment falsifying only clauses of F having the same literal l(x) of variable x. An l(x)-boundary point p mandates a resolution on variable x. Adding the resolvent of this resolution to F eliminates p as an l(x)-boundary point. Any resolution proof has to eventually e...

The McCoy-Roan integral representation for gaps of the integrable Znsymmetric Chiral Potts quantum chain is used to calculate the boundary of the incommensurable phase for various n. In the limit n → ∞ an analytic formula for this phase boundary is obtained. The McCoy-Roan formula gives the gaps in terms of a rapidity. For the lowest gap we conjecture the relation of this rapidity to the physic...

We show that the optimal stopping boundary for the early exercise Asian call option with floating strike can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary). The key argument in the proof relies upon a local time-space formula.

We define generalized Atiyah-Patodi-Singer boundary conditions of product type for Dirac operators associated to C∗-vector bundles on the product of a compact manifold with boundary and a closed manifold. We prove a product formula for the K-theoretic index classes, which we use to generalize the product formula for the topological signature to higher signatures.

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...

The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions ...

We present a signature formula for compact 4k-manifolds with corners of codimension two which generalizes the formula of Atiyah, Patodi and Singer for manifolds with boundary. The formula expresses the signature as a sum of three terms, the usual Hirzebruch term given as the integral of an L-class, a second term consisting of the sum of the eta invariants of the induced signature operators on t...

We consider the general supersymmetric one-dimensional quantum system with boundary, critical in the bulk but not at the boundary. The renormalization group (RG) flow on the space of boundary conditions is generated by the boundary beta functions β(λ) for the boundary coupling constants λ. We prove a gradient formula ∂ ln z/∂λ = −g abβ where z(λ) is the boundary partition function at given temp...

The initialand boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behavior (termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. To this aim, we derive a new formula representing solutions of this initialand boundary-value problem by inverting the operat...