We show that integrating a (positively) homogeneous function f on a compact domain Ω ⊂ Rn reduces to integrating a related function on the boundary ∂Ω. The formula simplifies when the boundary ∂Ω is determined by homogeneous functions. Similar results are also presented for integration of exponentials and logarithms of homogeneous functions.

To make the ππ state with non-zero relative momentum as the leading exponential, we impose anti-periodic boundary condition on the pion, which is implemented by imposing G-parity or H-parity on the quark fields at the boundary. With this, we calculate the I = 2 ππ phase shift from lattice simulation by using Lüscher's formula.

In this paper, we first define the Teodorescu operator [Formula: see text] related to the Helmholtz equation and discuss its properties in quaternion analysis. Then we propose the Riemann boundary value problem related to the Helmholtz equation. Finally we give the integral representation of the boundary value problem by using the previously defined operator.

We derive the general formula, at a finite cutoff, for the change in the boundary condition of a scalar field in AdS under a Multiple-trace deformation of the dual CFT. Our analysis suggests that fluctuations around the classical solution in AdS should not be constrained by boundary conditions.

Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end. E-mail address: [email protected] 1 1 Introducntion Determinant representations of correlation functions of one dimensional quantum integrable models were studied extensively[1]. Especially Essler et. al. studie...

We study a new class of backward stochastic di€erential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial di€erential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.

We compute the relation between the Quillen metric and and the canonical metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we present a general formula relating the ζdeterminant and the canonical determinant for a class of higher-order elliptic boundary value problems.

the problem of downward continuation of the gravity field from the earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the earth’s surface. downward continuation is a...