A new boundary-integral formulation is proposed to analyze the heat transfer in zoned three-dimensional geometries. The proposed formulation couples the boundary formula, the gradient of the boundary formula, and the exterior formula. An advantage of this formulation over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formul...

3 The Exterior Algebra 6 3.1 Dimension of the Exterior Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Bilinear Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 Other Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3.1 The determinant formula . . . . . . . . . . . . . . . . . . . . . . . . . ...

We have recently derived a Schwarz-Christoffel formula for the conformal mapping of the exterior of a finite number of disks to the exterior of a set of polygonal curves [5]. In this work we show how to formulate a set of equations for determining the parameters of such a map. A number of examples are computed, including exteriors of multiple slits. We also recall the derivation of the mapping ...

A diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of ∂M . We derive a formula for the boundary slope of a diagonal surface in the exterior of a 2-bridge link which is analogous to the formula for the boundary slope of a 2-bridge knot found b...

A formula for the generalized Schwarz–Christoffel conformal mapping from a bounded multiply connected circular domain to an unbounded multiply connected polygonal domain is derived. The formula for the derivative of the mapping function is shown to contain a product of powers of Schottky–Klein prime functions associated with the circular preimage domain. Two analytical checks of the new formula...

A natural Hasse-Schmidt derivation on the exterior algebra of a free module realizes the (small quantum) cohomology ring of the grassmannian Gk(C ) as a ring of operators on the exterior algebra of a free module of rank n. Classical Pieri’s formula can be interpreted as Leibniz’s rule enjoyed by special Schubert cycles with respect to the wedge product.

A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivity m ≥ 2 thereby extending the results of Christoffel (1867) and Schwarz (1869) for m = 1 and Komatu (1945), m = 2. A formula for f, the conformal map of the exterior of m bounded disks to the exterior of m bounded, disjoint polygons, is derived. The derivation characterizes the global preSchwarzian f...

A classical theorem of MacMahon states that the number of lozenge tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula. In this paper, we present a counterpart of this formula, corresponding to the exterior of a concave hexagon obtained by turning 120° after drawing each side (MacMahon’s hexagon is obtained by turning 60° af...

General relativity predicts that two freely counter-revolving test particles in the exterior field of a central rotating mass take different periods of time to complete the same full orbit; this time difference leads to the gravitomagnetic clock effect. The effect has been derived for circular equatorial orbits; moreover, it has been extended via azimuthal closure to spherical orbits around a s...

 . We discuss the electrodynamics of a rapidly rotating perfectly conducting magnetized sphere rotating with constant angular velocity about an axis which is inclined to the magnetic dipole field. An exact special relativistic solution is obtained for the electromagnetic field in the interior. The exterior solution is also determined and matched to the interior by using the appropriate boundar...