For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an intimate relation between these two counting functions. A similar counting function and reciprocity law exists for the sum of all solid angles at integer points in dilates of P . We derive a unifying generalization of the...

Integral representations are derived from a differential-type boundary value problem using a fundamental solution. A set of integral representations is equivalent to a set of differential equations. If the boundary conditions are substituted into the integral representations, the integral equations are obtained, and the unknown variables are determined by solving the integral equations. In othe...

Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...

We show that a càdlàg, local martingale has conditionally independent increments and symmetric jumps if and only if its law is invariant under integral transformations which preserve quadratic variation.

We present observations in eight wavebands from 1.25− 24 μm of four dense cores: L204C-2, L1152, L1155C-2, and L1228. Our goals are to study the YSO population of these cores and to measure the mid-infrared extinction law. With our combined near-infrared and Spitzer photometry, we classify each source in the cores as, among other things, background stars, galaxies, or embedded young stellar obj...

We define a sample of 62 galaxies in the Chandra Deep Field-North whose Spitzer IRAC SEDs exhibit the characteristic power-law emission expected of luminous AGN. We study the multiwavelength properties of this sample, and compare the AGN selected in this way to those selected via other Spitzer color-color criteria. Only 55% of the power-law galaxies are detected in the X-ray catalog at exposure...

In this paper, we propose a nonlinear guidance law for missiles against maneuvering targets. First, we derive the equations of motion described in the line-of-sight reference frame and then we define the equilibrium subspace of the nonlinear system to guarantee target interception within a finite time. Using Sontag’s formula, we derive a nonlinear guidance law that always delivers the state to ...

The nearby BL Lacertae (BL Lac) object Markarian 421 (Mkn 421) at a red shift z = 0.031 was observed to undergo strong TeV γ-ray outbursts in the observational periods from December 1999 until May 2001. The time averaged flux level F (E > 1TeV) in the 1999/2000 season was (1.43± 0.04) ·10−11 ph cm−2 s−1, whereas in the 2000/2001 season the average integral flux increased to (4.19±0.04) ·10−11 p...

In this paper, a feedback boundary controller for an unstable heat equation is designed. The boundary control law is designed in the form of an integral operator with a known, continuous kernel function which can be interpreted as a back stepping control law. This interpretation provides a Lyapunov function for proving stability of the system. The control is applied by insulating one end of the...