A new simple formula for the radiation efficiency of a resonant rectangular microstrip patch antenna is presented. The formula is obtained by using a tabu search algorithm, which is a quite new optimization technique based on the principles of intelligent problem solving. The formula is valid for substrates with relative permittivities between 1 and 12.8 and for the complete range of thicknesse...

We introduce a simple and convenient fitting formula for the thermal annihilation line from pair plasmas in cosmic sources. The fitting formula is accurate to 0.04% and is valid at all photon energies and temperatures of interest. The commonly used Gaussian line profile is not a good approximation for broader lines.

We derive an elementary formula for the trace of a Hecke operator acting on a space of algebraic modular forms, as a sum of character values. We describe explicit computations in the case of the unitary group U(4), allowing the determination of the eigenvalues of a certain Hecke operator. This produces numerical evidence for a U(2, 2) analogue of Harder’s conjecture, on congruences between Heck...

We give a Euler-Maclaurin formula with remainder for the sum of a smooth function on the integral points in a simple integral lattice polytope. Our proof uses elementary methods.

Given z ∈ C and A ∈ Z, we consider the problem of evaluating the counting function h(y; z) := P { z |x∈Z;Ax=y, x≥0}. We provide an explicit expression for h(y; z) as well as an algorithm with possibly numerous but very simple calculations. In addition, we exhibit finitely many fixed convex cones of R explicitly and exclusively defined by A such that for any y ∈ Z, the sum h(y; z) can be obtaine...

Gauss diagram formulas are extensively used to study Vassiliev link invariants. Now we apply this approach to invariants of 3-manifolds, considering a manifold as a result ML of surgery on a framed link L in S . We study the lowest degree case – the celebrated Casson-Walker invariant λw of rational homology spheres. This paper is dedicated to a detailed treatment of 2-component links; a general...

Simple approximate formulas for the ground resistance and the potential distribution that have quite good accuracy are presented. The use of these formulas can simplify and make faster the calculation of ground path coupling.

When various observers obtain information in an independent fashion about a classical system, there is a simple rule which allows them to pool their knowledge, and this requires only the statesof-knowledge of the respective observers. Here we derive an equivalent quantum formula. While its realm of applicability is necessarily more limited, it does apply to a large class of measurements, and we...

Let g be a complex simple Lie algebra. Vogel derived a universal decomposition of S2g into (possibly virtual) Casimir eigenspaces, S2g = C⊕Y2 ⊕Y ′ 2 ⊕Y ′′ 2 which turns out to be a decomposition into irreducible modules. If we let 2t denote the Casimir eigenvalue of the adjoint representation (with respect to some invariant quadratic form), these modules respectively have Casimir eigenvalues 4t...

On the other hand, while current technique is arguably much more sophisticated, the questions addressed are commensurately more complicated, so that simplification of a proof of a basic Siegel-Weil formula may get lost in more difficult issues. For example, the work of Kudla-Rallis on regularization addresses much more delicate questions than the simple equality of holomorphic Eisenstein series...