44 research outputs found
On the Application of Numerical Methods to Hallen's Equation : The Case of a Lossy Medium
No full textA previous paper (Fikioris and Wu, 2001) analyzed in detail the difficulties associated with the application of numerical methods to Hallen's integral equation with the approximate kernel for the case of a lossless surrounding medium. This letter extends to the case where the medium is conducting and points out similarities and differences between the two cases. Our main tool is an analytical/asymptotic study of the antenna of infinite length.</p
An extension to "A subsemigroup of the rook monoid"
No full textA recent paper studied an inverse submonoid of the rook monoid, by
representing the nonzero elements of via certain triplets belonging to
. In this short note, we allow the triplets to belong to
. We thus study a new inverse monoid , which is a
supermonoid of . We point out similarities and find essential differences.
We show that is a noncommutative, periodic, combinatorial,
fundamental, completely semisimple, and strongly -unitary inverse monoid
A subsemigroup of the rook monoid
No full textWe define a subsemigroup of the rook monoid and investigate its
properties. To do this, we represent the nonzero elements of (which are
matrices) via certain triplets of integers, and develop a
closed-form expression representing the product of two elements; these tools
facilitate straightforward deductions of a great number of properties. For
example, we show that consists solely of idempotents and nilpotents, find
the numbers of idempotents and nilpotents, and compute nilpotency indexes.
Furthermore, we give a necessary and sufficient condition for the th root of
a nonzero element to exist in , show that existence implies uniqueness,
and compute the said root explicitly. We also point to several combinatorial
aspects; describe a number of subsemigroups of ; and, using rook
-diagrams, graphically interpret many of our results
Mellin-transform method for integral evaluation
No full textThis book introduces the Mellin-transform method for the exact calculation of one-dimensional definite integrals, and illustrates the application if this method to electromagnetics problems. Once the basics have been mastered, one quickly realizes that the method is extremely powerful, often yielding closed-form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals. Yet, as opposed to other methods, the present method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. Two functions, the general
