This study presents miscellaneous properties of pseudo-factorials, which are numbers whose recurrence relation is a twisted form of that of usual factorials. These numbers are associated with special elliptic functions, most notably, a Dixonian and a Weierstraß function, which parametrize the Fermat cubic curve and are relative to a hexagonal lattice. A continued fraction expansion of the ordin...

In this paper we explore two sets of polynomials, the orthogonal polynomi-als and the residual polynomials, associated with a preconditioned conjugate gradient iteration for the solution of the linear system Ax = b. In the context of preconditioning by the matrix C, we show that the roots of the orthogonal polynomials, also known as generalized Ritz values, are the eigenvalues of an orthogonal ...

In this paper, to increase normalized throughput of the optical code-divisionmultiple-access (CDMA) system, optical-CDMA systems with multi-pulse pulse position modulation (MPPM) using the modified pseudo orthogonal M-sequence sets is proposed. The throughput performance and bit error rate (BER) are evaluated by theoretical analysis. Consequently, the normalized throughput of the proposed syste...

A K-user pseudo-orthogonal (PO) randomly spread CDMA system, equivalent to transmission over a subset of K ′ ≤ K single-user Gaussian channels, is introduced. The high signal-to-noise ratio performance of the PO-CDMA is analyzed by rigorously deriving its asymptotic multiuser efficiency (AME) in the large system limit. Interestingly, the K -optimized PO-CDMA transceiver scheme yields an AME whi...

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...

We report on the complete computer search for a strongly regular graph with parameters (36,15,6,6) and chromatic number six. The result is that no such graph exists.

A pseudo-arc in PG(3n− 1, q) is a set of (n− 1)-spaces such that any three of them span the whole space. A pseudo-arc of size qn + 1 is a pseudo-oval. If a pseudo-oval O is obtained by applying field reduction to a conic in PG(2, qn), then O is called a pseudo-conic. We first explain the connection of (pseudo-)arcs with Laguerre planes, orthogonal arrays and generalised quadrangles. In particul...