A cap in a projective or affine geometry is a set of points with the property that no line meets the set in more than two points. Barwick, et al. (Conics and caps. J. Geom., 100:15–28, 2011) provide a construction of caps in PG(4, q) by “lifting” arbitrary caps of PG(2, q2), such as conics. In this article, we extend this construction by considering when the union of two or more conics in AG(2,...

It is widely accepted that Mars had an atmosphere at least 4 Gyr ago. The processes that led to the loss of the Martian atmosphere are still debated. Solar-wind-induced sputtering, impact erosion, weathering, sequestration into the regolith and polar caps, and photodissociative reactions are the mechanisms believed to be responsible for removing the atmosphere. No one process has been shown to ...

|S|=n a(S) m. Specifically, we present an explicit formula for F (m,n) as a product of two matrices, ultimately yielding a polynomial in q = pd. The first matrix is independent of n while the second makes no mention of finite fields. However, the complexity of calculating each grows with m. The main tools here are the Schur-Weyl duality theorem, and some elementary properties of symmetric funct...

A d-dimensional dual arc in PG(n, q) is a higher dimensional analogue of a dual arc in a projective plane. For every prime power q other than 2, the existence of a d-dimensional dual arc (d ≥ 2) in PG(n, q) of a certain size implies n ≤ d(d + 3)/2 (Theorem 1). This is best possible, because of the recent construction of d-dimensional dual arcs in PG(d(d + 3)/2, q) of size ∑d−1 i=0 qi , using th...

This paper is concerned with constructing caps embedded in line Grassman-nians. In particular, we construct a cap of size q 3 + 2q 2 + 1 embedded in the Klein quadric of P G(5; q) for even q, and show that any cap maximally embedded in the Klein quadric which is larger than this one must have size equal to the theoretical upper bound, namely q 3 + 2q 2 + q + 2. It is not known if caps achieving...

The travel agency industry is currently experiencing profound changes such as commission caps and cuts, increased popularity of online travel agents, and the emergence of automated travel management systems. These developments forced many travel agents to exit the market or to surrender to lower profitability. This case study examines how a mega-agency responded to these threats, the obstacles ...

We develop a tractable and flexible stochastic volatility multifactor model of the term structure of interest rates. It features unspanned stochastic volatility factors, correlation between innovations to forward rates and their volatilities, quasi-analytical prices of zerocoupon bond options, and dynamics of the forward rate curve, under both the actual and risk-neutral measures, in terms of a...

In this work we summarize some recent results to be included in a forthcoming paper [2]. In the projective space PG(N, q) over the Galois field of order q, N ≥ 3, an iterative step-by-step construction of complete caps by adding a new point at every step is considered. It is proved that uncovered points are evenly placed in the space. A natural conjecture on an estimate of the number of new cov...

We construct large caps in projective spaces of small dimension (up to 11) defined over fields of order at most 9. The constructions are both theoretical and computer-supported. Some more computergenerated 4-dimensional caps over larger fields are also mentioned.