Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 4. Assume that the intersection numbers of Γ satisfy ai = 0 for 0 ≤ i ≤ D − 1 and aD 6= 0. We show that Γ is a polygon, a folded cube, or an Odd graph.

This paper provides a broad-ranging review in a global context of many aspects of developing changes in intellectual property rights (IPR) in response to the currently rapidly changing technological and information industries. As such, it covers such matters as knowledge ownership, the IPR framework, TRIPS and WTO in relation to developing countries, technology transfer and balance in a world-w...

Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider two new q-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with q-Fibonacci polynomials and the recent works on the combinatorics of the Matrix Ansatz of the PASEP.

The Causal Theory of Properties (CTP) (Shoemaker, 1980a, 1980b, 1998) presents a striking picture: although a property might ultimately be distinct from the causal powers it confers on its instantiations (Shoemaker, 1998, p. 64), those causal powers limn the property’s identity. In the words of CTP’s leading proponent, Sydney Shoemaker, “The formulation of the causal theory of properties I now ...

Property testers are algorithms whose goal is distinguishing between inputs that have a certain property and inputs which are far from all instances with this property. We show that for a wide variety of properties, there exists no deterministic tester that queries only a sublinear number of input entries. Therefore, most sublinear property testers must be probabilistic algorithms. Nevertheless...

These problems are inspired by a careful study of the papers of concerning bipartite distance-regular graphs. Throughout these notes we let Γ = (X, R) denote a bipartite distance-regular graph with diameter D ≥ 3 and standard module V = C X. We fix a vertex x ∈ X and let E denote the corresponding dual primitive idempotents. We define the matrices R = D i=0 E * i+1 AE * i , L= D i=0 E * i−1 AE ...

We prove that for almost all σ ∈ G(Q)e the field Q̃(σ) has the following property: For each absolutely irreducible affine variety V of dimension r and each dominating separable rational map φ: V → Ar there exists a point a ∈ V (Q̃(σ)) such that φ(a) ∈ Zr. We then say that Q̃(σ) is PAC over Z. This is a stronger property then being PAC. Indeed we show that beside the fields Q̃(σ) other fields which ...

Latin squares of order n exist for each n ≥ 1. There are severalways of constructing Latin squares. Also for n≥ 2, if the number of reduced Latin squares isknown, then the number of general Latin squares canbecalculated. This paperproposed a generalmethod to constructsymmetric Latin squares of orderq by using blocks of order q which have the basic property of a recursivealgorithmwith the use of...

More generally, in the first claim we can replace the Lp(Q) norm with any norm || · || on F with the Riesz property, which is that |f | ≤ |g| (pointwise) implies ||f || ≤ ||g||. For the second claim, we can use any norm that has the Riesz property and for which the norm of the constant function f ≡ 1 is 1, which is clearly satisfied by Lp(Q) when Q is a probability measure. With these more gene...

A matroid is GF(q)-regular if it is representable over all proper superfields of the field GF(q). We show that, for highly connected matroids having a large projective geometry over GF(q) as a minor, the property of GF(q)-regularity is equivalent to representability over both GF(q) and GF(q) for some odd integer t ≥ 3. We do this by means of an exact structural description of