REQUISITE AND QUALIFYING CONDITIONS OF ARTESIAN WELLS*1

Governance and Metagovernance: On Reflexivity, Requisite Variety, and Requisite Irony

There has been growing interest in the past twenty years or so in the potential contribution of new forms of governance to solving coordination problems in and across a wide range of specialized social systems (such as the economy, the legal system, the political system, and the health system) and in the lifeworld (or, broadly understood, civil society). This interest is reflected in growing am...

Qualifying Examination

so ‖f‖p ≤ ‖f‖q · μ(X) 1 p − 1 q . Hence if f is in Lq, the left-hand side is finite hence so is the right-hand side, so f is in Lp. Also, the inequality shows that if ‖f‖p is small then ‖f‖q is also small, hence the inclusion Lq ↪→ Lp is continuous 2. Let X ⊂ Pn be an irreducible projective variety of dimension k, G(`, n) the Grassmannian of `-planes in Pn for some ` < n− k, and C(X) ⊂ G(`, n) ...

Qualifying Examination

2. (T) Let CPn be complex projective n-space. (a) Describe the cohomology ring H∗(CPn,Z) and, using the Kunneth formula, the cohomology ring H∗(CPn × CPn,Z). (b) Let ∆ ⊂ CPn×CPn be the diagonal, and δ = i∗[∆] ∈ H2n(CP×CP,Z) the image of the fundamental class of ∆ under the inclusion i : ∆ → CPn × CPn. In terms of your description of H∗(CPn × CPn,Z) above, find the Poincaré dual δ∗ ∈ H2n(CPn × C...

Qualifying Examination

1. (a) Prove that the Galois group G of the polynomial X6 + 3 over Q is of order 6. (b) Show that in fact G is isomorphic to the symmetric group S3. (c) Is there a prime number p such that X6 + 3 is irreducible over the finite field of order p? Solution. We initially work over any field k in which the polynomial X6 + 3 is irreducible. Clearly k cannot have characteristic 2 or 3. Let α be a root...

A Review of Medical Cannabis Studies relating to Chemical Compositions and Dosages for Qualifying Medical Conditions