Number and rationality

Firms, Workers, and Human Capital in Ghanaian Manufacturing My model is a much simplified version of so-called “multicommunity” models. I maintain the usual assumptions that the number of communities is fixed and finite, and that access to desirable communities is rationed through the real estate market.19 There is no private sector that would de-link school quality from residential location. Although some authors (i.e. Epple and Zelenitz, 1981) include a supply side of the housing market, I assume that communities are endowed with perfectly inelastic stocks of identical houses....

168p mualan_mualan 25-02-2013 77 8   Download

By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables. 1. Introduction Early work of Lewis [14] and Birch [3], [4], now almost a half-century old, shows that pairs of quite general homogeneous cubic equations possess non-trivial integral solutions whenever the dimension of the corresponding intersection is suitably large (modern refinements have reduced this permissible affine dimension to 826; see [13]). ...

32p noel_noel 17-01-2013 60 6   Download

Let p be a prime number, F a totally real field such that [F (µp ) : F ] = 2 and [F : Q] is odd. For δ ∈ F × , let [ δ ] denote its class in F × /F ×p . In this paper, we show Main Theorem. There are infinitely many classes [ δ ] ∈ F × /F ×p such that the twisted affine Fermat curves Wδ : have no F -rational points. Remark. It is clear that if [ δ ] = [ δ ], then Wδ is isomorphic to Wδ over F . For any δ ∈ F × , Wδ /F has rational points locally everywhere.

25p noel_noel 17-01-2013 43 6   Download

It is known that nonergodic directions in a rational billiard form a subset of the unit circle with Hausdorff dimension at most 1/2. Explicit examples realizing the dimension 1/2 are constructed using Diophantine numbers and continued fractions. A lower estimate on the number of primitive lattice points in certain subsets of the plane is used in the construction.

19p tuanloccuoi 04-01-2013 45 5   Download

In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.

13p thulanh8 19-09-2011 67 4   Download

In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.

37p thulanh8 19-09-2011 58 14   Download

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers...

19p thulanh6 15-09-2011 65 2   Download

What makes work with rational numbers and integers comfortable are the essential properties they have, especially the unique factorization property (the Main Theorem of Arithmetic). However, the might of the arithmetic in Q is bounded. Thus, some polynomials, although they have zeros, cannot be factorized into polynomials with rational coefficients.

7p phuctran399 14-11-2010 73 6   Download