Estate Planning and Farm Transfer in a Changing Legislative Environment: North Carolina, U.S.A. an Example

Since the enactment of the Economic Growth and Tax Relief Reconciliation Act of 2001, owners and operators of farms and ranches have opportunities to evaluate new estate planning strategies for the transfer of farm businesses to subsequent generations. However, with provisions of the Act to be phased in over several years, consideration must be given to having a "staged" estate plan. Under provisions of the current law, estate tax is repealed in the year 2010, but if Congress does not act, the legislation sunsets and returns to prior law January 1, 2011. This fact provides planning challenges for owners and operators of farms and ranches as the phase-in of provisions, the repeal in 2010, and the return to prior law relative to estate planning and business inter-generational transfer of property. This paper investigates the planning process and options available as they relate to a family-owned property in North Carolina, USA. Plans made must take into consideration the dynamics of a changing legislative environment, special-use valuation of land, opportunity cost of alternative uses for land, and off-farm heirs.Farm Management,

Faster polynomial multiplication over finite fields

Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two polynomials in F_p[X] of degree less than n. For n large compared to p, we establish the bound M_p(n) = O(n log n 8^(log^* n) log p), where log^* is the iterated logarithm. This is the first known F\"urer-type complexity bound for F_p[X], and improves on the previously best known bound M_p(n) = O(n log n log log n log p)

Quasi-optimal multiplication of linear differential operators

We show that linear differential operators with polynomial coefficients over a field of characteristic zero can be multiplied in quasi-optimal time. This answers an open question raised by van der Hoeven.Comment: To appear in the Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS'12

Dimension in the realm of transseries

Let $\mathbb T$ be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of ${\mathbb T}^n$, also in relation to its codimension in the ambient space ${\mathbb T}^n$. The case of dimension $0$ is of special interest, and can be characterized both in topological terms (discreteness) and in terms of the Herwig-Hrushovski-Macpherson notion of co-analyzability. The proofs use results by the authors from "Asymptotic Differential Algebra and Model Theory of Transseries", the axiomatic framework for "dimension" in [L. van den Dries, "Dimension of definable sets, algebraic boundedness and Henselian fields", Ann. Pure Appl. Logic 45 (1989), no. 2, 189-209], and facts about co-analyzability from [B. Herwig, E. Hrushovski, D. Macpherson, "Interpretable groups, stably embedded sets, and Vaughtian pairs", J. London Math. Soc. (2003) 68, no. 1, 1-11].Comment: 16 pp; version 2, taking into account comments by the refere

Redistribution Does Matter Growth and Redistribution for Poverty Reduction

Poverty, Inequality, Growth, Redistribution

Towards a Model Theory for Transseries

The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field, and report on our efforts to understand its first-order theory.Comment: Notre Dame J. Form. Log., to appear; 33 p