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 Under provisions of the current law, estate tax is repealed in the year 2010, but if Congress does not act, the legislation sunsets and returns to prior law January 1, 2011.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,

On an independence result in the theory of lawless sequences

The open data axiom LS3 for lawless sequences is actually an infinite list of axiom schemata: for each n we have LS3(n): A(a*,.... Un)AAi<jln CZi#Uj+%i ~ 3al... 2u,3a, y&Et41... Wn E htAi<jsn Bi*Bj+A(B19--*,/%I)); here oi, pi range over lawless sequences, and the ui range over finite sequences; ‘a E U ’ stands for ‘a has initial segment u’. In [D] it was shown that LS3(1) does not imply LS3(2) by using Cohen generic sequences. In [DL], this method was used to show that LS3(2) does not imply LS3(3). The aim of this note is to give simple proofs of these facts, by using the models described in [HM]. Our method also shows that LS3(3) does not imply LS3(4), but we have not been able to prove a similar independence result for larger n. For n L 4 a different approach seems necessary for showing LS3(n)f* 74LS3(n + 1). We observe here that the models described below all satisfy the axioms LSI (decidable equality) and LS2 (density), and that the models which show tha

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)

Redistribution does matter

Peer reviewe

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

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

On the complexity of skew arithmetic

13 pagesIn this paper, we study the complexity of several basic operations on linear differential operators with polynomial coefficients. As in the case of ordinary polynomials, we show that these complexities can be expressed in terms of the cost of multiplication

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