Case Study: Minimizing Food Wastage From Farm to Consumer Products – A Systems Approach

Sterman Masser, Inc. is committed to minimizing food loss throughout the process of growing, harvesting, and packaging a consumer ready product through the use of cutting edge technology industry leading techniques. Combining Integrated Pest Management with crop rotations and more resistant potato varieties, SMI has minimized the potential for crop destroying fungi and insects to propagate. In response to hazards from rocks in the soil and the stresses from harvesting we have acquired rock crushers capable of pulverizing everything down to a powder and new harvesters designed to reduce the stresses of harvesting. Potatoes, coming from the fields, enter our state-of-the-art cold storage facility that combines ideal climate conditions with treatment by gassing and sprout inhibitors to combat food loss due to decay and significantly extend the useable life of the potatoes. Potatoes entering SMI’s packing facility are processed with low impact techniques and equipment, on a First In, First Out policy designed to get product from the field to the consumer in the shortest possible time. In the past, product not suited for table stock quality was simply removed and discarded. Today, thanks to the construction of the Keystone Potato Products facility, we can salvage what was previously considered waste product. In the event of a natural disaster, KPP has the capacity to process every single potato, no matter what defect, to provide nourishment to those in need. Potatoes with small to moderate defects can be processed into fresh cut consumer products through automated equipment capable of identifying and removing those parts unfit for human consumption. Potatoes unfit for the fresh cut process, as well as the waste generated by that process, can be further refined into dehydrated products ensuring every single potato can be made useable for human consumption. Even the peel waste can be salvaged for use as feed for livestock

Multiplicative isogeny estimates

The theory of isogeny estimates for Abelian varieties provides ‘additive bounds' of the form ‘d is at most B' for the degrees d of certain isogenies. We investigate whether these can be improved to ‘multiplicative bounds' of the form ‘d divides B'. We find that in general the answer is no (Theorem 1), but that sometimes the answer is yes (Theorem 2). Further we apply the affirmative result to the study of exceptional primes in connexion with modular Galois representations coming from elliptic curves: we prove that the additive bounds for of Masser and Wüstholz (1993) can be improved to multiplicative bounds (Theorem 3

Rational points on Grassmannians and unlikely intersections in tori

In this paper, we present an alternative proof of a finiteness theorem due to Bombieri, Masser and Zannier concerning intersections of a curve in the multiplicative group of dimension n with algebraic subgroups of dimension n-2. The proof uses a method introduced for the first time by Pila and Zannier to give an alternative proof of Manin-Mumford conjecture and a theorem to count points that satisfy a certain number of linear conditions with rational coefficients. This method has been largely used in many different problems in the context of "unlikely intersections".Comment: 16 page

Torsion points, Pell's equation, and integration in elementary terms

The main results of this paper involve general algebraic differentials $\omega$ on a general pencil of algebraic curves. We show how to determine if $\omega$ is integrable in elementary terms for infinitely many members of the pencil. In particular, this corrects an assertion of James Davenport from 1981 and provides the first proof, even in rather strengthened form. We also indicate analogies with work of André and Hrushovski and with the Grothendieck-Katz Conjecture. To reach this goal, we first provide proofs of independent results which extend conclusions of relative Manin-Mumford type allied to the Zilber-Pink conjectures: we characterize torsion points lying on a general curve in a general abelian scheme of arbitrary relative dimension at least 2. In turn, we present yet another application of the latter results to a rather general pencil of Pell equations $A^2-DB^2=1$ over a polynomial ring. We determine whether the Pell equation (with squarefree $D$) is solvable for infinitely many members of the pencil

Polynomial-exponential equations -- some new cases of solvability

Recently Brownawell and the second author proved a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure". Here we treat some significant new cases. In particular these settle completely the problem of solving polynomial-exponential equations in two complex variables. The methods of proof are also new, as is the consequence, for example, that there are infinitely many complex $z$ with $e^z+e^{1/z}=1$.Comment: 26 page

CM relations in fibered powers of elliptic families

Let $E_\lambda$ be the Legendre family of elliptic curves. Given $n$ linearly independent points $P_1,\dots , P_n \in E_\lambda\left(\overline{\mathbb{Q}(\lambda)}\right)$ we prove that there are at most finitely many complex numbers $\lambda_0$ such that $E_{\lambda_0}$ has complex multiplication and $P_1(\lambda_0), \dots ,P_n(\lambda_0)$ are dependent over $End(E_{\lambda_0})$. This implies a positive answer to a question of Bertrand and, combined with a previous work in collaboration with Capuano, proves the Zilber-Pink conjecture for a curve in a fibered power of an elliptic scheme when everything is defined over $\overline{\mathbb{Q}}$.Comment: The formulation of Theorem 2.1 is now correc

An effective "Theorem of André” for CM-points on a plane curve

It is a well known result of Y. André (a basic special case of the André-Oort conjecture) that an irreducible algebraic plane curve containing infinitely many points whose coordinates are CM-invariants is either a horizontal or vertical line, or a modular curve Y 0(n). André's proof was partially ineffective, due to the use of (Siegel's) class-number estimates. Here we observe that his arguments may be modified to yield an effective proof. For example, with the diagonal line X 1+X 2=1 or the hyperbola X 1 X 2=1 it may be shown quite quickly that there are no imaginary quadratic τ1,τ2 with j(τ1)+j(τ2)=1 or j(τ1)j(τ2)=1, where j is the classical modular functio