The Cal Poly ITRC irrigation evaluation programs have been widely used to assess the global distribution uniformity (DU) of drip and microsprayer irrigation systems. The field procedures and formulas used in the program are presented in this paper. The system DU is estimated by mathematically combining the component DU values. DU components include pressure differences, "other causes" (such as ...

We develop the theory of Frobenioids associated to nonarchimedean [mixed-characteristic] and archimedean local fields. In particular, we show that the resulting Frobenioids satisfy the properties necessary to apply the main results of the general theory of Frobenioids. Moreover, we show that the reciprocity map in the nonarchimedean case, as well as a certain archimedean analogue of this recipr...

We determined the effectiveness of soy milk with calcium for prevention of enamel erosion caused by chlorinated water. Thirty-six bovine teeth without wear or caries, sized 8 x 10 mm, were placed in resin acrylic blocks. All specimens had an initial enamel microhardness of 270-320 VHN and were randomly allocated into 3 groups (n = 12/group): control (not treated), casein phosphopeptide-amorphou...

We prove that there are 0/1 polytopes P ⊆ R that do not admit a compact LP formulation. More precisely we show that for every n there is a sets X ⊆ {0, 1}n such that conv(X) must have extension complexity at least 2. In other words, every polyhedron Q that can be linearly projected on conv(X) must have exponentially many facets. In fact, the same result also applies if conv(X) is restricted to ...

A secret-sharing scheme enables a dealer to distribute a secret among n parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f : {0, 1}n → {0, 1}. A family of secret-sharing schemes i...

Let A(x) be the characteristic function of A. Consider the function Fk (x1, . . . , xk) = A(x1) · · ·A(xk). We show that if F A k can be computed with fewer than k queries to some set X then A ∈ P/poly. A generalization of this result has applications to bounded query classes, circuits, and enumerability. In particular we obtain the following. (1) Assuming Σp3 6= Π p 3, there are functions comp...

We have seen that there exist “very hard” languages (i.e., languages that require circuits of size (1 − ε)2n/n). If we can show that there exists a language in NP that is even “moderately hard” (i.e., requires circuits of super-polynomial size) then we will have proved P 6 = NP. (In some sense, it would be even nicer to show some concrete language in NP that requires circuits of super-polynomia...