Visual Supports Checklist

The Visual Supports Checklist is based on a review of current literature, practical knowledge, and reported experiences from early childhood educators on the topic of visual supports

Cutting a part from many measures

Holmsen, Kyncˇl and Valculescu recently conjectured that if a finite set X with in points in Rd that is colored by m different colors can be partitioned into n subsets of i points each, such that each subset contains points of at least d different colors, then there exists such a partition of X with the additional property that the convex hulls of the n subsets are pairwise disjoint. We prove a continuous analogue of this conjecture, generalized so that each subset contains points of at least c different colors, where we also allow c to be greater than d. Furthermore, we give lower bounds on the fraction of the points each of the subsets contains from c different colors. For example, when n ≤ 2, d ≤ 2, c ≤ d with m ≤ n(c - d) d are integers, and µ1, . . . ,µm are m positive finite absolutely continuous measures on Rd , we prove that there exists a partition of Rd into n convex pieces which equiparts the measures µ1, . . . ,µd−1, and in addition every piece of the partition has positive measure with respect to at least c of the measures µ1, . . . ,µm . 2010 Mathematics Subject Classification: 52C35, 51M20 (primary); 55R20, 55N25 (secondary

Abelian Magnetic Monopoles and Topologically Massive Vector Bosons in Scalar-Tensor Gravity with Torsion Potential

A Lagrangian formulation describing the electromagnetic interaction - mediated by topologically massive vector bosons - between charged, spin-(1/2) fermions with an abelian magnetic monopole in a curved spacetime with non-minimal coupling and torsion potential is presented. The covariant field equations are obtained. The issue of coexistence of massive photons and magnetic monopoles is addressed in the present framework. It is found that despite the topological nature of photon mass generation in curved spacetime with isotropic dilaton field, the classical field theory describing the nonrelativistic electromagnetic interaction between a point-like electric charge and magnetic monopole is inconsistent.Comment: 18 pages, no figure

Nonlinear Realization and Weyl Scale Invariant p=2 Brane

The action of Weyl scale invariant p=2 brane which breaks the target super Weyl scale symmetry in the N=1, D=4 superspace down to the lower dimensional Weyl symmetry W(1,2) is derived by the approach of nonlinear realization. The dual form action for the Weyl scale invariant supersymmetric D2 brane is also constructed. The interactions of localized matter fields on the brane with the Nambu-Goldstone fields associated with the breaking of the symmetries in the superspace and one spatial translation directions are obtained through the Cartan one-forms of the Coset structures. The covariant derivatives for the localized matter fields are also obtained by introducing Weyl gauge field as the compensating field corresponding to the local scale transformation on the brane world volume.Comment: 20 page

Effect of Consecutive Cut and Vegetation Stage on Cncps Protein Fractions in Alfalfa (Medicago Sativa L.)

Crude protein (CP) of forages can be separated into fractions of differentiated abilities to provide available amino acids in the lower gut of ruminants. This knowledge is critical to develop feeding systems and to predict animal responses. The objective of this research was to asses whether CP concentrations and the relative proportion of CP fractions by CNCPS in alfalfa (Medicago sativa L.) cv K-28 were affected by different cuts and vegetation stages. Fraction B2, which represents true protein of intermediate ruminal degradation rate, was the largest single fraction in all cuts except in the third cut. Soluble fraction A was less than 400 g kg-1 CP in all cuts except in the third cut, while the unavailable fraction C ranged from 56 g kg-1 CP in the first cut to 134.8 g kg-1 CP in the fourth cut. The remaining fraction B3 (true protein of very low degradation rate) only represented less than 60 g kg-1 of total CP. Results showed that undegraded dietary protein represented a small proportion of total CP in alfalfa from the first to the fourth cut