Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation

Motivated by some recent results on the stabilization of homogeneous systems, we present a gain-scheduling approach for the stabilization of non-linear systems. Given a one-parameter family of stabilizing feedbacks and associated Lyapunov functions, we show how the parameter can be rescaled as a function of the state to give a new stabilizing controller. In the case of homogeneous systems, we obtain generalizations of some existing results. We show that this approach can also be applied to nonhomogeneous systems. In particular, the main application considered in this paper is to the problem of stabilization with magnitude limitations. For this problem, we develop a design method for single-input controllable systems with eigenvalues in the left closed plane

On distinguishing trees by their chromatic symmetric functions

Let $T$ be an unrooted tree. The \emph{chromatic symmetric function} $X_T$, introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of $T$. The \emph{subtree polynomial} $S_T$, first considered under a different name by Chaudhary and Gordon, is the bivariate generating function for subtrees of $T$ by their numbers of edges and leaves. We prove that $S_T =$, where $$ is the Hall inner product on symmetric functions and $\Phi$ is a certain symmetric function that does not depend on $T$. Thus the chromatic symmetric function is a stronger isomorphism invariant than the subtree polynomial. As a corollary, the path and degree sequences of a tree can be obtained from its chromatic symmetric function. As another application, we exhibit two infinite families of trees (\emph{spiders} and some \emph{caterpillars}), and one family of unicyclic graphs (\emph{squids}) whose members are determined completely by their chromatic symmetric functions.Comment: 16 pages, 3 figures. Added references [2], [13], and [15

Measurement of the Higgs mass via the channel : e+e- -> ZH -> e+e- + X

In this communication, the mass declined for the decay channel, e+e- -> ZH -> e+e- + X, as measured by the ILD detector was studied. The Higgs mass is assumed to be 120 GeV and the center of mass energy is 250 GeV. For an integrated luminosity of 250 fb-1, the accuracy of the reconstruction and the good knowledge of the initial state allow for the measurement of the Higgs boson mass with a precision of about 100 MeV.Comment: 7 pages, 14 figures, LCWS/ILC 2010 (International Linear Collider Workshop 2010 LCWS10 and ILC10

Alien Registration- Morin, Marguerite L. (Limerick, York County)

https://digitalmaine.com/alien_docs/3451/thumbnail.jp

Alien Registration- Morin, Armand L. (Biddeford, York County)

https://digitalmaine.com/alien_docs/4401/thumbnail.jp

Relationship between cavity form, restorative technology and strength of restored teeth

The results of an experimental and theoretical stress analysis of an invitro human tooth are presented. The experimental work involved developing a technique utilizing strain gauge technology to evaluate the surface strains of a tooth which are produced under a variety of cavity and restorative conditions. The results indicated that a tooth with a cavity preparation is significantly less stiff than a intact, sound tooth. When the tooth was restored with a traditional, non-bonding, restorative material the overall stiffness showed no difference from that of the tooth with the cavity preparation. Bonding the restorative material to enamel and dentin resulted in a significant recovery of stiffness approaching that of the sound tooth. Also, the bonded restorations displayed much less hysteresis as compared to the non-bonded restorations. The theoretical work consisted of formulating and validating a mathematical model to simulate the strain generation and distribution in a tooth under a variety of cavity and restorative conditions. The model used the plane strain assumption and was based on the finite element method. Results demonstrated that when the restorative material is bonded to both the enamel and the dentin the strain distribution approximantes that of a sound tooth. When bonding to just enamel is utilized in the restoration, the overall strain distribution approximates the sound tooth but localized areas of strain concentration still exist in the region bounded by the pulpal floor of the cavity and the pulp chamber. The modelling of a non-bonding restoration demonstrated no reduction in the strain magnitude or concentration

Using Schematic-Based and Cognitive Strategy Instruction to Improve Math Word Problem Solving for Students with Math Difficulties

For students with math difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine a math word problem solving strategy, bar model drawing, to support students with MD. The study extended previous research that suggested that schematic-based instruction (SBI) training delivered within an explicit instruction framework can be effective in teaching various math skills related to word problem solving. As a more generic schema approach, bar model drawing may serve as an effective form of SBI that can be developed across word problems. Moreover, the bar model approach has the potential to enhance students\u27 awareness of cognitive strategies through paraphrasing, visualizing, hypothesizing about problem solutions, and checking work, all of which are explicitly taught through the use of the bar-model drawing protocol. A multiple-baseline design replicated across groups was used to evaluate the effects of the intervention of bar model drawing on student performance on math world problem solving. Student performance was investigated in terms of increased accurate use of cognitive strategies and overall accuracy of math word problem solving. Both of these dependent variables increased and remained stable throughout intervention, and remained high during the maintenance phase of the research. Pre and posttesting results were also favorable. Participants reported high social validity for the intervention. However, the results of the research also yielded some surprises and raised some questions. Conclusions drawn from the data include a discussion of the implications for action and recommendations for further research. Limitations of the study are also discussed

A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

What controls the large-scale magnetic fields of M dwarfs?

Observations of active M dwarfs show a broad variety of large-scale magnetic fields encompassing dipole-dominated and multipolar geometries. We detail the analogy between some anelastic dynamo simulations and spectropolarimetric observations of 23 M stars. In numerical models, the relative contribution of inertia and Coriolis force in the global force balance -estimated by the so-called local Rossby number- is known to have a strong impact on the magnetic field geometry. We discuss the relevance of this parameter in setting the large-scale magnetic field of M dwarfs.Comment: 4 pages, 3 figures, conference proceeding, IAUS 302 'Magnetic Fields Throughout the Stellar Evolution', (26-30 Aug 2013, Biarritz, France