Search for second and third generation leptoquarks including production via technicolor interactions in p&pmacr; collisions at radicals = 1.8 TeV

We report the results of a search for second and third generation leptoquarks using 88 pb(-1) of data recorded by the Collider Detector at Fermilab. Color triplet technipions, which play the role of scalar leptoquarks, are investigated due to their potential production in decays of strongly coupled color octet technirhos. Events with a signature of two heavy flavor jets and missing energy may indicate the decay of a second (third) generation leptoquark to a charm (bottom) quark and a neutrino. As the data are found to be consistent with standard model expectations, mass limits are determined.     

Intramolecular cyclization of bis-α-diazoketones: A new synthesis of γ-tropolone

Catalytic decomposition of bis-α-diazoketones (3, n = 3), in inert solvents, under high dilution affords cycloalk-2-ene-1,4-diones (4, n = 3). The method has been applied to a new synthesis of γ-tropolone 5 in five steps from glutaconic acid 6.     

Cryopreservation of cultivated and wild Arachis species embryonic axes using desiccation and vitrification methods

The effects of two methods of cryopreservation involving chemical vitrification and air desiccation) were studied on isolated embryonic axes of A. hypogaea. Vitrification with PVS2 and desiccation in a laminar flow cabinet resulted in high levels (70-90%) of whole plant recovery after cryopreservation. A desiccation protocol based on 1h exposure of explants to the air flow was successfully applied to six wild species of section Extranervosae, resulting in recovery levels of 70-90% after liquid nitrogen treatment.     

Regularity of Invariant Manifolds for Nonuniformly Hyperbolic Dynamics

For any sufficiently small perturbation of a nonuniform exponential dichotomy, we show that there exist invariant stable manifolds as regular as the dynamics. We also consider the general case of a nonautonomous dynamics defined by the composition of a sequence of maps. The proof is based on a geometric argument that avoids any lengthy computations involving the higher order derivatives. In addition, we describe how the invariant manifolds vary with the dynamics.      

Qualitative analysis of the anisotropic two-body problem under Seeliger's potential

In this paper we study the two-body problem that describes the motion of two-point masses in an anisotropic space under the influence of the Seeliger potential. We will show that the set of initial conditions leading to collisions and ejections has positive measure and study the capture and escape solutions in the positive-energy case using the infinity manifold. We will also apply the Melnikov method to show that the flow on the zero-energy manifold of another potential which is the sum of the classical Keplerian potential and the anisotropic Seeliger's potential perturbation is chaotic.     

Hyperbolic Sequences of Linear Operators and Evolution Maps

For a nonautonomous dynamics defined by a sequence of linear operators on a Banach space, we give a characterization of its nonuniform hyperbolicity in terms of the hyperbolicity of an associated evolution map. We also obtain a generalization of this characterization to the class of nonuniformly hyperbolic cocycles over a locally compact topological space with values on the set of bounded linear operators.     

Stable invariant manifolds for delay equations with piecewise constant argument

We construct smooth stable invariant manifolds for a class of delay equations with piecewise constant delay, for any sufficiently small perturbation of a nonuniform exponential dichotomy. We build on former work for perturbations of a uniform exponential dichotomy, also for delay equations with piecewise constant delay. These equations can be described as delay equations with an impulsive behavior of the derivative, such that at certain times the derivative changes abruptly.     

Learning to notice students’ mathematical thinking through on-line discussions

The goal of this research is to characterize prospective mathematics teachers?? development of professional noticing of students?? mathematical thinking in on-line contexts. Specifically, we are interested in how the participation in on-line discussions, when prospective teachers solve specific tasks, supports the development of professional noticing of students?? mathematical thinking. Findings show that an aspect in which the on-line discussions, as an example of asynchronous collaborative communication interfaces, support this development is related to the role of writing; participating in an on-line discussion plays a significant role since the final written text is functional as regards the activity of interpreting students?? mathematical thinking collaboratively.