High-resolution electron microscopy of montmorillonite and montmorillonite/epoxy nanocomposites

With the use of high-resolution transmission electron microscopy the structure and morphology of montmorillonite (MMT), a material of current interest for use in polymer nanocomposites, was characterized. Using both imaging theory and experiment, the procedures needed to generate lattice images from MMT were established. These procedures involve careful control of the microscope's objective lens defocus to maximize contrast from features of a certain size, as well as limiting the total dose of electrons received by the sample. Direct images of the MMT lattice were obtained from neat Na+ MMT, organically modified MMT, and organically modified MMT/epoxy nanocomposites. The degree of crystallinity and turbostratic disorder were characterized using electron diffraction and high-resolution electron microscopy (HREM). Also, the extent of the MMT sheets to bend when processed into an epoxy matrix was directly visualized. A minimum radius of curvature tolerable for a single MMT sheet during bending deformation was estimated to be 15 nm, and from this value a critical failure strain of 0.033 was calculated. HREM can be used to improve the understanding of the structure of polymer nanocomposites at the nanometer-length scale.     

Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules

Control design belongs to the most important and difficult tasks of control engineering and has therefore been treated by many prominent researchers and in many textbooks, the systems being generally described by their transfer matrices or by Rosenbrock equations and more recently also as behaviors. Our approach to controller design uses, in addition to the ideas of our predecessors on coprime factorizations of transfer matrices and on the parametrization of stabilizing compensators, a new mathematical technique which enables simpler design and also new theorems in spite of the many outstanding results of the literature: (1) We use an injective cogenerator signal module ? over the polynomial algebra [Formula: see text] (F an infinite field), a saturated multiplicatively closed set T of stable polynomials and its quotient ring [Formula: see text] of stable rational functions. This enables the simultaneous treatment of continuous and discrete systems and of all notions of stability, called T-stability. We investigate stabilizing control design by output feedback of input/output (IO) behaviors and study the full feedback IO behavior, especially its autonomous part and not only its transfer matrix. (2) The new technique is characterized by the permanent application of the injective cogenerator quotient signal module [Formula: see text] and of quotient behaviors [Formula: see text] of [Formula: see text]-behaviors B. (3) For the control tasks of tracking, disturbance rejection, model matching, and decoupling and not necessarily proper plants we derive necessary and sufficient conditions for the existence of proper stabilizing compensators with proper and stable closed loop behaviors, parametrize all such compensators as IO behaviors and not only their transfer matrices and give new algorithms for their construction. Moreover we solve the problem of pole placement or spectral assignability for the complete feedback behavior. The properness of the full feedback behavior ensures the absence of impulsive solutions in the continuous case, and that of the compensator enables its realization by Kalman state space equations or elementary building blocks. We note that every behavior admits an IO decomposition with proper transfer matrix, but that most of these decompositions do not have this property, and therefore we do not assume the properness of the plant. (4) The new technique can also be applied to more general control interconnections according to Willems, in particular to two-parameter feedback compensators and to the recent tracking framework of Fiaz/Takaba/Trentelman. In contrast to these authors, however, we pay special attention to the properness of all constructed transfer matrices which requires more subtle algorithms.     

The Radical Anion,Dianion and Electron Transport Properties of Tetraiodotetraazapentacene

Tetraiodotetraazapentacene I₄TAP , the last missing derivative in the series of halogenated silylated tetraazapentacenes, was synthesized via condensation chemistry from a TIPS-ethynylated diaminobenzothiadiazol in three steps. Single and double reduction furnished its air-stable monoanion and relatively air-stable dianion, both of which were characterized by crystallography. All three species are structurally and spectroscopically compared to non-halogenated TAP and Br₄TAP . I₄TAP is an n-channel material in thin-film transistors with average electron mobilities exceeding 1 cm² (Vs)⁻¹.     

Time-resolved probing of the ground state coherence in rubidium

We demonstrate the preparation and probing of the coherence between the hyperfine ground states |S(1/2),F=1> and |5S(1/2),F=2> of the Rb87 isotope. The effects of various coherence control techniques, i.e., fractional stimulated Raman adiabatic passage and coherent population return, on the coherence are investigated. These techniques are implemented using nearly degenerate pump and Stokes lasers at 795 nm (Rb D1 transition), which couple the two hyperfine ground states via the excited state |5P(1/2),F=1> through a resonant two-photon process in which a coherent superposition of the two hyperfine ground states is established. The medium is probed by an additional weak laser, which generates a four-wave mixing signal proportional to the ground state coherence and allows us to monitor its evolution in time. The experimental data are compared with numerical simulations.     

Transfer Operators and State Spaces for Discrete Multidimensional Linear Systems

This paper treats multidimensional discrete input-output systems from the constructive point of view. We adapt and improve recursive algorithms, derived earlier by E. Zerz and the second author from standard Gröbner basis algorithms, for the solution of the canonical Cauchy problem for linear systems of partial difference equations with constant coefficients on the lattices N = ^r1 × ^r2. These recursive algorithms, in turn, furnish four other solution methods for the initial value problem, namely by transfer operators, by canonical Kalman global state equations, by parametrizations of controllable systems and, for systems with proper transfer matrix and left bounded input signals, by convolution with the transfer matrix. In the 2D-case N = ² the last method was studied by S. Zampieri. Minimally embedded systems are studied and give rise to especially simple Kalman equations. The latter also imply a useful characterization of the characteristic or polar variety of the system by eigenvalue spectra. For N = ^r we define reachability of a system and prove that controllability implies reachability, but not conversely. Moreover we solve, in full generality, the modelling problem which was introduced and partially solved by F. Pauer and S. Zampieri. Various algorithms have been implemented by the first author in axiom, and examples are demonstrated by means of computer generated pictures. Related work on state space representations has been done by the Padovian and Groningian system theory schools.     

Is the madison convention really convenient at low energies?: The reaction 6Li(d)4He at 400 keV

It is shown that s-wave induced reactions with polarized particles can be described much more conveniently in new coordinates. Even with higher partial waves, cross sections can be fitted with less parameters than in conventional expansions.     

Über Untergruppen Endlicher Algebraischer Gruppen

Let k be a commutative ring, GG finite affine algebraic k-groups, and HH the dual Hopfalgebras of the affine algebras of G resp. G. The main results of this paper are: (I) If k is semilocal (e.g. k a field) there is an H-linear, HH-colinear, unitary, augmented isomorphism HHH H, where HH is the coalgebra belonging to G/G. (II) If the k-submodule of the fixelements of (HH)^* is isomorphic to k (e.g. k principal or semilocal), then HH is a Frobeniusextension of the second kind.     

Calcium signals can freely cross the nuclear envelope in hippocampal neurons: somatic calcium increases generate nuclear calcium transients

Background  

In hippocampal neurons, nuclear calcium signaling is important for learning- and neuronal survival-associated gene expression. However, it is unknown whether calcium signals generated by neuronal activity at the cell membrane and propagated to the soma can unrestrictedly cross the nuclear envelope to invade the nucleus. The nuclear envelope, which allows ion transit via the nuclear pore complex, may represent a barrier for calcium and has been suggested to insulate the nucleus from activity-induced cytoplasmic calcium transients in some cell types.