A Class of k-Quantum Nonlinear Coherent States and Some of Their Properties

A class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers B ^k (k lj21488w43/xxlarge8805.gif" alt="ge" align="MIDDLE" BORDER="0"> 3) of the annihilation operator lj21488w43/10773_2004_Article_496715_TeX2GIFIE1.gif" alt=" $$B = a\frac{1}{{f(N)}}$$ " align="middle" border="0"> of f-oscillators, is obtained and its completeness is investigated. An alternative method to construct them is proposed. We introduce a new kind of higher-order squeezing and sub-Poissonian distribution. The quantum statistical properties of the k states are studied. The result shows that all of the eigenstates can be generated by a linear superposition of k Roy-type nonlinear coherent states. These states may form a complete Hilbert space, and the M-th order [M = (n + 1/2)k; n = 0,1, ...] squeezing effects exist in all of the k states when k is even. There is the sub-Poissonian distribution in all of the states.     

The elimination of fast variables in complex chemical reactions. II. Mesoscopic level (reducible case)

The master equation for chemical reactions that proceed through a number of steps (complex reactions) is considered. Examples are studied in which the reaction constant of one of the steps is much larger than the others, and a reduced master equation is derived by means of a projection operator formalism. This reduction amounts to an elimination of intermediates. The consistency of the scheme is shown by means of thelj7g45/xxlarge937.gif" alt="OHgr" align="BASELINE" BORDER="0">-expansion.     

A Tsallis’ statistics based neural network model for novel word learning

We invoke the Tsallis entropy formalism, a nonextensive entropy measure, to include some degree of non-locality in a neural network that is used for simulation of novel word learning in adults. A generalization of the gradient descent dynamics, realized via nonextensive cost functions, is used as a learning rule in a simple perceptron. The model is first investigated for general properties, and then tested against the empirical data, gathered from simple memorization experiments involving two populations of linguistically different subjects. Numerical solutions of the model equations corresponded to the measured performance states of human learners. In particular, we found that the memorization tasks were executed with rather small but population-specific amounts of nonextensivity, quantified by the entropic index q. Our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems.     

ANALYSIS OF MATERIAL MECHANICAL PROPERTIES FOR SINGLE-WALLED CARBON NANOTUBES

Abstract The carbon-carbon bond between two nearest-neighboring atoms is modeled as a beam and the single-walled carbon nanotubes are treated as the space frame structures in order to analyze the mechanical properties of carbon nanotubes. Based on the theory of TersoffBrenner force field, the energy relationships between the carbon-carbon bond and the beam model are obtained, and the stiffness parameters of the beam are determined. By applying the presentmodel, the Young‘s moduli of the single-walled carbon nanotubes with different tube diameters are determined. And the present results are compared with available data.     

Effect ofβ-cyclodextrin complexation on the photohaemolitic activity induced by Ketoprofen and Naproxen sensitization

Red blood cell lysis photosensitized by two non-steroidal anti-inflammatory drugs Naproxen (NAP) and Ketoprofen (KPF) was investigated in the presence of lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin (lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd). The photohaemolysis was inhibited by the addition of lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd both for NAP and, to a lesser extent, for KPF. The protective action was found only in a restricted range of concentration of lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd. Higher amounts of lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd interfered with the resistance of the cell to the osmotic shock induced by the photosensitization process. The complexing action of lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd was ascertained through UV-vis absorption spectroscopy, induced circular dichroism and emission spectroscopy.The isolated complexes Naproxen-lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd (NAP-lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd) and Ketoprofen-lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd (KPF-lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd) were found to protect from the photosensitized membrane damage induced by the two drugs, even if it occurred only in a limited range of concentration. This suggests a valid tool in alleviating thein vitro phototoxic consequences caused by these compounds, even if care has to be taken in therapeutic administration due to the presence of the uncomplexed lj25625542537102/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Cyd.     

Minimal attractors in digraph system models of neuronal networks

We study a class of discrete dynamical systems models of neuronal networks. In these models, each neuron is represented by a finite number of states and there are rules for how a neuron transitions from one state to another. In particular, the rules determine when a neuron fires and how this affects the state of other neurons. In an earlier paper [D. Terman, S. Ahn, X. Wang, W. Just, Reducing neuronal networks to discrete dynamics, Physica D 237 (2008) 324-338], we demonstrate that a general class of excitatory-inhibitory networks can, in fact, be rigorously reduced to the discrete model. In the present paper, we analyze how the connectivity of the network influences the dynamics of the discrete model. For randomly connected networks, we find two major phase transitions. If the connection probability is above the second but below the first phase transition, then starting in a generic initial state, most but not all cells will fire at all times along the trajectory as soon as they reach the end of their refractory period. Above the first phase transition, this will be true for all cells in a typical initial state; thus most states will belong to a minimal attractor of oscillatory behavior (in a sense that is defined precisely in the paper). The exact positions of the phase transitions depend on intrinsic properties of the cells including the lengths of the cells’ refractory periods and the thresholds for firing. Existence of these phase transitions is both rigorously proved for sufficiently large networks and corroborated by numerical experiments on networks of moderate size.     

Duration of transient oscillations in ring networks of unidirectionally coupled neurons

Properties of the duration of long lasting transient oscillations in ring networks of unidirectionally coupled sigmoidal neurons are derived with a kinematical model of traveling waves in the network. The duration of the transient oscillations occurring from random initial conditions increases exponentially as the number of neurons. The distribution of the duration is approximated by a power-law function when the number of neurons is large. Further, transient oscillations which oscillate about one thousand cycles before ceasing are observed in a network of forty neurons in circuit experiments though the duration decreases owing to random biases.     

Bifurcation in neuronal networks with hub structure

We investigate bifurcations in neuronal networks with a hub structure. It is known that hubs play a leading role in characterizing the network dynamical behavior. However, the dynamics of hubs or star-coupled systems is not well understood. Here, we study rather subnetworks with a star-like configuration. This coupled system is an important motif in complex networks. Thus, our study is a basic step for understanding structure formation in large networks. We use the Morris-Lecar neuron with class I and class II excitabilities as a node. Homogeneous (coupling the same class neurons) and heterogeneous (coupling different class neurons) cases are considered for both excitatory and inhibitory coupling. For the homogeneous system class II neurons are suitable for achieving both complete and cluster synchronization in excitatory and inhibitory coupling, respectively. For the heterogeneous system with inhibitory coupling, the class I hub neuron has a wider parameter region of synchronous firings than the class II hub. Moreover, the class I hub neuron with the excitatory synapse gives rise to bifurcations of synchronized states and multi-stability (coexistence of a few different states) is observed.     

Zur Synthese von isocamphananalogem Ephedrin

The synthesis of two new bicyclic phenylethylamine derivatives with potentially simpathomimetic effects is described. The synthesis of the isocamphane analogous apoephedrine (4) starts from the bicyclic methylketone5 and leads via its lj357q8/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-bromoderivative6 and the corresponding tosylamidoketone8 to4. The synthesis of the title compound2 has been accomplished by preparing the lj357q8/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-oximinoketone19 from the bicyclic ethylketone15 with subsequent reduction to the amino alcohol derivative20 and final selective monomethylation by theJohnstone procedure via the corresponding trifluoroacetamide.

Herrn Prof. Dr.K. Kratzl mit den besten Wünschen zum 70. Geburtstag gewidmet.