An Alternative Way to Generalize the Pentagon

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.     

A variational approach to second-order approximability of sliding mode control systems

We consider robustness properties of second-order methods for the sliding mode control of nonlinear ordinary differential equations. A new approach is presented based on the theory of well-posed optimization problems. It is shown that the convergence of the real states of the control system to the ideal one is intimately related to Tykhonov well-posedness of suitably defined dynamic optimization problems.     

Cousin I condition and Stein spaces

Here we give a few n-dimensional extensions of a recent result of M. Abe concerning a Cousin I characterization of two-dimensional Stein manifolds.     

Analysis for some properties of discrete time Markov decision processes

This paper investigates properties of the optimality equation and optimal policies in discrete time Markov decision processes with expected discounted total rewards under weak conditions that the model is well defined and the optimality equation is true. The optimal value function is characterized as a solution of the optimality equation and the structure of optimal policies is also given.     

Determination of the swelling behavior of superabsorbent polymers by a tracer-assisted on-line spectroscopic measurement

This work reports on a method for the accurate determination of kinetic swelling behavior and properties of superabsorbent polymers by a tracer-assisted on-line spectroscopic measurement. Based on monitoring the spectral absorption of a tracer compound (blue dextran 2000) at 610 nm in a superabsorbent polymer containing solution, the swelling (water absorption) of the polymer during the process can be followed, from which the parameters in a kinetic equation can be obtained. The results showed that the data obtained by the present method has a good measurement precision and accuracy, in which the relative differences were less than 4.0% when comparing the data measured by a reference method (i.e., the tea bag method). Since the present method can perform an on-line measurement, it is much superior to the current tea bag method and therefore is very suitable to be used in the process related study for the swelling behavior of superabsorbent polymers in many applications.     

Optimal Groomings with Grooming Ratios Six and Seven

Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs.     

Scanning tunneling microscopy/spectroscopy on Au nanoparticles assembled using lauryl amine (LAM) and octadecane thiol (ODT)

In this report, we demonstrate scanning tunneling microscopy and spectroscopy on thin films of lauryl amine (LAM) and octadecane thiol (ODT) protected gold nanoparticles. We show that the zero current in the I-V curves (measure of Coulomb blockade (CB) of the nanoparticles) depends on the properties of the spacer molecule. In both the cases the gap voltage and the tunneling current at which the images are obtained are quite different which is further confirmed from the fitting performed based on the orthodox theory. The values for the capacitance and charging energy obtained from the fitting for ODT capped particles are comparable to the values obtained using spherical capacitor model. In contrast, values of these parameters were found to differ for LAM capped nanoparticles. While imaging, ODT capped nanoparticles were observed to drag along the scan direction leading to ordering of particles. Images of LAM capped gold nanoparticles show local ordering in self-assembly of particles although no evidence of large scale ordering in spatial Fourier transform was seen. These observations suggest that nanoparticles with larger CB would be imaged nonevasively in contrast to small CB systems for which tip induced effects will be dominant. In both the systems the current was found to rise faster than theoretical curves based on the orthodox theory suggesting that mechanism of charge transfer in this case may involve field emission rather than tunneling through a rectangular barrier. An attempt has been made to explain charge transfer based on Fowler-Nordheim (F-N) plots of the I-V curves.     

Twisted Poincaré Duality for some Quadratic Poisson Algebras

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a corollary we compute the Poisson cohomology of R, and so retrieve a result obtained by direct methods (so completely different from ours) by Monnier. This research of the first author was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme. The second author was supported by EPSRC Grant EP/D034167/1.     

Rota–Baxter Algebras and New Combinatorial Identities

The word problem for an arbitrary associative Rota–Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects are indicated.