Dynamics of non-autonomous difference equation

In this paper we study the asymptotic behavior and periodicity of the equation \(x_{n+1}=p_{n}+\frac{x_{n}}{x_{n-1}}\), where \(x_{0}\ge 0, x_{-1}>0\) and \(p_{n}\) is a positive bounded sequence.     

Radially polarized 3 kW beam from a CO2 laser with an intracavity resonant grating mirror

A 3 kW radially polarized beam is generated from a CO(2) laser by means of a resonant grating mirror. The design results and spectral characterization of a broadband polarizing mirror are presented as well as the mirror's operation in a CO(2) laser resonator. In a long-term experiment a radially polarized beam with a power of 2.7 kW was observed for several hours, proving the high stability of this polarizing scheme.     

Enantioselective CD analysis of amino acids based on chiral amplification with a stereodynamic probe

The condensation between stereolabile 1,8-bis(3′-formyl-4′-hydroxyphenyl)naphthalene, 1, and two amino acid molecules results in the formation of chiral diimines exhibiting strong CD signals. This reaction has been used to develop a chiroptical sensing method for the determination of the absolute configuration and enantiomeric composition of unprotected amino acids. This sensing approach is based on distinctive chiral amplification due to central-to-axial chirality induction within the diimine scaffold formed and does not require the use of an enantiopure ligand or metal complex.     

Drive to miniaturization: integrated optical networks on mobile platforms

With rapid growth of the Internet, bandwidth demand for data traffic is continuing to explode. In addition, emerging and future applications are becoming more and more network centric. With the proliferation of data communication platforms and data-intensive applications (e.g. cloud computing), high-bandwidth materials such as video clips dominating the Internet, and social networking tools, a networking technology is very desirable which can scale the Internet’s capability (particularly its bandwidth) by two to three orders of magnitude. As the limits of Moore’s law are approached, optical mesh networks based on wavelength-division multiplexing (WDM) have the ability to satisfy the large- and scalable-bandwidth requirements of our future backbone telecommunication networks. In addition, this trend is also affecting other special-purpose systems in applications such as mobile platforms, automobiles, aircraft, ships, tanks, and micro unmanned air vehicles (UAVs) which are becoming independent systems roaming the sky while sensing data, processing, making decisions, and even communicating and networking with other heterogeneous systems. Recently, WDM optical technologies have seen advances in its transmission speeds, switching technologies, routing protocols, and control systems. Such advances have made WDM optical technology an appealing choice for the design of future Internet architectures. Along these lines, scientists across the entire spectrum of the network architectures from physical layer to applications have been working on developing devices and communication protocols which can take full advantage of the rapid advances in WDM technology. Nevertheless, the focus has always been on large-scale telecommunication networks that span hundreds and even thousands of miles. Given these advances, we investigate the vision and applicability of integrating the traditionally large-scale WDM optical networks into miniaturized mobile platforms such as UAVs. We explain the benefits of WDM optical technology for these applications. We also describe some of the limitations of WDM optical networks as the size of a vehicle gets smaller, such as in micro-UAVs, and study the miniaturization and communication system limitations in such environments.     

Investigating the topology of interacting networks

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere’s three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere’s vertical stratification and general circulation. Specifically, the new measure “cross-betweenness” identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective.     

A convenient one-pot synthesis of polysubstituted pyrroles from N-protected succinimides

The dienamine products formed by the reaction between polysubstituted succinimides and the Petasis reagent were subjected to isomerization under mild acidic conditions to give polysubstituted pyrroles in excellent yields (85–95%). The scope and limitations of this methodology are explored.     

Characterizing demand functions with price dependent income

We consider the demand function of consumer whose wealth depends on prices. This extends the two traditional cases when the consumer holds a goods bundle, so that his wealth depends linearly on prices, and when his wealth is prescribed, independently of prices. We extend the Slutsky relations to this general case, and we show that they fully characterize the demand functions, as in the traditional cases.     

Surface modification and characterization of Jordanian kaolinite: Application for lead removal from aqueous solutions

Kaolinite clay was tested for removal of lead ions from aqueous solution. This clay was washed with sulfuric acid solution followed by chemical surface modification using 3-chloropropyltriethoxysilane and sodium hydroxide. XRF results showed that silica to alumina ratio was 2.8:1 for the treated sample compared to 1.6:1 for the raw one.XRD analysis displayed different distinct kaolinite and quartz peaks before treatment while kaolinite peaks were diminished after the treatment. SEM morphology indicated that the raw kaolinite appears as plate structure with no local pores on the plates. However, after treatment the surface was found to have micropores.Different adsorption isotherm models were applied to the experimental data and found that Shawabkeh-Tutunji equation best fit these data adequately. It was also found that chemisorption took place at the surface of the modified kaolinite with maximum adsorption capacity of 54.35 mg/g.