A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.     

Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Adsorption of dicarboxylates on nano-sized gibbsite particles: effects of ligand structure on bonding mechanisms

The adsorption of the dicarboxylates o-phthalate, maleate, fumarate, malonate, and oxalate (representing ligands with the general composition ⁻O₂C---C_n---CO₂⁻; n=0, 1, or 2) on gibbsite were studied by means of quantitative batch adsorption experiments and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. The interpretations of ATR-FTIR spectra were aided by comparison with IR spectra of solution species and by results from theoretical frequency calculations. The main objectives of the study were to identify the molecular level bonding mechanisms of the dicarboxylates to gibbsite, and to investigate how these were influenced by the composition and structure of the ligands. Carboxylates with n=2 formed predominantly outer sphere complexes, whereas the importance of inner sphere complexes progressively increased for n=1 and 0. The inner sphere structures were identified as mononuclear chelates with one oxygen from each carboxylate group bonded to Al(III) at the surface. This showed the importance of chelate ring structure for the formation of inner sphere surface complexes, with stabilities of the complexes increasing in the order seven-membered ring less than six-membered ring less than five-membered ring. For ligands with n=2 only small variations in surface speciation were observed as a function of steric factors; irrespective of the relative positions of the carboxylate groups and bulkiness of the ligands outer sphere bonding is the dominating adsorption mode. Adsorption experiments were also conducted with gibbsite particles exhibiting differences in shape and surface roughness. These experiments showed that inner sphere complexes were favored on the less well-developed and more irregular gibbsite particles.     

Pensions modelling

Valuable insights into the problem of how to fund defined benefitpension schemes can be obtained by analysis using the standardBlack–Scholes/Merton option pricing model, consideringthe pension fund finances jointly with those of the sponsoringcompany. The nature of the fund assets and liabilities is completelydifferent, and this lies behind current controversies aboutthe appropriate discount rate, valuation, financial accountingand preferential status for pension fund claimants in insolvency.     

Limits of Functions as They Developed Through Time and as Students Learn Them Today

This article compares first-year university students' development of the concept of limits to mathematicians' historical development of the concept. The aim was to find out if students perceive the notion as mathematicians of the past did, as understandings of the concept evolved. The results imply that there are some similarities—for example, the struggle with rigor and attainability. Knowledge of such critical areas can be used to improve students' opportunities of learning limits of functions. Some teaching aspects related to the study are also discussed.     

Conversions between ordered and disordered cellulose. Effects of mechanical treatment followed by cyclic wetting and drying

An investigation into the effects of mechanical treatment and hydration on the order of cellulose substrates (microcrystalline cellulose and Cladophora cellulose) was performed by the use of ball milling followed by cyclic wetting and drying. The results, monitored by¹³C-CP/MAS NMR-spectroscopy, were evaluated by calculation of the crystallinity indices and principal component analysis of the NMR data acquired. The results showed that a large part of the disorder induced by the mechanical treatment of cellulose by ball milling is reversible and reordering upon hydration leads to the cellulose I form initially present. The C4 signals corresponding to the reversibly disordered cellulose chains are observed in the amorphous region between 79 and 86 ppm in the¹³C-CP/MAS NMR-spectra together with signals from cellulose chains on the surface of ordered regions. The peak cluster which contains the C2, C3 and C5 ring carbons can be divided into two specific spectral regions; one between 74 and 77 ppm largely originates from ring carbons within disordered cellulose structures, and one between 70 and 74 ppm contains larger contributions from ordered cellulose. The behaviour of the celluloses upon milling is in accordance with a concept of ordered cellulose fibrils containing amorphous cellulose mainly as surface layers and induced reversible lattice distortions.