On Central Cantor Sets with Self-Arithmetic Difference of Positive Lebesgue Measure

We prove the existence of C^r - (but not C^r+1-) regular centralCantor sets with zero Lebesgue measure such that their selfarithmetic difference is a Cantor set with positive Lebesguemeasure. This is motivated by a conjecture in the field of bifurcationsof dynamical systems posed by Jacob Palis.     

An approach to substituted dihydroisoquinolin-1(2H)-ones from Baylis-Hillman adducts

In this communication we describe an easy and straightforward alternative method for the preparation of 3,4-substituted isoquinolin-1(2H)-ones, using Baylis-Hillman adducts as starting material.     

Potential of prodendronic polyamines with modulated segmental charge density as novel coating for fast and efficient analysis of peptides and basic proteins by CE and CE‐MS

In this work, the suitability of a new polymer family has been investigated as capillary coatings for the analysis of peptides and basic proteins by CE. This polymer family has been designed to minimize or completely prevent protein–capillary wall interactions and to modify the EOF. These coating materials are linear polymeric chains bearing as side cationizable moiety a dentronic triamine derived from N,N,N’,N’‐tetraethyldiethylenetriamine (TEDETA), which is linked to the backbone through a spacer (unit labeled as TEDETAMA). Four different polymers have been prepared and evaluated: a homopolymer which comprised only of those cationizable repetitive units of TEDETAMA, and three copolymers that randomly incorporate TEDETAMA together with neutral hydrosoluble units of N‐(2‐hydroxypropyl) methacrylamide (HPMA) at different molar percentages (25:75, 50:50 and 75:25). It has been demonstrated that the composition of the copolymers influences the EOF and therefore the separation of the investigated biopolymers. Among the novel polymers studied, poly‐(TEDETAMA‐co‐HPMA) 50:50 copolymer was successfully applied as coating material of the inner capillary surface in CE‐UV and CE‐MS, providing EOF reversing together with fast and efficient baseline separation of peptides and basic proteins. Finally, the feasibility of the polymer‐coated capillary was shown through the analysis of lysozyme in a cheese sample.     

Polymeric Gene Carriers Bearing Pendant β‐Cyclodextrin: The Relevance of Glycoside Permethylation on the “In Vitro” Cell Response

The incorporation of cyclodextrins (CDs) to nonviral cationic polymer vectors is very attractive due to recent studies that report a clear improvement of their cytocompatibility and transfection efficiency. However, a systematic study on the influence of the CD derivatization is still lacking. In this work, the relevance of β‐CD permethylation has been addressed by preparing and evaluating two series of copolymers of the cationic N‐ethyl pyrrolidine methacrylamide (EPA) and styrenic units bearing pendant hydroxylated and permethylated β‐CDs (HCDSt and MeCDSt, respectively). For both cell lines, CDs permethylation shows a strong influence on plasmid DNA complexation, “in vitro” cytocompatibility and transfection efficiency of the resulting copolymers over two murine cell lines. While the incorporation of the hydroxylated CD moiety increased the cytotoxicity of the copolymers in comparison with their homopolycationic counterpart, the permethylated copolymers have shown full cytocompatibility as well as superior transfection efficiency than the controls. This behavior has been related to the different chemical nature of both units and tentatively to a different distribution of units along the polymeric chains. Cellular internalization analysis with fluorescent copo­lymers supports this behavior.

     

Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems arising in the setting in which the value function acts on a compound process that is modified by the actions taken at the stopping times. This class of problem is particularly relevant in insurance and risk management settings and we demonstrate this on an important application domain based on insurance strategies in Operational Risk management for financial institutions. In this area of risk management the most prevalent class of loss process models is the Loss Distribution Approach (LDA) framework which involves modelling annual losses via a compound process. Given an LDA model framework, we consider Operational Risk insurance products that mitigate the risk for such loss processes and may reduce capital requirements. In particular, we consider insurance products that grant the policy holder the right to insure k of its annual Operational losses in a horizon of T years. We consider two insurance product structures and two general model settings, the first are families of relevant LDA loss models that we can obtain closed form optimal stopping rules for under each generic insurance mitigation structure and then secondly classes of LDA models for which we can develop closed form approximations of the optimal stopping rules. In particular, for losses following a compound Poisson process with jump size given by an Inverse-Gaussian distribution and two generic types of insurance mitigation, we are able to derive analytic expressions for the loss process modified by the insurance application, as well as closed form solutions for the optimal multiple stopping rules in discrete time (annually). When the combination of insurance mitigation and jump size distribution does not lead to tractable stopping rules we develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.     

In situ assessment of atorvastatin impurity using MALDI mass spectrometry imaging (MALDI-MSI)

The analysis of impurities and degradation products in pharmaceutical preparations are usually performed by chromatographic techniques such as high-performance liquid chromatography (HPLC). This approach demands extensive analysis time, mostly due to extraction and separation phases. These steps must be carried out in samples in order to adapt them to the requirements of the analytical method of choice. In the present contribution, matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) was employed to quantify an important degradation product in atorvastatin calcium 80 mg tablets: the atorvastatin lactone. Through the standard of the impurity, it was possible to perform quantitative analysis directly on the drug tablet, using a quick and novel approach, suitable for quality control processes in the pharmaceutical industry.     

Synthesis and Structure Elucidation of New Regioisomeric 2‐Alkylamino‐6‐aryl‐8,9‐dihydropyrimido[4,5‐b][1,4]diazepin‐4(7H)‐ones

Novel 2‐Alkylamino‐6‐aryl‐8,9‐dihydropyrimido[4,5‐b][1,4]diazepin‐4(7H)‐ones 5a , 5b , 5c , 5d , 5e , 5f , 5g , 5h , 5i , 5j , 5k , 5l , 5m , 5n , 5o were prepared regioselectively by the reaction of 2‐alkylamino‐5,6‐diaminopyrimidin‐4(3H)‐ones 3a , 3b , 3c and dimethylamino propiophenones (Mannich bases) 4a , 4b , 4c , 4d , 4e , 4f . The combination of conventional heating and microwave irradiation approaches provided the possibility of working with both stable and sensitive diaminopyrimidines by controlling parameters such as reaction rates, temperature, and power of irradiation. All products were fully characterized by detailed NMR measurements.     

Effects of self-assembled materials prepared from V2O5 for lithium ion electroinsertion

Self-assembled materials consisting of V(2)O(5), polyallylamine (PAH) and silver nanoparticles (AgNPs) were obtained by the layer-by-layer (LbL) method, aiming at their application as electrodes for lithium-ion batteries and electrochromic devices. The method employed herein allowed for linear growth of visually homogeneous films composed of V(2)O(5), V(2)O(5)/PAH, and V(2)O(5)/PAH/AgNP with 15 bilayers. According to the Fourier transform infrared spectra, interaction between the oxygen atom of the vanadyl group and the amino group should be responsible for the growth of these films. This interaction also enabled establishment of an electrostatic shield between the lithium ions and the sites with higher negative charge, thereby raising the ionic mobility and consequently increasing the energy storage capacity and reducing the response time. According to the site-saturation model and the electrochemical and spectroelectrochemical results, the presence of PAH in the self-assembled host matrix decreased the number of V(2)O(5) electroactive sites. Thus, AgNPs were stabilized in PAH and inserted into the nanoarchitecture, so as to enhance the specific capacity. This should provide new conducting pathways and connect isolated V(2)O(5) particles in the host matrix. Therefore, new nanoarchitectures for specific interactions were formed spontaneously and chosen as examples in this work, aiming to demonstrate the potentiality of the adopted self-assembled method for enhancing the charge transport rate into the host matrices. The obtained materials displayed suitable properties for use as electrodes in lithium batteries and electrochromic devices.     

Photoreactive surfactants: a facile and clean route to oxide and metal nanoparticles in reverse micelles

A new class of photoreactive surfactants (PRSs) is presented here, consisting of amphiphiles that can also act as reagents in photochemical reactions. An example PRS is cobalt 2-ethylhexanoate (Co(EH)(2)), which forms reverse micelles (RMs) in a hydrocarbon solvent, as well as mixed reversed micelles with the standard surfactant Aerosol-OT (AOT). Small-angle neutron scattering (SANS) data show that mixed AOT/PRS RMs have a spherical structure and size similar to that of pure AOT micelles. Excitation of the ligand-to-metal charge transfer (LMCT) band in the PRSs promotes electron transfer from PRS to associated metal counterions, leading to the generation of metal and metal-oxide nanoparticles inside the RMs. This work presents proof of concept for employing PRSs as precursors to obtain nearly monodisperse inorganic nanoparticles: here both Co(3)O(4) and Bi nanoparticles have been synthesized at high metal concentration (10(-2) M) by simply irradiating the RMs. These results point toward a new approach of photoreactive self-assembly, which represents a clean and straightforward route to the generation of nanomaterials.