1,3-Dipolar Cycloreversions

The 1,3-dipolar cycloreversion reaction represents a general scheme of fragmentation of pentaatomic heterocycles to produce 1,3-dipolar systems and dipolarophiles. This review summarize cycloreversions which give rise to octet-stabilized 1,3-dipoles. The reaction can be either thermal or photochemical or electron impact induced. The aim of the article is to survey the published results, to emphasize the synthetic potential of this reaction, and to stimulate the study of its several not yet unambiguously defined mechanistic aspects.     

Solution and solid-state preparation of 18-crown[6] complexes with M[HSO4]n salts (M = NH4+, K+, Sr2+ and n = 1, 2) and an investigation of solvation/desolvation processes and crystal polymorphism

18-Crown[6] ether has been used to prepare a new class of organic-inorganic complexes of general formula 18-crown[6]M[HSO(4)](n) (where M = NH(4) (+), K(+), Sr(2+) and n = 1, 2) by reacting directly in solution or in the solid state the crown ether 18-crown[6] with inorganic salts such as [NH(4)][HSO(4)], K[HSO(4)], and Sr[HSO(4)](2). The structures of 18-crown[6][NH(4)][HSO(4)]2 H(2)O (12 H(2)O), 18-crown[6][NH(4)][HSO(4)] (1), 18-crown[6]K[HSO(4)]2 H(2)O (22 H(2)O), 18-crown[6]K[HSO(4)] (2), and 18-crown[6]Sr[HSO(4)](2) (3) have been characterized by single-crystal X-ray diffraction. The reversible water loss in compounds 12 H(2)O and 22 H(2)O leads to formation of the corresponding anhydrous phases 18-crown[6][NH(4)][HSO(4)] (1), and 18-crown[6]K[HSO(4)] (2), which undergo, on further heating, enantiotropic solid-solid transitions very likely associated with the on-set of a solid state dynamical process. Similar high-temperature behavior is shown by 18-crown[6]Sr[HSO(4)](2) (3). The dehydration and phase-transition processes have been investigated by differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and variable temperature X-ray powder diffraction.     

Synthesis and self-assembly of spin-labile and redox-active manganese(III) complexes

New amphiphilic and spin-labile Mn(III) complexes based on dianionic N(4)O(2)-hexadentate sal(2)trien or sal(2)bapen ligands, which contain OC(6)H(13), OC(12)H(25), or OC(18)H(37) alkoxy substituents at different positions of the salicylidene unit were prepared (H(2)sal(2)trien = N,N'-bis(salicylidene)-1,4,7,10-tetraazadecane, H(2)sal(2)bapen = N,N'-bis(salicylidene)-1,5,8,12-tetraazadodecane). According to electrochemical measurements, these complexes undergo two (quasi)reversible redox processes. Temperature-dependent magnetic measurements revealed a high-spin configuration for all sal(2)trien complexes (S = 2) and gradual spin crossover for sal(2)bapen complexes from high to low spin (S = 1). The chain length strongly influences the spin crossover, as C(18)-functionalization stabilizes the low spin state at much higher temperatures than shorter alkyl chains. Moreover, long alkyl chains allow for spontaneous self-assembly of the molecules, which was investigated in single crystals and in Langmuir-films at the air-water interface. Long alkyl chains (C(12) or C(18)) as well as a mutual syn-orientation of these molecular recognition sites were required for the Langmuir monolayers to be stable.     

BK-type inequalities and generalized random-cluster representations

Recently, van den Berg and Jonasson gave the first substantial extension of the BK inequality for non-product measures: they proved that, for $k$ -out-of- $n$ measures, the probability that two increasing events occur disjointly is at most the product of the two individual probabilities. We show several other extensions and modifications of the BK inequality. In particular, we prove that the antiferromagnetic Ising Curie–Weiss model satisfies the BK inequality for all increasing events. We prove that this also holds for the Curie–Weiss model with three-body interactions under the so-called negative lattice condition. For the ferromagnetic Ising model we show that the probability that two events occur ‘cluster-disjointly’ is at most the product of the two individual probabilities, and we give a more abstract form of this result for arbitrary Gibbs measures. The above cases are derived from a general abstract theorem whose proof is based on an extension of the Fortuin–Kasteleyn random-cluster representation for all probability distributions and on a ‘folding procedure’ which generalizes an argument of Reimer.     

Potential of porphyrins as chromogenic reagents for determining metals in capillary electrophoresis

Although capillary electrophoresis (CE) with photometric detection is a well-established technique for the determination of various inorganic ions, its limited sensitivity has hindered greater development in this area. In this work, we used a mixture of metals consisting of Co(II), Ni(II), Zn(II) and Mn(II) to demonstrate that the sensitivity of CE with ultraviolet–visible (UV–vis) detection can be improved by using chromogenic reagents such as porphyrins. To this end, the metals were reacted with 5,10,15,20-tetrakis(4-sulphophenyl)-porphine dodecahydrate (TPPS₄) to obtain their respective porphyrinato complexes, which were then separated by CE with a citrate buffer and detected at 410 nm. The ensuing electrophoretic method has a limit of detection (LOD) of 3 × 10⁻⁶ M (180 μg L⁻¹) for Co(II), 2 × 10⁻¹⁰ M (0.012 μg L⁻¹) for Ni(II), 4 × 10⁻⁶ M (260 μg L⁻¹) for Zn(II) and 4 × 10⁻⁹ M (0.219 μg L⁻¹) for Mn(II). The method is a highly promising choice for the ultratrace determination of Ni(II) and Mn(II).     

Ageing of calcium silicate cements for endodontic use in simulated body fluids: a micro‐Raman study

To evaluate bioactivity properties, a calcium silicate experimental cement (wTC) and a phosphate‐doped wTC cement (wTC‐TCP) were aged for different times (1–180 days) at 37 °C in two simulated body fluids, i.e. Dulbecco's phosphate buffered saline (DPBS) and Hank's balanced salt solution (HBSS). The cements were analyzed by micro‐Raman spectroscopy to investigate the presence of calcium phosphate deposits and the composition changes as a function of the storage time (hydration of anhydrite/gypsum and formation of ettringite; hydration of belite/alite and formation of hydrated silicates). After 1 day of ageing in DPBS, the two cements already showed a different behavior: only the surface of wTC‐TCP cement showed the band at 965 cm⁻¹, suggesting the formation of a detectably thick calcium phosphate deposit. The trend of the I₉₆₅/I₉₉₀ Raman intensity ratio indicated the formation of a meanly thicker apatite deposit on the wTC‐TCP cement until 90 days. After 60 days of ageing in DPBS, the thickness of the apatite deposit on wTC and wTC‐TCP was about 200 and 500 µm, respectively, whereas at 180 days, the two cements did not appear significantly different (thickness of about 900 µm). The bioactivity of both cements in HBSS was less pronounced than in DPBS, according to the lower phosphate concentration of HBSS; at the same time, higher amounts of calcite were found on the surface of both cements. The wTC‐TCP cement showed a higher bioactivity in this medium also; after 180 days, the thickness of the apatite deposit on wTC and wTC‐TCP was < 50 µm and about 100 µm, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

Average root numbers in families of elliptic curves

We introduce a height measure on to count rational numbers. Through it, we prove a density result on the average value of the root numbers of families of twists of elliptic curves.

     

PID feedback controller used as a tactical asset allocation technique: The G.A.M. model

The objective of this paper is to illustrate a tactical asset allocation technique utilizing the PID controller. The proportional-integral-derivative (PID) controller is widely applied in most industrial processes; it has been successfully used for over 50 years and it is used by more than 95% of the plants processes. It is a robust and easily understood algorithm that can provide excellent control performance in spite of the diverse dynamic characteristics of the process plant.In finance, the process plant, controlled by the PID controller, can be represented by financial market assets forming a portfolio. More specifically, in the present work, the plant is represented by a risk-adjusted return variable. Money and portfolio managers’ main target is to achieve a relevant risk-adjusted return in their managing activities. In literature and in the financial industry business, numerous kinds of return/risk ratios are commonly studied and used.The aim of this work is to perform a tactical asset allocation technique consisting in the optimization of risk adjusted return by means of asset allocation methodologies based on the PID model-free feedback control modeling procedure. The process plant does not need to be mathematically modeled: the PID control action lies in altering the portfolio asset weights, according to the PID algorithm and its parameters, Ziegler-and-Nichols-tuned, in order to approach the desired portfolio risk-adjusted return efficiently.