Aqueous Sulfate Separation by Sequestration of [(SO4)2(H2O)4]4− Clusters within Highly Insoluble Imine‐Linked Bis‐Guanidinium Crystals

Selective crystallization of sulfate with a simple bis‐guanidinium ligand, self‐assembled in situ from terephthalaldehyde and aminoguanidinium chloride, was employed as an effective way to separate the highly hydrophilic sulfate anion from aqueous solutions. The resulting bis‐iminoguanidinium sulfate salt has exceptionally low aqueous solubility (K_sp=2.4×10^?10), comparable to that of BaSO₄. Single‐crystal X‐ray diffraction analysis showed the sulfate anions are sequestered as [(SO₄)₂(H₂O)₄]^4? clusters within the crystals. Variable‐temperature solubility measurements indicated the sulfate crystallization is slightly endothermic (ΔH_cryst=3.7 kJ mol^?1), thus entropy driven. The real‐world utility of this crystallization‐based approach for sulfate separation was demonstrated by removing up to 99 % of sulfate from seawater in a single step.     

α,α′,α″,α′″-meso-tetrahexyltetramethyl-calix[4]pyrrole: an easy-to-prepare,isomerically pure anion extractant with enhanced solubility in organic solvents

α,α′,α″,α′″-meso-Tetrahexyltetramethyl-calix[4]pyrrole is easily obtained as a single diastereomer in a one-pot reaction. It exhibits enhanced solubility in organic solvents, including aliphatic solvents, relative to its parent meso-octamethylcalix[4]pyrrole (1). Somewhat surprisingly, the tetrahexyl derivative 2 complexes with tributylmethylammonium chloride in chloroform more strongly than does 1 as shown by NMR titrations. However, 1 and 2 exhibit comparable complexation strength in extraction experiments, the difference between the NMR and extraction results being attributed to the effect of organic-phase water in the extraction systems. Mass-action analysis indicates the formation of the predominant complex TBMA⁺(1 or 2)Cl^? in both NMR and extraction systems, and equilibrium constants are reported. x-Ray crystal structures were obtained for the free ligand 2 and its complex with tetramethylammonium chloride. The free ligand crystallises in the 1,3-alt conformation with equatorial hexyl arms. In the chloride complex with 2 in its cone conformation, the hexyl arms adopt an axial orientation, enveloping the anion. DFT calculations show this binding conformation to be the most stable, mostly owing to destabilising steric interactions involving the pyrrole C–H and alkyl C–H groups positioned equatorially.     

Structural analysis and biomedical potential of novel salicyloyloxy estrane derivatives synthesized by microwave irradiation

New estrane salicyloyloxy or D-homo derivatives were synthesized under microwave (MW) or conventional heating from estrane precursors and methyl salicylate. The MW technique provides advantages regarding product yield and reaction time, and represents a more environmentally friendly approach than conventional heating. Considering the biomedical potential of estrane compounds, we evaluated the antioxidant activity and cytotoxicity of synthesized estrane derivatives in a series of in vitro tests, as well as their 3β-hydroxysteroid dehydrogenase/Δ⁵ → Δ⁴ isomerase (3βHSD) and 17β-hydroxysteroid dehydrogenase types 1, 2 and 3 (17βHSD1, 17βHSD2 and 17βHSD3) inhibition potentials. In DPPH tests, 3-methoxyestra-1,3,5(10)-trien-17β-yl salicylate displayed antioxidant potential, while all compounds exhibited OH radical neutralization activity. 3-Oxoestr-4-en-17β-yl salicylate showed strong cytotoxicity against MDA-MB-231 breast cancer cells, while 17-oxoestra-1,3,5(10)-trien-3-yl salicylate, estra-1,3,5(10)-triene-3,17β-diyl 3-benzoate 17-salicylate and 3-benzyloxy-17-salicyloyloxy-16,17-secoestra-1,3,5(10)-triene-16-nitrile showed the strongest inhibition of PC-3 prostate cancer cell growth. 3-Hydroxyestra-1,3,5(10)-trien-17β-yl salicylate was the best inhibitor of 17βHSD2, suggesting potential use in treating pathological conditions associated with estrogen depletion. For 3-methoxyestra-1,3,5(10)-trien-17β-yl salicylate and 3-oxoestr-4-en-17β-yl salicylate, X-ray crystal structure analysis and molecular energy optimization were performed to define their conformations and energy minima. Very good overlap in the region of the steroidal nucleus was observed for the molecular structures of each analyzed molecule in the crystalline state and after energy optimization, while conformer analysis indicates conformational flexibility in the form of rotation around the C17···O2 bond. Structural geometry analysis for these compounds shows that the region of ring A in steroids, and especially the C3 atom functional group, is important structural features concerning antiproliferative activity against MDA-MB-231 cells.

     

Continuation Theory for Contractions on Spaces with Two Vector-Valued Metrics

We develop a continuation theory for contractive maps on spaces with two vector-valued metrics. Applications are presented for systems of operator equations in Banach spaces and, in particular, for systems of abstract Hammerstein integral equations. The use of vector-valued metrics makes it possible for each equation of a system to have its own Lipschitz property, while the use of two such metrics makes it possible for the Lipschitz condition to be expressed with respect to an incomplete metric.     

Metric regularity of epigraphical multivalued mappings and applications to vector optimization

In this work we combine in a meaningful way two techniques of variational analysis and nonsmooth optimization. On one hand, we use the error bound approach to study the metric regularity of some special types of multifunctions and, on the other hand, we exploit the incompatibility between the metric regularity and the Pareto minimality. This method allows us to present some $\varepsilon $ -Fermat rules for set-valued optimization problem in the setting of general Banach spaces. Our results are comparable to several recent results in literature.     

A Model Predictive Control Algorithm Applied To Non-Linear Processes

Model predictive control (MPC) is an optimization-based approach that has been successfully applied to a wide variety of control problems. In most of nonlinear strategies, the controllers are based on linear models with fixed parameters so that the vast body of linear control theory can be applied. Other solutions include the use of a nonlinear analytical model, combinations of linear empirical models, etc. This paper presents an MPC algorithm which uses on-line simulation and rule-based control. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The noncommutative Wiener lemma, linear independence, and spectral properties of the algebra of time-frequency shift operators

In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracial state on this algebra which proves the algebra contains no compact operators. As a corollary we obtain a special case of the Heil-Ramanathan-Topiwala conjecture regarding linear independence of finitely many time-frequency shifts of one function. We also estimate the coefficient decay of the inverse of finite linear combinations of time-frequency shifts.

     

On Drazin inverse of operator matrices

In this short paper, we offer (another) formula for the Drazin inverse of an operator matrix for which certain products of the entries vanish. We also give formula for the Drazin inverse of the sum of two operators under special conditions.     

A Generalization of the Hutchinson Measure

The Hutchinson measure is the invariant measure associated with an iterated function system with probabilities. Generalized iterated function systems (GIFS) are generalizations of iterated function systems which are obtained by considering contractions from X × X to X, rather than contractions from a metric space X to itself. Along the lines of this generalization we consider GIFS with probabilities. In this paper we prove the existence of an analogue of Hutchinson measure associated with a GIFS with probabilities and present some of its properties. The work was supported by CNCSIS grant 8A;1067/2006.     

Multiparameter QKD authentication protocol design over optical quantum channel

Quantum cryptography is the first application of quantum physics at the single photon level. The most important application of quantum cryptography is Quantum Key Distribution (QKD). One of the biggest problems of QKD implementation is enormous number of possible attacks, which puts out specific need for more refined simulation strategies in bridging the gap between theoretic models and their implementation. In this work we have introduced generalized optical architecture which can provide various solutions of some actual problems for two mostly used QKD protocols: BB84 and B92 protocols. Simulations, which included the influence of optical losses over a quantum channel with concrete realistic lengths, have confirmed validity and high level of provable security of the proposed generalized QKD authentication architecture. Due to simplicity of the proposed architecture and obtained QKD B92 protocol communication efficiency, we believe that it can be implemented, solving out some of the most relevant implementation problems which are common for both QKD protocols.