Strong convexity and separation theorems

Characterizations of pairs of functions that can be separated by a strongly convex, approximately concave or c-quadratic-affine function are presented. As consequences, stability results of the Hyers-Ulam type are obtained.     

Colorectal Adenocarcinoma Cell Culture in a Microfluidically Controlled Environment with a Static Molecular Gradient of Polyphenol

To study the simultaneous effect of the molecular gradient of polyphenols (curcumin, trans-resveratrol, and wogonin) and biological factors released from tumor cells on apoptosis of adjacent cells, a novel microfluidic system was designed and manufactured. The small height/volume of microfluidic culture chambers and static conditions allowed for establishing the local microenvironment and maintaining undisturbed concentration profiles of naturally secreted from cells biochemical factors. In all trials, we observe that these conditions significantly affect cell viability by stimulating cell apoptosis at lower concentrations of polyphenols than in traditional multiwell cultures. The observed difference varied between 20.4–87.8% for curcumin, 11.0–37.5% for resveratrol, and 21.7–62.2% for wogonin. At low concentrations of polyphenols, the proapoptotic substances released from adjacent cells, like protein degradation products, significantly influence cell viability. The mean increase in cell mortality was 38.3% for microfluidic cultures. Our research has also confirmed that the gradient microsystem is useful in routine laboratory tests in the same way as a multiwell plate and may be treated as its replacement in the future. We elaborated the new repetitive procedures for cell culture and tests in static gradient conditions, which may become a gold standard of new drug investigations in the future.     

Effect of para-substituents on alkaline earth metal ion extraction by proton di-ionizable calix[4]arene-crown-6 ligands in cone, partial-cone and 1,3-alternate conformations

Two carboxylic acid or N-(X)sulfonyl carboxamide groups were incorporated into calix[4]arene-crown-6 compounds to afford di-ionizable ligands for use in divalent metal ion separations. Acidities of the N-(X)sulfonyl carboxamide groups were tuned by variation of the electron-withdrawing properties of X. Cone, partial-cone and 1,3-alternate conformations were obtained by different synthetic strategies and their structures verified by NMR spectroscopy. Competitive solvent extractions of alkaline earth metal cations from aqueous solutions into chloroform were performed and the results compared with those reported previously for di-ionizable p-tert-butylcalix[4]arene-crown-6 analogues to probe the influence of the para-substituent on the calix[4]arene scaffold on extraction selectivity and efficiency.     

A note on three-parameter families and generalized convex functions

The concept of generalized convex functions introduced by Beckenbach [E.F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937) 363–371] is extended to the two-dimensional case. Using three-parameter families, we define generalized convex (midconvex, M-convex) functions and show some continuity properties of them.     

Electrochemical characterization of Prussian blue type nickel hexacyanoferrate redox mediator for potential application as charge relay in dye-sensitized solar cells

A polynuclear electronically/ionically (redox) conducting mixed-valent inorganic material such as nickel(II) hexacyanoferrate(II,III), NiHCF, was considered for potential application as a redox mediator (charge relay) in dye-sensitized solar cell (DSSC). The NiHCF redox reactions were found fast and reversible not only when the system was studied as thin film exposed to an aqueous supporting electrolyte but also as bulk material (pasted powder) in solid state, i.e., in the absence of contact with external liquid electrolyte phase. Usefulness of NiHCF material was diagnosed using conventional electroanalytical approaches, solid-state voltammetric methodology, as well as the dynamic electrochemical impedance spectroscopy technique that permitted monitoring of impedance spectra under potentiodynamic conditions. The material was utilized in a mixed-valent state, i.e., as a mixture of K₄Ni^II[Fe^II(CN)₆] and K₃Ni^II[Fe^III(CN)₆] in which iron(II) and iron(III) sites were at the 1:1 ratio. Under such conditions, dynamics of electron-hopping between mixed-valent iron sites was maximized. Our DSSC utilized cis–dithiocyanoatobis(4,4′-dicarboxylic acid-2,2′-bipyridine) ruthenium(II) dye (N3) adsorbed onto TiO₂ semiconductor and NiHCF as redox mediator. Although performance of our DSSC was not optimized in terms of the NiHCF film thickness and morphology, as well as lower photocurrents in comparison to those characteristic of the iodine/iodide based DSSC were obtained, our system yielded readily fairly high open-circuit photovoltages on the level of 800 mV. An important issue was that the formal potential of NiHCF was more positive relative to the potential of the iodide/triiodide couple while being still more negative than that equivalent to the ground state of the N3 dye. Thus, NiHCF mediator was able to regenerate the dye.

     

Comparison of upper and lower rim-functionalized,di-ionizable calix[4]arene-crown-6 structural isomers in divalent metal ion extraction

Upper rim-functionalized, di-ionizable calix[4]arene-crown-6 ligands are synthesized and compared with structural isomers having the two acidic side arms attached to the lower rim. Solvent extractions of selected divalent metal cations (alkaline earth metal cations, Pb²⁺, and Hg²⁺) from aqueous solutions into chloroform by the upper and lower rim-functionalized, di-ionizable calix[4]arene-crown-6 isomers are utilized to assess the effects of this structural modification on metal ion complexation abilities of the ligands. The observed effects are compared with those reported for analogous di-ionizable calix[4]arene-crown-5 structural isomers.     

On relations between gradient and classical equivariant homotopy groups of spheres

We investigate relations between stable equivariant homotopy groups of spheres in classical and gradient categories. To this end, the auxiliary category of orthogonal equivariant maps, a natural enlargement of the category of gradient maps, is used. Our result allows for describing stable equivariant homotopy groups of spheres in the category of orthogonal maps in terms of classical stable equivariant groups of spheres with shifted stems. We conjecture that stable equivariant homotopy groups of spheres for orthogonal maps and for gradient maps are isomorphic.     

Partitioning of atmospheric carbon dioxide over Central Europe: insights from combined measurements of CO2 mixing ratios and their carbon isotope composition

Regular measurements of atmospheric CO (2) mixing ratios and their carbon isotope composition ((13)C/(12)C and (14)C/(12)C ratios) performed between 2005 and 2009 at two sites of contrasting characteristics (Krakow and the remote mountain site Kasprowy Wierch) located in southern Poland were used to derive fossil fuel-related and biogenic contributions to the total CO (2) load measured at both sites. Carbon dioxide present in the atmosphere, not coming from fossil fuel and biogenic sources, was considered 'background' CO (2). In Krakow, the average contribution of fossil fuel CO (2) was approximately 3.4%. The biogenic component was of the same magnitude. Both components revealed a distinct seasonality, with the fossil fuel component reaching maximum values during winter months and the biogenic component shifted in phase by approximately 6 months. The partitioning of the local CO (2) budget for the Kasprowy Wierch site revealed large differences in the derived components: the fossil fuel component was approximately five times lower than that derived for Krakow, whereas the biogenic component was negative in summer, pointing to the importance of photosynthetic sink associated with extensive forests in the neighbourhood of the station. While the presented study has demonstrated the strength of combined measurements of CO (2) mixing ratios and their carbon isotope signature as efficient tools for elucidating the partitioning of local atmospheric CO (2) loads, it also showed the important role of the land cover and the presence of the soil in the footprint of the measurement location, which control the net biogenic surface CO (2) fluxes.     

Metal ion complexation in acetonitrile by di-ionized calix[4]arenes bearing two dansyl fluorophores

The influence of metal cations (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, Ag⁺, Cd²⁺, Co²⁺, Fe²⁺, Hg²⁺, Mn²⁺, Pb²⁺, Zn²⁺ and Fe³⁺) on the spectroscopic properties of two dansyl (1-dimethylaminonaphthalene-5-sulfonyl) groups linked to the lower rims of a series of three, structurally related, di-ionized calix[4]arenes was investigated by means of absorption and emission spectrophotometry. Di(tetramethylammonium) salts of the di-ionized ligands, (TMA)₂L1, (TMA)₂L2 and (TMA)₂L3, which differ in having zero, two and four tert-butyl groups, respectively, on the upper rim of the calix[4]arene scaffold were utilized for the spectrofluorimetric titration experiments in acetonitrile. On complexation by alkaline earth metal cations, both the absorption and emission spectra undergo marked red shifts and quenching of the dansyl fluorescence. These effects are weaker with alkali metal cations. Transition metal cations interact strongly with the ligands. In particular, Fe³⁺, Hg²⁺ and Pb²⁺ cause greater than 97% quenching of the dansyl fluorescence in the di-ionized ligands.     

Space-Time Transfer Function-Noise Modelling of Rainfall-Runoff Process

An explanatory model class belonging to the family of Space-Time Transfer Function-Noise (STTFN) process is presented. The paper develops a three-stage iterative procedure for building STTFN models of the rainfall-runoff process. Four precipitation and runoff stations located in a watershed in southern Ontario, Canada, sampled at 15-day intervals are used for the numerical analysis. Three STTF models are identified. The model parameters are estimated by the polytope technique, a nonlinear optimization algorithm. Two of the developed space-time models proved adequate in describing the spatio-temporal characteristics of precipitation and runoff time series.