Ramsey partitions of integers and pair divisions

Ifk ₁ andk ₂ are positive integers, the partitionP = (₁,₂,..., _n ) ofk ₁+k ₂ is said to be a Ramsey partition for the pairk ₁,k ₂ if for any sublistL ofP, either there is a sublist ofL which sums tok ₁ or a sublist ofP –L which sums tok ₂. Properties of Ramsey partitions are discussed. In particular it is shown that there is a unique Ramsey partition fork ₁,k ₂ having the smallest numbern of terms, and in this casen is one more than the sum of the quotients in the Euclidean algorithm fork ₁ andk ₂.An application of Ramsey partitions to the following fair division problem is also discussed: Suppose two persons are to divide a cake fairly in the ratiok ₁k ₂. This can be done trivially usingk ₁+k ₂-1 cuts. However, every Ramsey partition ofk ₁+k ₂ also yields a fair division algorithm. This method yields fewer cuts except whenk ₁=1 andk ₂=1, 2 or 4.     

From Weakly Coordinating to Non‐Coordinating Anions? A Simple Preparation of the Silver Salt of the Least Coordinating Anion and Its Application To Determine the Ground State Structure of the Ag(η2‐P4)2+ Cation

The unexpected but facile preparation of the silver salt of the least coordinating [(RO)₃Al‐F‐Al(OR)₃]^? anion (R=C(CF₃)₃) by reaction of Ag[Al(OR)₄] with one equivalent of PCl₃ is described. The mechanism of the formation of Ag[(RO)₃Al‐F‐Al(OR)₃] is explained based on the available experimental data as well as on quantum chemical calculations with the inclusion of entropy and COSMO solvation enthalpies. The crystal structures of (RO)₃Al←OC₄H₈, Cs⁺[(RO)₂(Me)Al‐F‐Al(Me)(OR)₂]^?, Ag(CH₂Cl₂)₃⁺[(RO)₃Al‐F‐Al(OR)₃]^? and Ag(η²‐P₄)₂⁺[(RO)₃Al‐F‐Al(OR)₃]^? are described. From the collected data it will be shown that the [(RO)₃Al‐F‐Al(OR)₃]^? anion is the least coordinating anion currently known. With respect to the fluoride ion affinity of two parent Lewis acids Al(OR)₃ of 685 kJ mol^?1, the ligand affinity (441 kJ mol^?1), the proton and copper decomposition reactions (?983 and ?297 kJ mol^?1) as well as HOMO level and HOMO–LUMO gap and in comparison with [Sb₄F₂₁]^?, [Sb(OTeF₅)₆]^?, [Al(OR)₄]^? as well as [B(R^F)₄]^? (R^F=CF₃ or C₆F₅) the [(RO)₃Al‐F‐Al(OR)₃]^? anion is among the best weakly coordinating anions (WCAs) according to each value. In contrast to most of the other cited anions, the [(RO)₃Al‐F‐Al(OR)₃] anion is available by a simple preparation in conventional inorganic laboratories. The least coordinating character of this anion was employed to clarify the question of the ground state geometry of the Ag(η²‐P₄)₂⁺ cation (D_2h, D₂ or D_2d?). In agreement with computational data and NMR spectra it could be shown that the rotation along the Ag‐(P‐P‐centroid) vector has no barrier and that the structure adopted in the solid state depends on packing effects which lead to an almost D_2h symmetric Ag(η²‐P₄)₂⁺ cation (0 to 10.6° torsion) for the more symmetrical [Al(OR)₄]^? anion, but to a D₂ symmetric Ag(η²‐P₄)₂⁺ cation with a 44° twist angle of the two AgP₂ planes for the less symmetrical [(RO)₃Al‐F‐Al(OR)₃]^? anion. This implies that silver back bonding, suggested by quantum chemical population analyses to be of importance, is only weak.     

Structurally heterogeneous electrode films of polyacrylamide and acrylamide/vinylpyridine copolymeric gels: Mediation of ascorbic acid oxidation

The surface chemistry, i.e. adsorption and surface phase formation, on Rh, Ir, Pt and Au single-crystal electrodes in 0.5 M H₂SO₄ has been studied in the potential range between 0 and 4 V vs. a standard hydrogen electrode by X-ray photoelectron spectroscopy and cyclic voltammetry. Both methods gave complementary results which were interpreted as potential-dependent changes from physisorption of water to adsorption of hydroxyl groups, hydroxide film formation, and eventual growth of thick adlayers of oxyhydroxide (Rh, Ir and Au) or hydroxide (Pt) with increasing applied voltage.     

Modulatory Effect of Diosmin and Diosmetin on Metalloproteinase Activity and Inflammatory Mediators in Human Skin Fibroblasts Treated with Lipopolysaccharide

Diosmin is widely used as a venoactive drug in the pharmacological treatment of chronic venous disorders. It exerts a strong protective effect on blood vessels via an increase in the elasticity of vessel walls and reduces the permeability of capillary walls, thereby producing an anti-edematous effect. In this paper, we investigated the effectiveness of diosmin and diosmetin in modulating the level of proinflammatory factors in human skin fibroblasts treated with lipopolysaccharide (LPS). Two variants of the experiments were performed: the flavonoid was added 2 h prior to or 24 h after LPS stimulation. Our study revealed that both flavonoids reduced the levels of IL-6 and Il-1β as well as COX-2 and PGE2 but had no impact on IL-10. However, the addition of the compounds prior to the LPS addition was more effective. Moreover, diosmetin modulated the proinflammatory factors more strongly than diosmin. Our investigations also showed that both flavonoids were potent inhibitors of elastase and collagenase activity, and no differences between the glycoside and aglycone forms were observed.     

The DI-SPME Method for Determination of Selected Narcotics and Their Metabolites,and Application to Bone Marrow and Whole Blood Analysis

The present investigation utilised the quick and easy SPME/LC-MS method to determine selected narcotic substances and their metabolites in whole blood. The study included qualitative analysis and validation of the method. Analytes were determined in the linearity range of 25–300 ng/mL. The precision during and between days (in general CV < 13.41%), and the LOD which results in between 0.36 and 11.08 ng/mL, and the LOQ between 1.20 and 36.90 ng/mL were investigated. The validation results obtained, as well as the results of subsequent in-laboratory tests, confirmed the applicability of the method in the analysis of blood samples. An attempt to apply the method to the analysis of bone marrow samples has yielded promising results; however, more detailed studies are needed in this area.     

Synthesis and Luminescent Properties of s-Tetrazine Derivatives Conjugated with the 4H-1,2,4-Triazole Ring

New derivatives obtained by the combination of unique 1,2,4,5-tetrazine and 4H-1,2,4-triazole rings have great application potential in many fields. Therefore, two synthetic few-step methodologies, which make use of commercially available 4-cyanobenzoic acid (method A) and ethyl diazoacetate (method B), were applied to produce two groups of the aforementioned heterocyclic conjugates. In both cases, the target compounds were obtained in various combinations, by introducing electron-donating or electron-withdrawing substituents into the terminal rings, together with aromatic or aliphatic substituents on the triazole nitrogen atom. Synthesis of such designed systems made it possible to analyze the influence of individual elements of the structure on the reaction course, as well as the absorption and emission properties. The structure of all products was confirmed by conventional spectroscopic methods, and their luminescent properties were also determined.     

Formation of Carcinogens in Processed Meat and Its Measurement with the Usage of Artificial Digestion—A Review

Meat is a rich source of various nutrients. However, it needs processing before consumption, what in turn generates formation of carcinogenic compounds, i.a., polycyclic aromatic hydrocarbons (PAH), nitrosamines (NOCs), and the most mutagenic heterocyclic aromatic amines (HAAs). It was widely found that many factors affect the content of carcinogens in processed meat. However, it has recently been discovered that after digestion free HAAs are released, which are not detectable before enzymatic treatment. It was established that the highest percentage of carcinogens is released in the small intestine and that its amount can be increased up to 6.6-fold. The change in free HAAs content in analyzed samples was dependent on many factors such as meat type, doneness, particle size of meat, and the enzyme concentration used for digestion. In turn, introduction of bacteria naturally occurring in the human digestive tract into the model significantly decreases total amount of HAAs. Contrary, the addition of food ingredients rich in polyphenols, fiber, and water (pepper powder, onions, apples) increases free HAAs’ release up to 56.06%. Results suggests that in vitro digestion should be an integral step of sample preparation. Artificial digestion introduced before chromatographic analysis will allow to estimate accurately the content of carcinogens in processed meat.     

Development of hollow fiber‐supported liquid‐phase microextraction and HPLC‐DAD method for the determination of pyrethroid metabolites in human and rat urine

A simple hollow fiber liquid‐phase microextraction method for the determination of synthetic pyrethroid metabolites, 3‐phenoxybenzoic acid and 4‐hydroxy‐3‐phenoxybenzoic acid, in human and rat urine was developed and validated. A polypropylene hollow fiber tightly fitted onto a Nylon rod and impregnated with organic solvent served as a disposable extraction device. Desorption of analytes was carried out in NaOH solution, analyzed further by gradient HPLC and diode array detection method. Important factors were identified using Taguchi OA16 (4⁵) orthogonal array design and further optimized using univariate approach. The optimum method performance was observed when 1 mL of urine hydrolyzed with 0.2 mL of concentrated HCl was further supplemented with 100 mg of NaCl and extracted for 120 min into dihexyl ether immobilized in the pores of the hollow fiber. Metabolites were desorbed into 0.1 mL of 0.1 M NaOH for another 120 min. Limits of detection and quantitation of 15 and 50 ng/mL were obtained for both analytes. Relative standard deviations of 1.6–12.6% over the linear range (50–10,000 ng/mL, r > 0.9906) were observed. Intra‐ and inter‐day accuracies of the method ranged from 98.3 to 109.5% and from 93.3 to 110.9%, respectively. The optimized method was applied to the analysis of real urine samples collected from rats exposed orally to cypermethrin. Copyright © 2013 John Wiley & Sons, Ltd.