What is the theory without power set?

We show that the theory , consisting of the usual axioms of but with the power set axiom removed—specifically axiomatized by extensionality, foundation, pairing, union, infinity, separation, replacement and the assertion that every set can be well‐ordered—is weaker than commonly supposed and is inadequate to establish several basic facts often desired in its context. For example, there are models of in which ω₁ is singular, in which every set of reals is countable, yet ω₁ exists, in which there are sets of reals of every size , but none of size , and therefore, in which the collection axiom fails; there are models of for which the ?o? theorem fails, even when the ultrapower is well‐founded and the measure exists inside the model; there are models of for which the Gaifman theorem fails, in that there is an embedding of models that is Σ₁‐elementary and cofinal, but not elementary; there are elementary embeddings of models whose cofinal restriction is not elementary. Moreover, the collection of formulas that are provably equivalent in to a Σ₁‐formula or a Π₁‐formula is not closed under bounded quantification. Nevertheless, these deficits of are completely repaired by strengthening it to the theory , obtained by using collection rather than replacement in the axiomatization above. These results extend prior work of Zarach 18 .     

Matrix molecularly imprinted mesoporous sol–gel sorbent for efficient solid-phase extraction of chloramphenicol from milk

Highly selective and efficient chloramphenicol imprinted sol–gel silica based inorganic polymeric sorbent (sol–gel MIP) was synthesized via matrix imprinting approach for the extraction of chloramphenicol in milk. Chloramphenicol was used as the template molecule, 3-aminopropyltriethoxysilane (3-APTES) and triethoxyphenylsilane (TEPS) as the functional precursors, tetramethyl orthosilicate (TMOS) as the cross-linker, isopropanol as the solvent/porogen, and HCl as the sol–gel catalyst. Non-imprinted sol–gel polymer (sol–gel NIP) was synthesized under identical conditions in absence of template molecules for comparison purpose. Both synthesized materials were characterized by Scanning Electron Microscopy (SEM), Fourier Transform Infrared Spectroscopy (FT-IR) and nitrogen adsorption porosimetry, which unambiguously confirmed their significant structural and morphological differences.     

Rapid detection of bacterial endotoxins in ophthalmic viscosurgical device materials by direct analysis in real time mass spectrometry

Bacterial endotoxins are lipopolysaccharides bound to the bacterial cell wall and released when bacteria rupture or disintegrate. Possible contamination of endotoxin in ophthalmic devices can cause a painful eye inflammation or result in toxic anterior segment syndrome after cataract surgery. Measurement of bacterial endotoxin in medical device materials is difficult since endotoxin binds with polymer matrix and some of the materials are very viscous and non-water soluble, where traditional enzyme-based Limulus amebocyte lysate (LAL) assay cannot be applied. Here we propose a rapid and high throughput ambient ionization mass spectrometric (MS) method using direct analysis in real time (DART) for the evaluation of endotoxin contamination in medical device materials. Large and structurally complex endotoxin instantaneously breaks down into low-mass characteristic fragment ions using DART and is detected by MS in both positive and negative ion modes. This method enables the identification and separation of endotoxin from medical materials with a detection limit of 0.03 ng mL⁻¹ endotoxins in aqueous solution. Ophthalmic viscosurgical device materials including sodium hyaluronate (NaHA), non-water soluble perfluoro-n-octane (PFO) and silicone oil (SO) were spiked with different known concentrations of endotoxin and analyzed by DART MS, where the presence of endotoxin was successfully detected and featured small mass fragment ions were generated for NaHA, PFO and SO as well. Current findings showed the feasibility of measuring endotoxin contamination in medical device materials using DART-MS, which can lead to a one-step analysis of endotoxins in different matrices, avoiding any potential contamination during sample pre-treatment steps.     

Near-Quantitative Preparation of Short Single-Stranded DNA Circles

Small, single-stranded DNA (ssDNA) circles have many applications, such as templating rolling circle amplification (RCA), capturing microRNAs, and scaffolding DNA nanostructures. However, it is challenging to prepare such ssDNA circles, particularly when the DNA size becomes very small (e.g. a 20 nucleotide (nt) long ssDNA circle). Often, such short ssDNA dominantly form concatemers (either linear or circular) due to intermolecular ligation, instead of forming monomeric ssDNA circles by intramolecular ligation. Herein, a simple method to overcome this problem by designing the complementary linker molecules is reported. It is demonstrated that ssDNA, as short as 16 nts, can be enzymatically ligated (by the commonly used T4 DNA ligase) into monomeric ssDNA circles at high concentration (100 μM) with high yield (97 %). This method does not require any special sequence, thus, it is expected to be generally applicable. The experimental protocol is identical to regular DNA ligation, thus, is expected to be user friendly for general chemists and biologists.     

Bis- and tris(2-seleno-1-methylimidazolyl)hydroborato complexes, {[BseMe]ZnX}2(X=Cl, I), [BseMe]2Zn and [TseMe]Re(CO)3: structural evidence that the [BseMe] ligand is not merely a "heavier" version of the sulfur counterpart, [BmMe

New bidentate and tridentate ligands that feature selenium donors, namely the bis- and tris(2-seleno-1-methylimidazolyl)hydroborato ligands [BseMe] and [TseMe], have been constructed via the reaction of MBH4(M=Na, K) with 1-methylimidazole-2-selone. Comparison of the structure of {[BseMe]ZnI}2 with its sulfur counterpart, [BmMe]ZnI, demonstrates that the seleno ligand exhibits a greater tendency than the mercapto ligand to bridge two metal centers, while comparison of [TseMe]Re(CO)3 and [TseMes]Re(CO)3 indicates that the [TseMe] ligand is more electron donating and less sterically demanding than the [TseMes] ligand.     

Interplay between kinetically slow thermal spin-crossover and metastable high-spin state relaxation in an iron(II) complex with similar T1/2 and T(LIESST)

This paper describes the first material to show the well-known light-induced excited spin-state trapping (LIESST) effect, the metastable excited state of which relaxes at a temperature approaching its thermal spin-crossover. Cooling polycrystalline [FeL(2)][BF(4)](2).x H(2)O (L=2,6-bis[3-methylpyrazol-1-yl]pyridine; x=0-1/3) at 1 K min(-1) leads to a cooperative spin transition, taking place in two steps centered at 147 and 105 K, that is only 54 % complete by magnetic susceptibility. Annealing the sample at 100 K for 2 h results in a slow decrease in chi(M)T to zero, showing that the remainder of the spin-crossover can proceed, but is kinetically slow. The crystalline high- and fully low-spin phases of [FeL(2)][BF(4)](2).x H(2)O are isostructural (C2/c, Z=8), but the spin-crossover proceeds via a mixed-spin intermediate phase that has a triple unit cell (C2/c, Z=24). The water content of the crystals is slowly lost on exposure to air without causing decomposition. However, the high-spin/mixed-spin transition in the crystal proceeds at 110+/-20 K when x=1/3 and 155+/-5 K when x=0, which correspond to the two spin-crossover steps seen in the bulk material. The high-spin state of the compound is generated quantitatively by irradiation of the low-spin or the mixed-spin phase at 10 K, and in approximately 70 % yield by rapidly quenching the sample to 10 K. This metastable high-spin state relaxes back to the low-spin ground state at 87+/-1 K in one, not two, steps, and without passing through the intermediate phase. This implies that thermal spin-crossover and thermally activated high-spin-low-spin relaxation in this material become decoupled, thus avoiding the physical impossibility of T(LIESST) being greater than T(1/2).     

Effect of p-tert-butylcalix[4]arene fitted with phosphinoyl pendant arms as synergistic agent in the solvent extraction of trivalent lanthanoids with 4,4,4-trifluoro-1-(2-thienyl)-1,3-butanedione and structural study of solid complexes by IR,NMR and X-ray

The synergistic solvent extraction of five selected lanthanoid ions (La³⁺, Nd³⁺, Eu³⁺, Ho³⁺ and Lu³⁺) with 4,4,4-trifluoro-1-(2-thienyl)-1,3-butanedione (HL) and 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetrakis-(dimethylphosphinoylmethoxy)calix[4]arene, (S) in CHCl₃ has been studied. It was found that in presence of this phosphorus-containing calix[4]arene the lanthanoid ions have been extracted as [LnL₃S₂]. The values of the equilibrium constants and the separation factor have been calculated. The influence of the synergistic agent on the extraction process has been discussed.     

HPLC determination of cefotaxime and cephalexine residues in milk and cephalexine in veterinary formulation

An HPLC method was developed and validated for the determination of the cephalosporins cefotaxime and cephalexine in skimmed bovine milk. The analytical column, Kromasil C₁₈ (250 mm × 4.0 mm, 5 μm) was operated at ambient temperature. Mobile phase consisted of CH₃OH-acetate buffer (pH = 4.0) and it was delivered isocratically at a flow rate of 1.0 mL · min⁻¹. Total analysis time was less than 5 min. Caffeine was used as internal standard (5 ng · μL⁻¹). UV detection was performed at 265 nm. Method validation was performed by means of intra-day (n = 5) and inter-day accuracy and precision (n = 8), sensitivity and linearity. Limits of detection (LOD) and limits of quantification (LOQ) were 0.1 and 0.3 ng · μL⁻¹, respectively. The method was applied to the analysis of a veterinary drug (CEPOREX) containing cephalexine. The results were quite accurate with the relative error varying from −8.0 to −3.5%. Solid-phase extraction was applied to remove all matrix interference from milk samples. High extraction recoveries (average 84–121%) were achieved by using Abselut NEXUS cartridges with acetonitrile as eluent and a rinsing step with water and n-butanol. A pre-concentration step was necessary in a 1/10 level to reach the EU MRL concentration level (100 μg · kg⁻¹). RSD values were less than 7% for both cephalosporins. Correspondence: Ioannis N. Papadoyannis, Laboratory of Analytical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece     

Structural studies of cyclic ureas: 1. Enthalpies of formation of imidazolidin-2-one and N,N′-trimethyleneurea

A thermophysical and thermochemical study has been carried out for crystalline imidazolidin-2-one and N,N′-trimethyleneurea [tetrahydropyrimidin-2(1H)-one]. The thermophysical study was made by differential scanning calorimetry, d.s.c., in the temperature intervals between T = 268 K and their respective melting temperatures. Several solid–solid transitions have been detected in imidazolidin-2-one. The standard (p^° = 0.1 MPa) molar enthalpies of formation, at T = 298.15 K, for crystalline imidazolidin-2-one and N,N′-trimethyleneurea [tetrahydropyrimidin-2(1H)-one], were determined using static-bomb combustion calorimetry. The standard molar enthalpies of sublimation, at T = 298.15 K, for the two compounds were derived from the variation of their vapour pressures, measured by the Knudsen effusion method, with the temperature. These two thermochemical parameters yielded the standard molar enthalpies of formation of the two cyclic urea compounds studied in the gaseous phase at T = 298.15 K. These values are discussed in terms of molecular structural contributions and interpreted on the bases of the “benzo-condensed effect” and of the ring strain of imidazolidin-2-one.