Unramified forcing preserving the law of double negation

Shoenfield's unramified version of Cohen's forcing is defined in two stages: one which does not preserve double negation and the other which modifies the former so as to preserve double negation. Here we express the unramified forcing, which preserves double negation, in a single stage. Surprisingly enough, the corresponding definition of forcing for equality acquires a rather simple form. In [2] forcing ∥- is expressed in terms of strong forcing \( \Vdash * \) viap∥-Q iffp \( \Vdash * \) ¬ ¬Q for every formulaQ ofZF set theory and every elementp of a partially ordered set (P, ≦). In its turn,p \( \Vdash * \) Q is defined by the following five clauses: (1) $$p \Vdash * a \in biff(\exists c)(\exists q \geqq p)((c,q) \in b \wedge p \Vdash * a = c)$$ (2) $$\begin{gathered} p \Vdash * a \ne biff(\exists c)(\exists q \geqq p)(((c,q) \in a \wedge p \Vdash * c \notin b) \hfill \\ ((c,q) \in b \wedge p \Vdash * c \notin a)) \hfill \\ \end{gathered} $$ (3) $$p \Vdash * \neg Qiff(\forall q)(q \leqq p \to \neg (q \Vdash * Q))$$ (4) $$p \Vdash * (Q \vee S)iff(p \Vdash * Q) \vee (p \Vdash * S)$$ (5) $$p \Vdash * (\exists x)Q(x)iff(\exists b)(p \Vdash * Q(b))$$ .     

Synthesis of a short-chain fullerene dimer

The synthesis of a short-chain fullerene dimer via bifunctional cycloaddition is demonstrated. A mono-functionalised C₆₀ species is isolated, and has the potential for further organic functionalisation.     

Purification by HPLC and the UV/Vis absorption spectra of the nitrogen-containing incar-fullerenes iNC60, and iNC70

We report the purification of the nitrogen-containing incar-fullerenes iNC(60) and iNC(70), and their characterisation by UV-Vis absorption spectroscopy.     

THE PREPARATION OF SULPHIDES AND POLYSULPHIDES FROM β-KETO-ESTERS AND 1,3-DIKETONES

Abstract

We have found that the treatment of certain β-keto-esters or 1,3-diketones with thionyl chloride gives either a sulphide or a sulphinyl chloride together with the chloro-compound depending on the structure of the active methylene compound. In certain cases cyclisation of sulphide provides a useful route to a 1,4-oxathiin.     

A 3D Porous Metal Organic Framework Based on Infinite 1D Nickel(II) Chains with Rutile Topology Displaying Open Metal Sites

The reaction of Ni^II with a tetra‐benzoate pyrene ligand produces a 3D porous framework based on infinite 1D Ni^II chains. The Ni^II–O connectivity and the formation of a hydroxo‐bridge (μ₃‐OH) responsible for the connection of the central Ni^II atoms within the 1D Ni^II–(μ₃‐OH)₂–Ni^II chains can be straightforwardly compared with the Ti^IV–O–Ti^IV connectivity seen in TiO₂. The arrangement of the TBAPy ligand around the 1D rutile‐based chains leads in the generation of a porous framework with two distinct types of pores; based on the chemistries of these two types of pores, one can be labelled as hydrophobic and the other as hydrophilic. The use of different activation methods results in the generation of either a porous framework free of guest molecules or a completely solvent‐free material, in which the terminal H₂O molecules bound to Ni^II were removed, leading thus to a framework with open Ni^II sites. CO₂ isotherms collected on both frameworks at 195 K and one barshowed type I isotherms characteristic of microporous materials (BET surface areas for: guest‐free framework: 257(3) m² · g^–1; solvent‐free framework: 362(2) m² · g^–1). The affinity of both networks at zero coverage for both CO₂ and CH₄ was found to be greater when the unsaturated Ni^II sites are available within the void space.     

Neutron activation analysis for determination of metal ions in biological fluids of patients after CoCrMo arthroplasty

Determination of metals and trace elements in patients with total knee or hip arthroplasty with CoCrMo alloy was performed. Blood, urine and cerebrospinal fluid (CSF) samples were analyzed and compared with samples from healthy people. Levels of Co, Cr as well as Na, Ca, Fe, Zn, Se, Rb, Sb and Br were determined by means of neutron activation analysis. The values of Cr and Co of the blood and urine measurements were elevated in patients with replacement, and according to the statistical analysis, significant differences of the elements Zn, Br, Co and Sb were found in the CSF (p?<?0.05).

     

Kinetics of adsorption of the cobalt ions on the "electrolytic solution/gamma-alumina" interface

In the present work we studied, for the first time, the kinetics of adsorption of the Co(H(2)O)(6)(2+) species on the "electrolytic solution/gamma-Al(2)O(3)" interface at pH = 7 and 25 degrees C for a very broad range of Co(II) surface concentrations ranged from 0.03 to 6 theoretical Co(H(2)O)(6)(2+) surface layers. Moreover, we studied the surface dissolution of gamma-alumina in the presence of the Co(H(2)O)(6)(2+) ions in the impregnating solution, the contribution of the Co(II) desorption on the whole deposition process and the deposition isotherm. It was found that under the conditions where the deposition has taken place, the dissolution of the gamma-alumina surface is negligible even in the presence of the Co(H(2)O)(6)(2+) species in the impregnating solution. It was, moreover, inferred that the Co(II) desorption does not participate significantly to the whole deposition process. It was found that the deposition kinetics may be described by the following kinetic expression r(Co,bulk) = k'C(Co,bulk)(2), which relates the rate of disappearance of the Co(H(2)O)(6)(2+) ions from the impregnating solution, r(Co,bulk,) with their concentration C(Co,bulk). This kinetic expression may be derived assuming the following deposition scheme: nS + 2[Co(H(2)O)(6)(2+)] --> S(n) - [Co(H(2)O)(x,x)(<)(6)(2+)](2), where S represents the surface reception sites. The above expressions indicated that two Co(H(2)O)(6)(2+) ions are involved, from the side of the interface, in the reaction with the reception sites. It seems probable that the deposition step involves the simultaneous adsorption and dimerization of the two interfacial Co(H(2)O)(6)(2+) ions through (hydr)oxobridges. On the other hand, the sigmoidal form of the deposition isotherm and the dependence of the apparent rate constant, k', on the interfacial Co(II) concentration suggested that the already deposited Co(II) species may be involved in the reception sites, S, promoting the adsorption and resulting to the formation of multinuclear complexes and Co(II) surface precipitates. Finally, reasonable interface potential values for oxides were determined for the first time using kinetic results.     

Engineering Homochiral Metal–Organic Frameworks by Spatially Separating 1D Chiral Metal–Peptide Ladders: Tuning the Pore Size for Enantioselective Adsorption

The reaction of the chiral dipeptide glycyl‐L(S)‐glutamate with Co^II ions produces chiral ladders that can be used as rigid 1D building units. Spatial separation of these building units with linkers of different lengths allows the engineering of homochiral porous MOFs with enhanced pore sizes, pore volumes, and surface areas. This strategy enables the synthesis of a family of isoreticular MOFs, in which the pore size dictates the enantioselective adsorption of chiral molecules (in terms of their size and enantiomeric excess).     

Making Solid‐Phase Peptide Synthesis Greener: A Review of the Literature

To date, the synthesis of peptides is concurrent with the production of enormous amounts of toxic waste. DMF, CH₂Cl₂, and NMP are three of the most toxic organic solvents used in chemical synthesis and are the most common solvents used for peptide synthesis. Additionally, concerns about the hepatotoxicity caused by exposure to DMF and from the toxic and allergenic nature of additives used in peptide synthesis necessitates the need for a green, environmentally friendly, and safer protocol for peptide synthesis. This review summarizes the current literature on green solid‐phase peptide synthesis successes and challenges encountered. The review concludes with suggestions for future research towards a simple and efficient green peptide synthesis protocol.     

Complex Macrophase‐Separated Nanostructure Induced by Microphase Separation in Binary Blends of Lamellar Diblock Copolymer Thin Films

The nanostructures of thin films spin‐coated from binary blends of compositionally symmetric polystyrene‐b‐polybutadiene (PS‐b‐PB) diblock copolymer having different molar masses are investigated by means of atomic force microscopy (AFM) and grazing‐incidence small‐angle X‐ray scattering (GISAXS) after spin‐coating and after subsequent solvent vapor annealing (SVA). In thin films of the pure diblock copolymers having high or low molar mass, the lamellae are perpendicular or parallel to the substrate, respectively. The as‐prepared binary blend thin films feature mainly perpendicular lamellae in a one‐phase state, indicating that the higher molar mass diblock copolymer dominates the lamellar orientation. The lamellar thickness decreases linearly with increasing volume fraction of the low molar mass diblock copolymer. After SVA, well‐defined macrophase‐separated nanostructures appear, which feature parallel lamellae near the film surface and perpendicular ones in the bulk.