Dominating Functions and Graphs

A graph is called dominating if its vertices can be labelledwith integers in such a way that for every function : thegraph contains a ray whose sequence of labels eventually exceeds. We obtain a characterization of these graphs by producinga small family of dominating graphs with the property that everydominating graph must contain some member of the family.     

Reaping Numbers of Boolean Algebras

A subset A of a Boolean algebra B is said to be (n,m)-reapedif there is a partition of unity p B of size n such that |{b p:b a 0}| m for all a A. The reaping number r_n,m (B) ofa Boolean algebra B is the minimum cardinality of a set A B\{0}which cannot be (n,m)-reaped. It is shown that for each n, thereis a Boolean algebra B such that r_n+1,2(B) r_n,2(B). Also, {r_n,m(B):mn } consists of at most two consecutive cardinals. The existenceof a Boolean algebra B such that r_n,m (B) r_n',m' (B) is equivalentto a statement in finite combinatorics which is also discussed.     

Novel radial oligothienyl silanes

A series of thiophene-based homologues with a silicon core surrounded by mono-, bi-, terthiophene, and their derivatives with alkylsilyl linkages has been prepared using hydrosilylation and Stille coupling methods.     

Retention of Cr(III) by high-performance chelation ion chromatography interfaced to inductively-coupled plasma mass spectrometric detection with collision cell

High-performance chelation ion chromatography (HPCIC) was employed to retain cationic Cr(III) on an anion-exchange column and hence allow the separation of the two most prevalent forms of chromium, Cr(II) and Cr(VI). A mobile phase of nitric acid was utilized at pH = 1.5; additionally, 2,6-pyridinedicarboxylic acid was used at a concentration of 6 mM. Additives with different structural characteristics were used in an effort to elucidate retention mechanisms. Inductively-coupled plasma mass spectrometry was used for chromium detection. A collision cell was utilized to reduce chloride-based polyatomic ions that may interfere with the detection of Cr(III), and a detection limit study yielded levels in the low part-per-billion range. The newly developed method was applied to the chromatographic analysis of samples of an incubation medium containing Cr(VI) incubated with cell nuclei.     

Synthesis and supramolecular properties of molecular clips with anthracene sidewalls

Novel molecular clips with anthracene sidewalls (1 a-c) were synthesized; they form stable host-guest complexes with a variety of electron-deficient aromatic and quinoid molecules. According to single-crystal structure analyses of clip 1 c and 1,2,4,5-tetracyanobenzene (TCNB) complex 14@1 b, the clips' anthracene sidewalls have to be compressed substantially during the complex formation to provide attractive pi-pi interactions between the aromatic guest molecule and the two anthracene sidewalls in the complex. The compression and expansion of aromatic sidewalls are calculated by molecular mechanics to be low-energy processes, so the energy required for compression of the anthracene sidewalls during complex formation is apparently overcompensated by the gain in energy resulting from the attractive pi-pi interactions. The finding that complexes of the clips 1 a-c are more stable than those of the corresponding clips 2 a-c can be explained in terms of the larger van der Waals contact surfaces of the anthracene sidewalls in 1 a-c (relative to the naphthalene sidewalls in 2 a-c). Color changes resulting from charge-transfer (CT) bands are observed in complex formation by 1 a-c: from colorless to red or purple with TCNB (14), and from yellow to green with 2,4,7-trinitro-9-fluorenone TNF (17). Independently, the host 1 b and guest 14 fluoresce from their respective excited singlet states, whilst in the complex 14@1 b the charge-transfer state quenches the higher-energy singlet states of the two components, and as a result luminescence is only observed from this new CT state. To the best of our knowledge, complex 14@1 b is the first example of CT luminescence from a host-guest complex. The binding constant determined for the formation of the TCNB complex 14@1 b from a UV/Vis titration experiment (Ka = 12 400 m(-1)) agrees well with the value (K(a) = 12 800 m(-1)) obtained by 1H NMR titration.     

Countable Fréchetα 1-spaces may be first countable

It is shown to be consistent that countable, Fréchet, ₁-spaces are first countable. The result is obtained by using a countable support iteration of proper partial orders of length ₂.The research of both authors is partially supported by NSERC     

A vinylsilane route to trans-7a-methylhydrind-4-en-1,6-dione

A stereoselective synthesis of the title compound is described. The overall yield is 34% starting with 2-methyl-2-cyclopentenone. The trans ring-fusion stereochemistry is established by a conjugate addition/trapping sequence.     

Novel Stereoselective Phase Transfer Catalytic Synthesis and Some Applications of ( E )-2-Chlorovinylthioarenes and Hetarenes

A novel two-step method for the preparation of ( E )-2-chlorovinylthioarenes (or hetarenes) from thiols and 1,1,2-trichloroethane in the phase transfer catalytic systems solid K 2 CO 3 /solid KI/18-crown-6/xylene and solid KOH/18-crown-6/toluene has been developed. ( E )-2-chlorovinylthioarenes were isolated in yields up to 98%. Utilization of ( E )-2-chlorovinylthioarenes in the Heck and Stille reactions has been shown.     

Certification of nitrate in spinach powder reference material SPIN-1 by high-precision isotope dilution GC–MS

A high-precision exact-matching quadruple isotope dilution method (ID⁴MS) was employed for the quantitation of nitrate in an air-dried spinach powder Certified Reference Material (CRM). The analyte was extracted in hot water following addition of ¹⁵NO\({}_{3}^{-}\) internal standard. The blend was then treated with sulfamic acid to remove nitrite and with triethyloxonium tetrafluoroborate to promote aqueous conversion of nitrate into volatile EtONO₂. The derivative was analyzed by headspace GC–MS with 3-min elution time. The method performance was validated with a series of tests which demonstrated adequate selectivity and ruggedness. This method supported the development of novel SPIN-1 CRM giving a modest contribution to its uncertainty (u_char = 0.85%). With respect to previous attempts, the SPIN-1 was proven stable, homogeneous (u_hom = 0.44%), and suitable for spinach monitoring under EU regulations. On dried basis, the nitrate content of SPIN-1 was found to be 22.53 ± 0.43 mg/g (U_c = 1.9%, k = 2). The material was also used in an inter-laboratory study where four laboratories employed a total of ten measurement methods.

SPIN-1 Certified Reference Material for nitrate in spinach powder