The Ontological Argument in the Tractatus

The intention of this article is to show that the Tractatus deals with the problem of the relation between reality, possibility, and necessity as traditionally considered in the ontological argument, that is, in relation to the idea of limit, and that in Section 5.5521, we find an especially clarifying formulation of this question; the formulation itself, however, is not at all clear, so that a lengthy commentary of it is justified.     

Synthesis of 4-methoxy-1H-phenalen-1-one: a subunit related to natural phenalenone-type compounds

4-Methoxy-1H-phenalen-1-one (4-methoxyperinaphthenone, 1), a subunit found in some Musa phytoalexins and related natural products from the Haemodoraceae, was synthesized starting from 2-methoxynaphthalene in five steps and an overall yield of 36%. A Heck–Fujiwara coupling between ethyl acrylate and 1-bromonaphthalene afforded the corresponding (E)-naphthylpropanoic acid which, after hydrogenolysis, was subjected to a one-pot Friedel–Crafts acylation–DDQ dehydrogenation procedure to furnish 1.     

Diophantine approximation in characteristiep

We study diophantine approximations to algebraic functions in characteristicp. We improve a theorem of Osgood, and give two classes of examples showing that this result is nearly sharp. One of these classes exhibits a new phenomenon.     

Stereochemistry of organic sulphur compounds: 12—Configurational assignment of 2-methylsulphinyl-1-phenylethanol and some O-derivatives

The conformational analysis of the diastereomeric 2-methylsulphinyl-1-phenylethanol and its O-methyl and O-acetyl derivatives has been performed by ¹H NMR spectroscopy. The study of the influence of dilution and solvent polarity changes on the coupling constants has permitted the configurational assignment of each diastereoisomer. The role played by hydrogen bonding in the hydroxysulphoxides has also been studied by IR spectroscopy.     

Density-functional theory (hyper)polarizabilities of push-pull pi-conjugated systems: treatment of exact exchange and role of correlation

The performance of the optimized effective potential procedure for exact exchange in calculating static electric-field response properties of push-pull pi-conjugated systems has been studied, with an emphasis on NO2-(CH=CH)n-NH2 chains. Good agreement with Hartree-Fock dipole moments and (hyper)polarizabilities is obtained; particularly noteworthy is the chain length dependence for beta/n. Thus, the problem that conventional density-functional theory functionals dramatically overestimate these properties is largely solved, although there remains a significant correlation contribution that cannot be accounted for with current correlation functionals.     

The folded, tetrameric phosph(III)azane macrocycle [(P(mu-NtBu))2(1,4-(NH)2C6H4)]4

The tetrameric macrocycle [(P(mu-NtBu))2(1,4-(NH)2C6H4)]4, obtained from the reaction of the phosphazane dimer [ClP(mu-NtBu)]2 with p-phenylenediamine, has an unusual folded conformation in the solid state and contains a roughly tetrahedral arrangement of endo N-H groups for the potential coordination of anions.     

Some results on construction of orthogonal Latin squares by the method of sum composition

A method of sum composition for construction of orthogona Latin squares was introduced by A. Hedayat and E. Seiden [1]. In this paper we exhibit procedures for constructing a pair of orthogonal Latin squares of size p^α + 4 for primes of the form 4m + 1 or p ≡ 1, 2, 4 mod 7. We also show that for any p > 2n and n even one can construct and orthogonal pair of Latin squares of size p^α + n using the method of sum composition. We observe that the restriction xy = 1 used by Hedayat and Seiden is sometimes necessary.     

Efficient Computation of Roots in Finite Fields

We present an algorithm to compute rth roots in $\mathbb{F}_{q^m}We present an algorithm to compute rth roots in with complexity ?[(log m + r log q) m log q] if (m,q) = 1 and either (q(q−1),r) = 1 or r|(q−1) and ((q−1)/r,r) = 1. This compares well to previously known algorithms, which need O(r m³ log³ q) steps. Paulo S. L. M. Barreto: Supported by Scopus Tecnologia S. A. José Felipe Voloch: Supported by NSA grant MDA904-03-1-0117.