Isomorphous replacement of M(II) ions in M(II)-Gd(III) dimers (M(II) = Cu(II), Mn(II), Ni(II), Co(II), Zn(II)): magnetic studies of the products

Complexes [M(II)Gd(III){pyCO(OEt)pyC(OH)(OEt)py}?](ClO?)?·EtOH [M(II) = Cu(II) (1), Mn(II) (2), Ni(II) (3), Co(II) (4) and Zn(II) (5)] crystallize in the monoclinic Cc space group and contain one hexacoordinate M(II) ion and one enneacoordinate Gd(III) ion, bridged by three {pyCO(OEt)pyC(OH)(OEt)py}? ligands. Magnetic susceptibility measurements indicate a ferromagnetic interaction for 1 and antiferromagnetic interactions for 2-4. Using the ? = -J?(Gd(III))?(M(II)) spin Hamiltonian formalism, fits to the magnetic susceptibility data yielded J values of +0.32 cm?1 for 1, -1.7 cm?1 for 2, and -0.22 cm?1 for 3. In complex 4, the orbital contributions of Co(II) precluded the determination of the magnetic coupling. The complex follows the Curie-Weiss law with θ = -2.07 K (-1.44 cm?1).     

Large transitive models in local ZFC

This paper is a sequel to Tzouvaras (Arch Math Log 49(5):571–601, 2010), where a local version of ZFC, LZFC, was introduced and examined and transitive models of ZFC with properties that resemble large cardinal properties, namely Mahlo and ${\Pi_1^1}$ -indescribable models, were considered. By analogy we refer to such models as “large models”, and the properties in question as “large model properties”. Continuing here in the same spirit we consider further large model properties, that resemble stronger large cardinals, namely, “elementarily embeddable”, “extendible” and “strongly extendible”, “critical” and “strongly critical”, “self-critical” and “strongly self-critical”, the definitions of which involve elementary embeddings. Each large model property ? gives rise to a localization axiom Loc ^? (ZFC) saying that every set belongs to a transitive model of ZFC satisfying ?. The theories LZFC ^?  = LZFC + Loc ^? (ZFC) are local analogues of the theories ZFC+“there is a proper class of large cardinals ψ”, where ψ is a large cardinal property. If sext(x) is the property of strong extendibility, it is shown that LZFC ^sext proves Powerset and Σ₁-Collection. In order to refute V = L over LZFC, we combine the existence of strongly critical models with an axiom of different flavor, the Tall Model Axiom (TMA). V = L can also be refuted by TMA plus the axiom GC saying that “there is a greatest cardinal”, although it is not known if TMA + GC is consistent over LZFC. Finally Vopěnka’s Principle (V P) and its impact on LZFC are examined. It is shown that LZFC ^sext  + V P proves Powerset and Replacement, i.e., ZFC is fully recovered. The same is true for some weaker variants of LZFC ^sext . Moreover the theories LZFC ^sext +V P and ZFC+V P are shown to be identical.     

An empirical study of PLAD regression using the bootstrap

Partial LAD regression uses the L ₁ norm associated with least absolute deviations (LAD) regression while retaining the same algorithmic structure of univariate partial least squares (PLS) regression. We use the bootstrap in order to assess the partial LAD regression model performance and to make comparisons to PLS regression. We use a variety of examples coming from NIR experiments as well as two sets of experimental data.     

Totally non‐immune sets

Let be a countable first‐order language and be an ‐structure. “Definable set” means a subset of M which is ‐definable in with parameters. A set is said to be immune if it is infinite and does not contain any infinite definable subset. X is said to be partially immune if for some definable A, is immune. X is said to be totally non‐immune if for every definable A, and are not immune. Clearly every definable set is totally non‐immune. Here we ask whether the converse is true and prove that it is false for every countable structure whose class of definable sets satisfies a mild condition. We investigate further the possibility of an alternative construction of totally non‐immune non‐definable sets with the help of a subclass of immune sets, the class of cohesive sets, as well as with the help of a generalization of definable sets, the semi‐definable ones (the latter being naturally defined in models of arithmetic). Finally connections are found between totally non‐immune sets and generic classes in nonstandard models of arithmetic.     

An improved method for the computation of the Moore-Penrose inverse matrix

In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better accuracy than the already proposed methods, while works for full and sparse matrices.     

Exo-cyclopamine--a stable and potent inhibitor of hedgehog-signaling

The combination of theoretical and computational studies with organic synthesis and biological investigations has led to exo-cyclopamine. This stable and highly potent derivative of cyclopamine promises big potential as an experimental drug against several types of human cancer.