Zinc‐Catalyzed Dual C–X and C–H Borylation of Aryl Halides

A zinc‐catalyzed combined C? X and C? H borylation of aryl halides using B₂pin₂ (pin=OCMe₂CMe₂O) to produce the corresponding 1,2‐diborylarenes under mild conditions was developed. Catalytic C? H bond activation occurs ortho to the halide groups if such a site is available or meta to the halide if the ortho position is already substituted. This method thus represents a novel use of a group XII catalyst for C? H borylation. This transformation does not proceed via a free aryne intermediate, but a radical process seems to be involved.     

Multiclass Distance-Weighted Discrimination

In this article, we extend the binary distance-weighted discrimination (DWD) to the multiclass case. In addition to the usual extensions that combine several binary DWD classifiers, we propose a global multiclass DWD (MDWD) that finds a single classifier that considers all classes at once. Our theoretical results show that MDWD is Fisher consistent, even in the particularly challenging case when there is no dominating class, that is, a class with probability bigger than 0.5. The performance of different multiclass DWD methods is assessed through simulation studies and application to real microarray datasets. Comparison with the support vector machines is also provided. MATLAB implementation of the proposed methods is given in the online supplementary materials.     

An Existence Proof for the Gravitating BPS Monopole

We prove the existence of the gravitating BPS monopole in Einstein-Yang-Mills-Higgs (EYMH) theory. Existence is established using a Newtonian perturbation argument which shows that a Yang-Mills-Higgs BPS monopole solution can be be continued analytically in powers of 1/c² to an EYMH solution. Communicated by Sergiu Klainerman submitted 2/04/04, accepted 29/08/05     

Parallel DNA Constrained by“CC~ Clamps”

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Functionalization of nanoparticles for dispersion in polymers and assembly in fluids

The fluorescent, magnetic, and conductive properties of nanoparticles can transform polymer-based materials into composites with higher levels of sophistication than found in polymers alone. The ligand chemistry of nanoparticles is critically important in the development of polymer–nanoparticle composites to prevent nanoparticle aggregation and direct their assembly within polymers. Nanoparticle ligands can also prevent aggregation in solution and direct the assembly of nanoparticles at fluid–fluid interfaces, where interfacial chemistries can be performed to provide new routes to ultrathin composite sheets and capsules. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5076–5086, 2006     

Arene–perfluoroarene interactions in crystal engineering. 4.

In the title complex, C₆F₆·C₁₄H₁₂, nearly parallel mol­ecules of trans-stilbene and librationally disordered hexa­fluoro­benzene form a mixed stack, with each molecule lying on an independent inversion centre. Adjacent stacks pack together in a herring-bone manner.     

Distribution of Primitive λ-Roots of Composite Moduli Ⅱ

We improve estimates for the distribution of primitive λ-roots of a composite modulus q yielding an asymptotic formula for the number of primitive λ-roots in any interval Ⅰ of length |I| (>>) q1/2+∈. Similar results are obtained for the distribution of ordered pairs (x, x-1) with x a primitive λ-root, and for the number of primitive λ-roots satisfying inequalities such as |x -x-1| ≤ B.     

Arene–perfluoroarene interactions in crystal engineering. 5.

In the title complex, C₁₀F₈·C₆H₄S₄, planar centrosymmetric mol­ecules of tetra­thia­fulvalene and octa­fluoro­naphthalene, inclined to each other by 9.6 (1)°, form a mixed stack which does not exhibit charge transfer. Adjacent stacks pack in a herring-bone motif.     

The implicit function theorem in a non-Archimedean setting

In this paper, the inverse function theorem and the implicit function theorem in a non-Archimedean setting will be discussed. We denote by N any non-Archimedean field extension of the real numbers that is real closed and Cauchy complete in the topology induced by the order; and we study the properties of locally uniformly differentiable functions from Nⁿ to N^m. Then we use that concept of local uniform differentiability to formulate and prove the inverse function theorem for functions from Nⁿ to Nⁿ and the implicit function theorem for functions from Nⁿ to N^m with m<n.