p-Laplacian boundary value problems on exterior regions

This paper treats some variational principles for solutions of inhomogeneous p  -Laplacian boundary value problems on exterior regions U?R^N$U?{\mathbb{R}}^N$ with dimension N?3$N?3$. Existence-uniqueness results when p∈(1,N)$p\in (1,N)$ are provided in a space E^1,p(U)$E^{1,p}(U)$ of functions that contains W^1,p(U)$W^{1,p}(U)$. Functions in E^1,p(U)$E^{1,p}(U)$ are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an L^p$L^p$-imbedding theorem. Also an existence result for a general variational problem of this type is obtained.     

An integrated quantum chemical and experimental approach for exploring the structures and properties of insensitive munitions interacting with ions in bulk water

Structural Chemistry - Alternatives to legacy munitions and explosives, materials that feature increased stability against external stimuli without compromising their energetic yields are currently...     

A High Yielding Synthesis of Racemic Hongconin

Racemic hongconin 1 has been synthesized from adduct 2 formed by reaction between 1-methoxycyclohexa-1,4-diene and benzoquinone. The synthetic strategy includes Fries and Claisen rearrangements, base and cerium(IV) initiated pyran ring formation, C-4 pyran ring hydroxylation and silver(II) mediated oxidation.     

Twist buckling and the foldable cylinder: an exercise in origami

Basic mechanisms for the buckling of a thin cylindrical shell under torsional loading are reviewed from a post-buckling perspective. Deflections are considered so far into the large-deflection range that the shell is allowed to fold to a flat two-dimensional form, in a mechanism reminiscent of a deployable structure. Critical and initial post-buckling effects are explored through concepts of energy minimization and hidden symmetries. For comparisons with the final large-deflection folded shape, a truss element program is employed. It is shown that, as buckling develops, the mode shape must change to accommodate both the symmetry-breaking aspects of the predominately inwards deflection, and the rotation of peak and valley lines of the buckle pattern necessary to accommodate the geometry of the final folded shape.     

A theory for the numerical analysis of compound branching

Zusammenfassung Eine allgemeine Theorie zur numerischen Berechnung eines konservativen Systems mitn Freiheitsgraden undm überlagerten Verzweigungspunkten wird dargestellt. Im Unterschied zu früheren Arbeiten wird kein Diagonalisierungsschema der totalen potentiellen Energie benötigt. Ein Störungsschema wird angegeben, umn–m verallgemeinerte Koordinaten mit Hilfe vonn–m Gleichgewichtsbedingungen zu eliminieren. Anschließend wird ein zweites Störungsschema angegeben, um die Ableitungen der 2 ^m –1 möglichen Äste der Last-Verformungskurven, die im kritischen Punkt entspringen, zu bestimmen. Anschließend wird die Theorie auf zweifache kritische Punkte angewendet, die beim Ausbeulen der durch gleichmäßigen Außendruck belasteten vollständigen Kugelschale auftreten.     

Point deletions of outerplanar blocks

Let G be a graph. If v is a vertex of G then the (? 1, v)-subgraphs of G are defined to be the point deletions of G, except for G ～ {v}, with v labeled on each. This paper first classifies all outerplanar blocks which have a pair of v-isomorphic (? 1, v)-subgraphs and next classifies all outerplanar blocks which have a pair of isomorphic point deletions. Finally, this classification is used to prove the Harary conjecture for outerplanar blocks, namely that an outerplanar block can be reconstructed from the isomorphism classes of its point deletions.     

Studies of peptide a- and b-type fragment ions using stable isotope labeling and integrated ion mobility/tandem mass spectrometry

The structures of peptide a- and b-type fragment ions were studied using synthetic peptides including a set of isomeric peptides, differing in the sequence location of an alanine residue labeled with ¹⁵N and uniformly with ¹³C. The pattern of isotope labeling of second-generation fragment ions derived via a _n and b _n ions (where n=4 or 5) suggested that these intermediates existed in part as macrocyclic structures, where alternative sites of ring opening gave rise to different linear forms whose simple cleavage might give rise to the observed final products. Similar conclusions were derived from combined ion mobility/tandem MS analyses where different fragmentation patterns were observed for isomeric a- or b-type ions that display different ion mobilities. These analyses were facilitated by a new approach to the processing of ion mobility/tandem MS data, from which distinct and separate product ion spectra are derived from ions that are incompletely separated by ion mobility. Finally, an example is provided of evidence for a macrocyclic structure for b _n ions where n=8 or 9.     

A general and efficient route to 6‐methyl‐pyrazin‐2‐yl‐amines: Alkylation of 2,6‐dichloropyrazine via malonate derivatives

We have developed a convenient two‐stage process for the synthesis of 6‐methylpyrazine‐2‐yl‐amines from commercially available materials. The procedure involves the synthesis of (6‐chloro‐pyrazin‐2‐yl)‐acetic acid via arylation of diethyl malonate and in situ hydrolysis/decarboxylation. A second decarboxylation takes place under the subsequent amination conditions allowing simple and efficient access to the intended pyrazines.