Synthesis and Conformation of Fluorinated β‐Peptidic Compounds

Experimental and theoretical data indicate that, for α‐fluoroamides, the F? C? C(O)? N(H) moiety adopts an antiperiplanar conformation. In addition, a gauche conformation is favoured between the vicinal C? F and C? N(CO) bonds in N‐β‐fluoroethylamides. This study details the synthesis of a series of fluorinated β‐peptides ( 1 – 8 ) designed to use these stereoelectronic effects to control the conformation of β‐peptide bonds. X‐ray crystal structures of these compounds revealed the expected conformations: with fluorine β to a nitrogen adopting a gauche conformation, and fluorine α to a C?O group adopting an antiperiplanar conformation. Thus, the strategic placement of fluorine can control the conformation of a β‐peptide bond, with the possibility of directing the secondary structures of β‐peptides.     

Solitary wave solutions to nonlinear evolution equations in mathematical physics

This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.     

Tensor products in generalized measure theory

Kläy, Randall, and Foulis established that the signed weight space of the tensor product of two quasimanuals each having a positive, finite-dimensional state space is isomorphic to the algebraic tensor product of the signed-weight spaces of the factors. We obtain a generalization of this result for arbitrary quasimanuals. A compactness condition due to Cook—here calleddiscreteness—is discussed and shown to be preserved under the formation of tensor products. It is shown that the predual of the signed weight space of a tensor product of discrete manuals is the projective (ordered) tensor product of the preduals of the signed weight spaces of the factors.     

Tensor product of frame manuals

Since its first use, there has been widespread dissatisfaction with the Hilbert-space tensor product as a device for coupling the Hilbert-space models of two separated quantum mechanical systems. The Hilbert-space model is paraphrased manual-theoretically by the assertion that quantum mechanical entities are represented by frame manuals. There is a natural, heuristically straightforward tensor product for (unital) manuals, and it is natural therefore to ask whether the tensor product of frame manuals might serve as an alternative model of separated quantum mechanical systems. It is shown that the states on a tensor product of complex frame manuals give rise uniquely to sesquilinear forms on the tensor product of the underlying Hibert spaces. In certain cases, these in turn give rise to operators, which, however, are not generally positive, and which, even if compact, need not be trace-class.     

Compact orthoalgebras

We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove that any compact regular TOA is atomistic , and has a compact center. We prove also that any compact TOA with isolated is of finite height. We then focus on stably ordered TOAs: those in which the upper set generated by an open set is open. These include both topological orthomodular lattices and interval orthoalgebras - in particular, projection lattices. We show that the topology of a compact stably-ordered TOA with isolated is determined by that of its space of atoms.