We have recently solved the inverse scattering problem for oneparameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev Petviashvili (dKP) equation. We showed, in particu...

Recently the study of Fay-type identities revealed some new features of the DKP hierarchy (also known as “the coupled KP hierarchy” and “the Pfaff lattice”). Those results are now extended to a Toda version of the DKP hierarchy (tentatively called “the Pfaff-Toda hierarchy”) . Firstly, an auxiliary linear problem of this hierarchy is constructed. Unlike the case of the DKP hierarchy, building b...

We have previously isolated a new actinomycete strain from Tunisian soil called Streptomyces sp. US24, and have shown that it produces two bioactive molecules including a Cyclo (L-Phe, L-Pro) diketopiperazine (DKP). To identify the structural genes responsible for the synthesis of this DKP derivative, a PCR amplification (696 bp) was carried out using the Streptomyces sp. US24 genomic DNA as te...

The problem of coupling between spin and torsion is analysed from a Lyra's manifold background for scalar and vector massive fields using the Duffin-Kemmer-Petiau (DKP) theory. We found the propagation of the torsion is dynamical, and the minimal coupling of DKP field corresponds to a non-minimal coupling in the standard Klein-Gordon-Fock and Proca approaches. The origin of this difference in t...

Aiming at restricting the conformational freedom of tryptophan-containing peptide ligands, we designed a THBC (tetrahydro-β-carboline)-DKP (diketopiperazine)-based peptidomimetic scaffold capable of arranging in an unusual α-turn conformation. The synthesis is based on a diastereoselective Pictet-Spengler condensation to give the THBC core, followed by an intramolecular lactamization to complet...

A strict proof of equivalence between DuÆn-Kemmer-Petiau (DKP) and Klein-Gordon (KG) theories is presented for physical S-matrix elements in the case of charged scalar particles interacting in minimal way with an external or quantized electromagnetic eld. First, Hamiltonian canonical approach to DKP theory is developed in matrix form. The theory is then quantized through the construction of the...

We describe novel acetohydroxamic acid derivatives with potent activity against cultured bloodstream-form Trypanosoma brucei and selectivity indices of >1000. These analogues were derived from conformationally constrained, lipophilic, spiro carbocyclic 2,6-diketopiperazine (2,6-DKP) scaffolds by attaching acetohydroxamic acid moieties to the imidic nitrogen. Optimal activity was achieved by pla...

We show that the Klein-Gordon equation on the quaternion field is equivalent to a pair of DKP equations. We shall also prove that this pair of DKP equations can be taken back to a pair of new KG equations. We shall emphasize the important difference between the standard and the new KG equations. We also present some qualitative arguments, concerning the possibility of interpreting anomalous sol...

In this paper we investigate Bare Plurals (BPs; NPPL) in English and Romanian and Bare Plural Partitives (BParts; i.e. des NPPL) in French. Romanian BPs and French BParts only share with English BPs the existential interpretation with obligatory narrow scope. We propose that this reading shared by all three comes from the same pieces: a non-kind-selecting predicate, a kind-denoting argument, an...