Some basic algebraic features of quasiparticle transformations are reviewed. Special nonlinear quasiparticle transformations are introduced leading to the second quantized counterparts of gerninal-type (correlated) wave functions. Algebraic representa-' tions of strong and weak orthogonality are discussed, and these issues are generalized to the case of non-orthogonal basis sets leading to the ...

For an odd integer r>0 and n>r, we introduce a notion of weakly r-separated collections subsets [n]={1,2,…,n}. When r=1, this corresponds to the concept weak separation introduced by Leclerc Zelevinsky. In paper, extending results due Leclerc-Zelevinsky, develop geometric approach establish number nice combinatorial properties maximal (such as exact upper bound on size collections, mutations ru...

The purpose of this work is to investigate the existence of fixed points of some mappings in fixed point theory by combining some important concepts which are F-weak contractions, multivalued mappings, integral transformations and α-admissible mappings. In fixed point theory, it is important to find fixed points of some classess under F- or F-weak contractions. Also multivalued mappings is the ...

Abstract We present a new generalized algorithm which allows the construction of Bäcklund transformations (BTs) for higher order ordinary differential equations (ODEs). This algorithm is based on the idea of seeking transformations that preserve the Painlevé property, and is applied here to ODEs of various orders in order to recover, amongst others, their autoBTs. Of the ODEs considered here, o...