For each p^ 1, Lp is a linear metric complete separable space. Let E be a set in Lp. The linear manifold M(E) determined by E is the set of all linear combinations (finite) of elements of £ . The span SP(E) of E in Lp is the closure in Lp of M (E) ; an element cj> of Lp belongs to SP(E) if and only if to each e > 0 corresponds an element f€ of M(E) such that | | 0 /« | | <e . L e t / G L p . Fo...

Trigonometric non-isospectral flows are defined for KP hierarchy. It is demonstrated that symmetry constraints of KP hierarchy associated with these flows give rise to trigonometric Calogero-Moser system.

Pityriasis rubra pilaris (PRP) has always been an intriguing topic ever since its inception. It is a group of chronic disorders characterized by reddish orange plaques with pityriasiform scaling showing follicular keratoses, palmoplantar keratoderma, and sometimes, erythroderma. It occurs all over the world but with racial variations. Its incidence might vary and the age at onset, behavior, cli...

Let Xp = Gp/Kp be homogeneous spaces (Kp a compact subgroup of a locally compact group Gp) with dimension parameter p such that the double coset spaces Gp//Kp can be identified with some fixed space X . Then we obtain projections Tp : Xp → X , and for a given probability measure ν ∈ M(X) there exist unique ”radial”, i.e. Kp-invariant measures νp ∈ M1(Xp) with Tp(νp) = ν and associated radial ra...

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the...

Given the two boson representation of the conformal algebra Ŵ∞, the second Hamiltonian structure of the KP hierarchy, I construct a bi-Hamiltonian hierarchy for the two associated currents. The KP hierarchy appears as a composite of this new and simpler system. The bi-Hamiltonian structure of the new hierarchy gives naturally all the Hamiltonian structures of the KP system.

An isomorphic factorisation of the complete graph Kj, is a partition of the lines of Kp into t isomorphic spanning subgraphs G; we then write G\Kj, and G G K^/t. If the set of graphs Ky/t is not empty, then of course t\p(p — l)/2. Our principal purpose is to prove the converse. It was found by Laura Guidotti that the converse does hold whenever (/,/>) » 1 or (t,p — 1) «= 1, We give a new and sh...

We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of Wn algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian ...

Using the determinant representation of gauge transformation operator, we have shown that the general form of τ function of the q-KP hierarchy is a q-deformed generalized Wronskian, which includes the q-deformed Wronskian as a special case. On the basis of these, we study the q-deformed constrained KP (q-cKP) hierarchy, i.e. l-constraints of q-KP hierarchy. Similar to the ordinary constrained K...

Data from the Astrid-2 satellite taken between April and July 1999 show several examples of dense ion clouds in the 0.1–2 keV energy range inside the inner magnetosphere, both in the northern and southern hemispheres. These inner magnetospheric ion clouds are found predominantly in the early morning sector, suggesting that they could have originated from substorm-related ion injections on the n...