BACKGROUND The importance of membrane compartmentalization into specific membrane microdomains has been shown in many biological processes such as immunoreceptor signaling, membrane trafficking, pathogen infection, and tumor progression. Microdomains like lipid rafts, caveolae and tetraspanin enriched microdomains are relatively resistant to solubilization by some detergents. Large detergent-re...

We define a Lax operator as monic pseudodifferential L(∂) of order N ≥ 1, such that the equations $$\frac{\partial L(\partial)}{\partial t_k}=[(L^\frac{k}{N}(\partial))_+,L(\partial)]$$ are consistent and non-zero for infinitely many positive integers k. Consistency an equation means its flow is defined by evolutionary vector field. In present paper we demonstrate traditional theory KP N-th KdV...

Having as starting point Barr’s description of topological spaces as lax algebras for the ultrafilter monad [2], in this paper we present further topological examples of lax algebras – such as quasi-metric spaces, approach spaces and quasi-uniform spaces – and show that, in a suitable setting, the categories of lax algebras have indeed a topological nature. Furthermore, we generalize to this se...

It is shown that the Lax pair equation L̇ = [L,A] can be given a neat tensorial interpretation for finite-dimensional quadratic Hamiltonians. The Lax matrices L and A are shown to arise from third rank tensors on the configuration space. The second Lax matrix A is related to a connection which characterizes the Hamiltonian system. The Toda lattice system is used to motivate the definition of the...

A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess classical Hamiltonian structures, in which the nonlinearized spatial system is intimately related to stationary AKNS ows. These nonlin-earized Lax systems also ...

A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess classical Hamiltonian structures, in which the nonlinearized spatial system is intimately related to stationary AKNS flows. These nonlinearized Lax systems also...

Recent investigations of lax algebras—in generalization of Barr’s relational algebras—make an essential use of lax extensions of monad functors on Set to the category Rel(V) of sets and V-relations (where V is a unital quantale). For a given monad there may be many such lax extensions, and different constructions appear in the literature. The aim of this article is to shed a unifying light on t...

Impaired long-axis motion is a sensitive marker of systolic myocardial dysfunction, but no data are available that relate long-axis changes in systole with those in diastole, particularly in subjects with diastolic dysfunction and a 'normal' left ventricular (LV) ejection fraction. A total of 311 subjects (including 105 normal healthy volunteers) aged 20-89 years with variable degrees of systol...

The pentagram map was introduced by R. Schwartz in 1992 and is now one of the most renowned discrete integrable systems. In present paper we prove that this map, as well all its known multidimensional generalizations, can be seen refactorization-type mappings Poisson-Lie group pseudo-difference operators. This brings into rich framework groups, both describing new structures simplifying reveali...

Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle ω = Sθ in terms of the incoming angle with S orthogonal and Id−S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact...