Introduction. In this note we develop a multistep formulation of the optimized Lax-Wendroff method for hyperbolic systems. This scheme was derived by Strang [6], [7]. The present formulation extends in a natural way, the two-step formulation of Richtmyer [5] for systems in one-space variable. We summarise this case in the next section. One Space Dimension. We consider the first-order conservati...

We discuss algebraic and analytic structure of rational Lax operators. With algebraic reductions of Lax equations we associate a reduction group-a group of twisted automor-phisms of the corresponding infinite dimensional Lie algebra. We present a complete study of dihedral reductions for sl(2, C) Lax operators with simple poles and corresponding integrable equations. In the last section we give...

The solution of the Lax tensor equations in the case Lαβγ = −Lβαγ was analyzed. The Lax tensors on the dual metrics were investigated. We classified all two dimensional metrics having the symmetric Lax tensor Lαβγ . The Lax tensors of the flat space, Rindler system and its dual were found.

We construct Boolean-valued term models and describe their universal properties. The underlying set of these models consists of the terms of the underlying language, while formulae are interpreted in the Lindenbaum-Tarski algebra of open formulae. Subspaces of the Stone space of the Lindenbaum-Tarski algebra of open formulae are shown to be homeomorphic to spaces of enumerated models models equ...

We study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theo...

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...

Square Complex Orthogonal Space Time Block Codes (COSTBC) with no zero entries are known for 2,4 and 8 transmit antennas. But, for 16 transmit antennas COSTBCs with no zero entries have not been reported. Zero entries in the design lead to the problem of switching off of transmit antenna, imposing severe constraints on hardware implementation. The zeros also result in the increase of the Peak t...

Previous results on quasi-classical limit of the KP and Toda hierarchies are now extended to the BKP hierarchy. Basic tools such as the Lax representation, the Baker-Akhiezer function and the tau function are reformulated so as to fit into the analysis of quasi-classical limit. Two subalgebras WB 1+∞ and w B 1+∞ of the Winfinity algebrasW1+∞ and w1+∞ are introduced as fundamental Lie algebras o...