A new set of on shell duality equations is proposed that leads to a map between strings moving on symmetric spaces with opposite curvatures. The transformation maps “waves” on a riemannian symmetric space M to “waves” on its dual riemannian symmetric space M̃ . This transformation preserves the energy momentum tensor though it is not a canonical transformation. The preservation of the energy mom...

the famous primary and cyclic decomposition theorems along with the tightly related rational and jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.

UNLABELLED PCCA (phylogenetic canonical correlation analysis) is a new program for canonical correlation analysis of multivariate, continuously valued data from biological species. Canonical correlation analysis is a technique in which derived variables are obtained from two sets of original variables whereby the correlations between corresponding derived variables are maximized. It is a very u...

We consider the problem of planar spanning tree transformation in a two-dimensional plane. Given two planar trees T1 and T2 drawn on a set S of n points in general position in the plane, the problem is to transform T1 into T2 by a sequence of simple changes called edge-flips or just flips. A flip is an operation by which one edge e of a geometric object is removed and an edge f (f 6= e) is inse...

We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from kernel by generalized gauge transformation. The is Hermitian and static, while time-dependent transformation operator has to $PT$ symmetric non-unitary general. Biorthogonal sets of eigenstates appear necessarily as consequence Hamiltonian. obtain analytically wa...

The aim of this research work is to define and characterize a new class of n-ary multialgebra that may be called canonical (m, n)&minus hypermodules. These are a generalization of canonical n-ary hypergroups, that is a generalization of hypermodules in the sense of canonical and a subclasses of (m, n)&minusary hypermodules. In addition, three isomorphism theorems of module theory and canonical ...