If m is Haar measure in G (normalized so that m(G) = 1) we consider the set function m'{E) = m{E). (E is the set of all x, # £ £ . ) Since m is a measure on G possessing all defining properties of m it follows from the uniqueness of Haar measure that ?n'(E) =m(E) for every measurable set E. In other words a is a measure preserving transformation of G; the purpose of this note is to investigate ...

Global change affects vegetation cover and processes through multiple pathways. Long 1 time series of surface land surface properties derived from satellite remote sensing give unique 2 abilities to observe these changes, particularly in areas with complex topography and limited research 3 infrastructure. Here, we focus on Nepal, a biodiversity hotspot where vegetation productivity is 4 limited...

In a concurrent logic language, mapping from the objects in a programmer's mind to actual processes and messages often results in less-than-optimum performance. One reason for this is that an incorrect prediction of the dynamic behavior and the resulting irrelevant mapping make the execution threads short and thus result in frequent suspensions. Also, good performance may be less important than...

In this paper we establish necessary and sufficient condition for zero duality gap of the optimization problem involving general perturbation mapping via characteringsetunder convex setting. An application to class composite problems will also be given show that our results can applied various classes problems.

This is the last in a series of papers in which we generalized the Tannaka-Krein duality to compact groupoids. In [A1] we studied the representation theory of compact groupoids. In particular, we showed that irreducible representations have finite dimensional fibres. We also proved the Schur’s lemma, Gelfand-Raikov theorem and Peter-Weyl theorem for compact groupoids. In [A2] we studied the Fou...

Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, offer numerous advantages for study many-body In this work, we suggest a method which introduces them world simulation too: feasible scheme implementing duality as operations, mapping...

Among the significant philosophical issues raised by the central role of physical dualities in recent fundamental research, one has a specific ontological flavor, as it concerns ‘dual entities’, i.e. entities exchanged by a duality mapping between theories. In particular, the type of duality that is known as weak/strong duality, or S-duality according to current terminology, seems to imply new ...

Borwein’s norm duality theorem establishes the equality between the outer (inner) norm of a sublinear mapping and the inner (outer) norm of its adjoint mappings. In this note we provide an extended version of this theorem with a new and self-contained proof relying only on the Hahn-Banach theorem. We also give examples showing that the assumptions of the theorem cannot be relaxed.

We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes to multiples of Schubert classes. This can be stated as a strange duality property for the Gromov-Witten invariants, which turn out to be very symmetric.