The p – q duality is a relation between the (p, q) model and the (q, p) model of two-dimensional quantum gravity. Geometrically this duality corresponds to a relation between the two relevant points of the Sato Grassmannian. Kharchev and Marshakov have expressed such a relation in terms of matrix integrals. Some explicit formulas for small p and q have been given in the work of Fukuma-Kawai-Nak...

highlighting the driving cause and its strict relationship with the formal cause and especially the final cause in the intrinsic elements of natural justice has caused the duality of reason and natural justice in the thinking of the proponents of the reason as the source. since the same emphasis makes the full understanding of the mechanisms of natural justice and its content for the human wisd...

ABSTRACT This paper provides a short introduction to the Lagrangian duality in convex optimization. At first the topic is motivated by outlining the importance of convex optimization. After that mathematical optimization classes such as convex, linear and non-convex optimization, are defined. Later the Lagrangian duality is introduced. Weak and strong duality are explained and optimality condit...

Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. Weextend Fourier-Motzkin elimination to semi-infinite linear programs which are linear programswith finitely many variables and infinitely many constraints. Applying projection leads to newcharacterizations of important properties for primal-dual pairs of semi-infinite programs suchas zero ...

We recast the phenomenon of duality cascades in terms of the Cartan matrix associated to the quiver gauge theories appearing in the cascade. In this language, Seiberg dualities for the different gauge factors correspond to Weyl reflections. We argue that the UV behavior of different duality cascades depends markedly on whether the Cartan matrix is affine ADE or not. In particular, we find examp...