The Liquid Drop Models (LDM) and the Independent Particle Models (IPM) have been known to provide two conflicting pictures of the nucleus. The IPM being quantum mechanical, is believed to provide a fundamental picture of the nucleus and hence has been focus of the still elusive unified theory of the nucleus. It is believed that the LDM at best is an effective and limited model of the nucleus. H...

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

Maxwell’s equations represent a culmination of classical mathematical physics by offering a compact mathematical formulation of all of electromagnetics including the propagation of light and radiation, as electromagnetic waves. But like in a Greek tragedy, the success of Maxwell’s equations prepared for the collapse of classical mathematical physics and the rise of modern physics based on a con...

This note briefly reviews the Mirror Principle as developed in the series of papers [19][20][21][22][23]. We illustrate this theory with a few new examples. One of them gives an intriguing connection to a problem of counting holomorphic disks and annuli. This note has been submitted for the proceedings of the Workshop on Strings, Duality and Geometry the C.R.M. in Montreal of March 2000.

A single mathematical theme underpins disparate physical phenomena in classical, quantum and statistical mechanical contexts. This mathematical “correspondence principle”, a kind of wave–particle duality with glorious realizations in classical and modern mathematical analysis, embodies fundamental geometrical and physical order, and yet in some sense sits on the edge of chaos. Illustrative case...

This paper presents a generalization of the minimax state estimation approach for singular linear Differential-Algebraic Equations (DAE) with uncertain but bounded input and observation’s noise. We apply generalized Kalman Duality principle to DAE in order to represent the minimax estimate as a solution of a dual control problem for adjoint DAE. The latter is then solved converting the adjoint ...

Uncertainty theory is a branch of axiomatic mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. And uncertain variable is a fundamental concept in uncertainty theory which is used to represent imprecise quantities. This paper proposes a definition of quadratic entropy to characterize the uncertainty of uncertain variables resulting fr...

In this paper we introduce a new method for manufacturing complex valued harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Riemannian Lie groups SO(n), SU(n), Sp(n). We then develop a duality principle and show how this can be used to construct the first known examples of harmonic mor-phisms from the non-compact semi-Riemanni...

In some recent theories including Quantum SuperString theory we encounter duality-it arises due to a non commutative geometry which in effect adds an extra term to the Heiserberg Uncertainity Principle. The result is that the micro world and the macro universe seem to be linked. We show why this is so in the context of a recent cosmological model and a physical picture emerges in the context of...

In this paper, first we extend the known definition of cross-ratio of collinear points to whole Moufang plane. Later we introduce the cross-ratios for lines and the known results about the cross-ratios of points which are adapted to crossratios of lines without using the principle of duality. Finally, we give a theorem which describes the relation between the cross-ratios of points and lines. M...