A discussion of wave-particle duality can be found in all modern textbooks dealing with theories of chemical structure and bonding (I). Almost all of these contain some summary of the experimental evidence in favor of such duality, which comes from studies of the physics of electromagnetic radiation (ohotons vs. waves) and "elementarv" oarticles ,. . such as electrons, protons, neutrons, etc. U...

Very recently, Gudder has given the mathematical theory for the duality computer [1]. In his timely work, he has provided two descriptions, one is in the pure state formalism and the other is in the mixed state formalism for the mathematics of duality computer. The duality computer is a new type of computing machine based on the general principle of quantum interference proposed in Ref.[2]. Not...

A duality theorem is proved for problems of optimal control of linear dynamical systems in continuous time subject to linear constraints and convex costs, such as penalties. Optimality conditions are stated in terms of a “minimaximum principle” in which the primal and dual control vectors satisfy a saddle point condition at almost every instant of time. This principle is shown to be equivalent ...

A recent concept in theoretical physics, motivated in string duality and M–theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. In view of these developments, we analyse some general properties that quantum mechanics must satisfy, if it is not to be formulated as a quantisation o...

This paper studies efficient risk-sharing rules for the concave dominance order. For a univariate risk, it follows from a comonotone dominance principle, due to Landsberger and Meilijson [27], that efficiency is characterized by a comonotonicity condition. The goal of the paper is to generalize the comonotone dominance principle as well as the equivalence between efficiency and comonotonicity t...

Recently the multitude of vacua in string theory have led some authors to advocate the anthropic principle as a possible resolution for the contrived set of parameters that seem to govern our universe. I suggest that string theories should be viewed as effective theories, and hence of limited utility rather than as “theories of everything”. I propose that quantum gravity should admit a form of ...

This paper reports a new reading for wavelets, which is based on the classical ’De Broglie’ principle. The waveparticle duality principle is adapted to wavelets. Every continuous basic wavelet is associated with a proper probability density, allowing defining the Shannon entropy of a wavelet. Further entropy definitions are considered, such as Jumarie or Renyi entropy of wavelets. We proved tha...

Mach’s principle is the concept that inertial frames are determined by matter. We propose and implement a precise formulation of Mach’s principle in which matter and geometry are in one-to-one correspondence. Einstein’s equations are not modified and no selection principle is applied to their solutions; Mach’s principle is realized wholly within Einstein’s general theory of relativity. The key ...

The possibility of reconciliation between canonical probability distributions obtained from the q-maximum entropy principle with predictions from the law of large numbers when empirical samples are held to the same constraints, is investigated into. Canonical probability distributions are constrained by both: (i) the additive duality of generalized statistics and (ii) normal averages expectatio...

Very recently, Gudder has given the mathematical theory for the duality computer [1]. In his timely work, he has provided two descriptions, one is in the pure state formalism and the other is in the mixed state formalism for the mathematics of duality computer. The duality computer is a new type of computing machine based on the general principle of quantum interference proposed in Ref.[2]. Not...