Related papers: Small perturbations on means and quasi-means
We establish a framework for the study of the effective theory of weak convergence of measures. We define two effective notions of weak convergence of measures on $\mathbb{R}$: one uniform and one non-uniform. We show that these notions are…
Within the framework of the hypothesis offered by authors about a complex-valued nature of physical quantities the stability of basic equations of the classical physics concerning complex-valued perturbations of parameters and boundary…
The pervasive presence in space of a flux of high-speed, electrically uncharged dark matter particles is examined here for potential consequences. Dark matter interactions with ordinary matter are considered, and a model of the dark matter…
We introduce a notion of a weak elementary fibration and prove that it does exist in certain interesting cases. Our notion is a modification of the M. Artin's notion of an elementary fibration.
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs…
Quantum work fluctuation theorems are known to hold when the work is defined as the difference between the outcomes of projective measurements carried out on the Hamiltonian of the system at the initial and the final time instants of the…
Assuming a minimum value for area measurement, the emergence of quantum mechanics can be easily motivated from naive consideration of gravitational force. Here we provide some pedagogical examples and extensions. At the same time, the role…
Harmonic, Geometric, Arithmetic, Heronian and Contraharmonic means have been studied by many mathematicians. In 2003, H. Evens studied these means from geometrical point of view and established some of the inequalities between them in using…
We show how a metric space induces a linear functional (a "mean") on real-valued functions with domains in that metric space. This immediately induces a "relative" measure on a collection of subsets of the underlying set.
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to…
Weak measurements can provide a complete characterization of post-selected ensembles, including the uncertainties of observables. Interestingly, the average uncertainties for pure initial and final states are always zero, suggesting the…
The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a…
A recent Letter in Physical Review Letters, "Contextual Values of Observables in Quantum Measurements", by J. Dressel, S. Agarwal, and A. N. Jordan (abbreviated DAJ below), introduces the concept of "contextual values" and claims that they…
On the setting of positive definite operators we study the near-order properties of power means such as the quasi-arithmetic mean (H\"{o}lder mean) and R\'{e}nyi power mean. We see the monotonicity of spectral geometric mean and Wasserstein…
Reasoning about unpredicted change consists in explaining observations by events; we propose here an approach for explaining time-stamped observations by surprises, which are simple events consisting in the change of the truth value of a…
Quantum weak measurement, measuring some observable quantities within the selected subensemble of the entire quantum ensemble, can produce many interesting results such as the superluminal phenomena. An outcome of such a measurement is the…
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a…
We consider the mean value properties for finite variation measures with respect to a Markov operator in a discrete environnement. We prove equivalent conditions for the weak mean value property in the case of general Markov operators and…
In this article we redefine various poverty measures in literature in terms of quantile functions instead of distribution functions in the prevailing approach. This enables provision for alternative methodology for poverty measurement and…