1,050 research outputs found
Use and misuse of variances for quantum systems in pure or mixed states
As a consequence of the place ascribed to measurements in the postulates of
quantum mechanics, if two differently prepared systems are described with the
same density operator \r{ho}, they are said to be in the same quantum state.
For more than fifty years, there has been a lack of consensus about this
postulate. In a 2011 paper, considering variances of spin components, Fratini
and Hayrapetyan tried to show that this postulate is unjustified. The aim of
the present paper is to discuss major points in this 2011 article, and in their
reply to a 2012 paper by Bodor and Diosi claiming that their analysis was
irrelevant. Facing some ambiguities or inconsistencies in the 2011 paper and in
the reply, we first try to guess their aim, then establish results useful in
this context, and finally discuss the use or misuse of several concepts implied
in this debate
Schauder bases under uniform renormings
[EN] Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone.First author supported by the grants MTM2005-08379 of MECD (Spain), 00690/PI/04 of Fundación Séneca (CARM, Spain) and AP2003-4453 of MECD (Spain), Second author supported by AV0Z10190503 and A100190502.Guirao Sánchez, AJ.; Hajek, P. (2007). Schauder bases under uniform renormings. Positivity. 11(4):627-638. https://doi.org/10.1007/s11117-007-2067-9S627638114R. Deville, G. Godefroy, V. Zizler, Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys 64, Longman Ed (1993).M. Fabian, P. Habala, P. Hájek, V. Montesinos, J. Pelant, V. Zizler, Functional analysis and infinite dimensional geometry. Canadian Math. Soc. Books, Springer Verlag, (2001).M. Fabian, V. Montesinos, V. Zizler, Smoothness in Banach spaces. Selected problems. Rev. R. Acad. Cien. Serie A Mat. 100, (2006), 101–125.T. Figiel, On the moduli of convexity and smoothness. Studia Math. 56, (1976), 121–155.M. Zippin, A remark on bases and reflexivity in Banach spaces. Isr. J. Math. 6, (1968), 74–79.P. Enflo, Banach spaces which can be given an equivalent uniformly convex norm. Isr. J. Math 13, (1972), 281–288
Moral and imoral in economical quantification
Could there be something immoral in economic measurements and quantification? Could there be immorality in statistics? It is often said that statistics is a lie, an untruth,a delusion. Lies are dishonoring and deeply immoral, and are incriminated by both religious and juridical norms. Where do these accusations against statistics come from? They derive from the obvious modern strive for excessive simplifications, from ignoring scientific rigor and from eluding theoretical principles by narrow pragmatic solutions. What is the critical point that shifts to economic thinking? In measurement: the formula. Who released it? Where and when was it released? By whom, where, when and how is it used? In quantification: aggregation and data systematization. We systemize and process data without asking ourselves how much of the economic and social content that we are studying remains in the shapes that we have built.quantifications; simplifications; formula; misinformation; delusion;
Introduction : création(s) et réception(s) de Patrick Deville
Einleitung des Beihefts „Création(s) et réception(s) de Patrick Deville“</strong
The memory space: Exploring future uses of Web 2.0 and mobile internet through design interventions.
The QuVis Quantum Mechanics Visualization project aims to address challenges
of quantum mechanics instruction through the development of interactive
simulations for the learning and teaching of quantum mechanics. In this
article, we describe evaluation of simulations focusing on two-level systems
developed as part of the Institute of Physics Quantum Physics resources.
Simulations are research-based and have been iteratively refined using student
feedback in individual observation sessions and in-class trials. We give
evidence that these simulations are helping students learn quantum mechanics
concepts at both the introductory and advanced undergraduate level, and that
students perceive simulations to be beneficial to their learning.Comment: 15 pages, 5 figures, 1 table; accepted for publication in the
American Journal of Physic
- …