Distribution of x ⋅ p for quantum states on a circle

We first give the proper definition of the particle's position-momentum dot product, the so-called posmomx ⋅ p, to quantum states on a circular circle, in which the momentum turns out to be the geometric one that is recently intensively studied. Second, we carry out the posmom distributions for eigenstates of the free motion on the circle, i.e. [Formula: see text], (m = 0, ±1, ±2, …). The results are not only potentially experimentally testable, but also reflect a fact that the embedding of the circle S1 in two-dimensional flat space R2 is physically reasonable.

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On the Application of the Generalized Means to Construct Multiresolution Schemes Satisfying Certain Inequalities Proving Stability

Mathematics ◽

10.3390/math9050533 ◽

2021 ◽

Vol 9 (5) ◽

pp. 533

Author(s):

Sergio Amat ◽

Alberto Magreñan ◽

Juan Ruiz ◽

Juan Carlos Trillo ◽

Dionisio F. Yañez

Keyword(s):

Numerical Experiments ◽

Order Of Approximation ◽

Two Dimensional ◽

Nonlinear Subdivision ◽

Proper Definition ◽

The Stability ◽

Definition Of ◽

Stability Issues ◽

Multiresolution Schemes ◽

Theoretical Results

Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence of discontinuities, and having the maximum possible order of approximation in smooth areas. Once we have these nonlinear reconstruction operators defined, we can build the related nonlinear subdivision and multiresolution schemes and prove more accurate inequalities regarding the contractivity of the scheme for the first differences and in turn the results about stability. In this paper, we also define a new nonlinear two-dimensional multiresolution scheme as non-separable, i.e., not based on tensor product. We then present the study of the stability issues for the scheme and numerical experiments reinforcing the proven theoretical results and showing the usefulness of the algorithm.

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Introductory paper

Symposium - International Astronomical Union ◽

10.1017/s0074180900053031 ◽

1966 ◽

Vol 24 ◽

pp. 3-5

Author(s):

W. W. Morgan

Keyword(s):

Line Intensity ◽

Classification Scheme ◽

Two Dimensional ◽

Spectral Classification ◽

Dimensional Array ◽

Rr Lyrae ◽

Metallic Line ◽

Introductory Paper ◽

Parameter Varying ◽

Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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Simultaneous heat and mass transfer during evaporation from a film of liquid into the turbulent gas

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19820766 ◽

1982 ◽

Vol 47 (3) ◽

pp. 766-775 ◽

Cited By ~ 2

Author(s):

Václav Kolář ◽

Jan Červenka

Keyword(s):

Experimental Data ◽

Mass Transfer ◽

Liquid Film ◽

Heat And Mass Transfer ◽

Driving Forces ◽

Proper Definition ◽

Definition Of ◽

Simultaneous Heat ◽

Theory And Experiment

The paper presents results obtained by processing a series of published experimental data on heat and mass transfer during evaporation of pure liquids from the free board of a liquid film into the turbulent gas phone. The data has been processed on the basis of the earlier theory of mechanism of heat and mass transfer. In spite of the fact that this process exhibits a strong Stefan's flow, the results indicate that with a proper definition of the driving forces the agreement between theory and experiment is very good.

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Multi-objective parametrization of interatomic potentials for large deformation pathways and fracture of two-dimensional materials

npj Computational Materials ◽

10.1038/s41524-021-00573-x ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Xu Zhang ◽

Hoang Nguyen ◽

Jeffrey T. Paci ◽

Subramanian K. R. S. Sankaranarayanan ◽

Jose L. Mendoza-Cortes ◽

...

Keyword(s):

Large Deformation ◽

Functional Form ◽

Principal Component ◽

Interatomic Potentials ◽

Two Dimensional ◽

Multi Objective ◽

Multi Objective Genetic Algorithm ◽

Two Dimensional Materials ◽

Definition Of

AbstractThis investigation presents a generally applicable framework for parameterizing interatomic potentials to accurately capture large deformation pathways. It incorporates a multi-objective genetic algorithm, training and screening property sets, and correlation and principal component analyses. The framework enables iterative definition of properties in the training and screening sets, guided by correlation relationships between properties, aiming to achieve optimal parametrizations for properties of interest. Specifically, the performance of increasingly complex potentials, Buckingham, Stillinger-Weber, Tersoff, and modified reactive empirical bond-order potentials are compared. Using MoSe2 as a case study, we demonstrate good reproducibility of training/screening properties and superior transferability. For MoSe2, the best performance is achieved using the Tersoff potential, which is ascribed to its apparent higher flexibility embedded in its functional form. These results should facilitate the selection and parametrization of interatomic potentials for exploring mechanical and phononic properties of a large library of two-dimensional and bulk materials.

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Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

Journal of High Energy Physics ◽

10.1007/jhep04(2021)030 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Clifford V. Johnson ◽

Felipe Rosso

Keyword(s):

Phase Structure ◽

Scalar Potential ◽

String Equation ◽

Two Dimensional ◽

Leading Order ◽

Classical Analysis ◽

First Order ◽

First Order Phase Transition ◽

Definition Of ◽

First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

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Bra-ket wormholes in gravitationally prepared states

Journal of High Energy Physics ◽

10.1007/jhep02(2021)009 ◽

2021 ◽

Vol 2021 (2) ◽

Cited By ~ 3

Author(s):

Yiming Chen ◽

Victor Gorbenko ◽

Juan Maldacena

Keyword(s):

Hyperbolic Space ◽

Path Integral ◽

Flat Space ◽

Low Energy ◽

Two Dimensional ◽

De Sitter ◽

Euclidean Case ◽

Fine Grained ◽

Entropy Formula ◽

First Case

Abstract We consider two dimensional CFT states that are produced by a gravitational path integral.As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology.As a second case, we consider a state produced by Lorentzian dS2 evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.

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WoCoVA consensus on the clinical use of in-line filtration during intravenous infusions: Current evidence and recommendations for future research

The Journal of Vascular Access ◽

10.1177/1129729821989165 ◽

2021 ◽

pp. 112972982198916

Author(s):

Ton Van Boxtel ◽

Mauro Pittiruti ◽

Annemarie Arkema ◽

Patrick Ball ◽

Giovanni Barone ◽

...

Keyword(s):

Potential Benefit ◽

Scientific Evidence ◽

Venous Access ◽

Current Evidence ◽

Future Research ◽

Global Awareness ◽

Current State ◽

Intravenous Infusions ◽

Proper Definition ◽

Definition Of

The need for filtering intravenous infusions has long been recognized in the field of venous access, though hard scientific evidence about the actual indications for in-line filters has been scarce. In the last few years, several papers and a few clinical studies have raised again this issue, suggesting that the time has come for a proper definition of the type of filtration, of its potential benefit, and of its proper indications in clinical practice. The WoCoVA Foundation, whose goal is to increase the global awareness on the risk of intravenous access and on patients’ safety, developed the project of a consensus on intravenous filtration. A panel of experts in different aspects of intravenous infusion was chosen to express the current state of knowledge about filtration and to indicate the direction of future research in this field. The present document reports the final conclusions of the panel.

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Artificially making Lifeform

International Journal for Research in Applied Science and Engineering Technology ◽

10.22214/ijraset.2021.38466 ◽

2021 ◽

Vol 9 (10) ◽

pp. 1290-1295

Author(s):

Souvik Das

Keyword(s):

Medical Community ◽

Programming Algorithm ◽

The Public ◽

For Profit ◽

Not For Profit ◽

Funding Agencies ◽

Proper Definition ◽

Inanimate Matter ◽

Living Organisms ◽

Definition Of

Abstract: The word ‘life’ is a mysterious word with a chart of attributes that have neither been completed nor has been agreed upon by the race of humans. Probably the proper definition of life is impossible to identify for humans (the proof for this claim is given later) but the handbook to the secret shall be updated till the end, thanks to the inquisitive attitude of humans. For this piece, we shall adopt the description from the professional medical community of today. Though this topic falls midway between science and philosophy, this project is strictly technical. To quote dictionary.com, Life is the condition that distinguishes organisms from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction and the power of adaptation to environment- through changes originating internally; cambridge.com teaches Life is the period between birth and death, or the experience or state of being alive; medicaldictionary.thefreedictionary.com states Life is the property or quality that distinguishes living organisms from dead organisms and inanimate matter, manifested in functions such as metabolism, growth, reproduction and response to stimuli or adaptation to the environment originating from within the organisms. There are several other definitions but to summarize, we can safely state that though the concept is somewhat vague, we could indeed point out some common principles. We shall, in this project, try to replicate the characteristics so as to attain life in medical terms. (The order does not base upon importance of the listed character since the characters, all of them are absolute essentials and cannot possibly be categorized as more or less important). 1) Metabolism 2) Growth 3) Adaptability 4) Birth 5) Death 6) Self-stimulated response to environment 7) Reproduction 8) Can sustain self without foreign intervention Keywords: artificial, life, intelligence, computer, programming, algorithm This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Discriminating intra-parasequence stratigraphic units from two-dimensional quantitative parameters

Journal of Sedimentary Research ◽

10.2110/jsr.2020.203 ◽

2021 ◽

Vol 91 (8) ◽

pp. 887-911

Author(s):

Manuel F. Isla ◽

Ernesto Schwarz ◽

Gonzalo D. Veiga ◽

Jerónimo J. Zuazo ◽

Mariano N. Remirez

Keyword(s):

High Frequency ◽

Two Dimensional ◽

Facies Associations ◽

Different Types ◽

Lateral Extent ◽

Successive Wave ◽

Shell Bed ◽

Definition Of ◽

High Resolution Sequence Stratigraphy ◽

Bounding Surfaces

ABSTRACT The intra-parasequence scale is still relatively unexplored territory in high-resolution sequence stratigraphy. The analysis of internal genetic units of parasequences has commonly been simplified to the definition of bedsets. Such simplification is insufficient to cover the complexity involved in the building of individual parasequences. Different types of intra-parasequence units have been previously identified and characterized in successive wave-dominated shoreface–shelf parasequences in the Lower Cretaceous Pilmatué Member of the Agrio Formation in central Neuquén Basin. Sedimentary and stratigraphic attributes such as the number of intra-parasequence units, their thickness, the proportions of facies associations in the regressive interval, the lateral extent of bounding surfaces, the degree of deepening recorded across these boundaries, and the type and lateral extent of associated transgressive deposits are quantitatively analyzed in this paper. Based on the analysis of these quantified attributes, three different scales of genetic units in parasequences are identified. 1) Bedset complexes are 10–40 m thick, basin to upper-shoreface successions, bounded by 5 to 16 km-long surfaces with a degree of deepening of one to three facies belts. These stratigraphic units represent the highest hierarchy of intra-parasequence stratigraphic units, and the vertical stacking of two or three of them typically forms an individual parasequence. 2) Bedsets are 2–20 m thick, offshore to upper-shoreface successions, bounded by up to 10 km long surfaces with a degree of deepening of zero to one facies belt. Two or three bedsets stack vertically build a bedset complex. 3) Sub-bedsets are 0.5–5 m thick, offshore transition to upper-shoreface successions, bounded by 0.5 to 2 km long surfaces with a degree of deepening of zero to one facies belt. Two or three sub-bedsets commonly stack to form bedsets. The proposed methodology indicates that the combination of thickness with the proportion of facies associations in the regressive interval of stratigraphic units can be used to discriminate between bedsets and sub-bedsets, whereas for higher ranks (bedsets and bedset complexes) the degree of deepening, lateral extent of bounding surfaces, and the characteristics of associated shell-bed deposits become more effective. Finally, the results for the Pilmatué Member are compared with other ancient and Holocene examples to improve understanding of the high-frequency evolution of wave-dominated shoreface–shelf systems.

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