Computer Tomography and Quantum Mechanics

1997 ◽  
Vol 29 (3) ◽  
pp. 595-606
Author(s):  
Lev B. Klebanov ◽  
Svetlozar T. Rachev
Keyword(s):  
Quantum Mechanics ◽  
Computer Tomography ◽  
Radon Transform ◽  
Stability Problem ◽  
Probability Distributions ◽  
New Approach ◽  
Wigner Distributions ◽  
Different Types ◽  
Tomographic Data ◽  
Mathematical Justification

In this paper we study some topics of interest to specialists in computer tomography. These are the following. (a) The Radon transform and its applications to computer tomography. (b) Problems of computer tomography with partially known data. Estimates of stability will be given for different types of distance in the space of probability distributions. We consider the problem with partially known tomographic data as a stability problem for appropriately chosen distances. This approach allows us to give a solution of the so-called computer tomography paradox. (c) The relation of quantum mechanics to computer tomography. An intriguing method for ‘measuring' wavefunctions by tomographic methods (CAT scans) opens a new approach to various problems in quantum mechanics. Using the method outlined for the solution of the computer tomography paradox, we derive inequalities that estimate the amount of information on the wavefunctions resulting from real CAT scans, i.e. CAT scans based on the finite number of measured marginals (projections) of the Wigner distributions. In conclusion, we propose a new version of the mathematical justification of CAT scans.

Computer Tomography and Quantum Mechanics

1997 ◽  
Vol 29 (03) ◽  
pp. 595-606
Author(s):  
Lev B. Klebanov ◽  
Svetlozar T. Rachev
Keyword(s):  
Quantum Mechanics ◽  
Computer Tomography ◽  
Radon Transform ◽  
Stability Problem ◽  
Probability Distributions ◽  
New Approach ◽  
Wigner Distributions ◽  
Different Types ◽  
Tomographic Data ◽  
Mathematical Justification

In this paper we study some topics of interest to specialists in computer tomography. These are the following. (a) The Radon transform and its applications to computer tomography. (b) Problems of computer tomography with partially known data. Estimates of stability will be given for different types of distance in the space of probability distributions. We consider the problem with partially known tomographic data as a stability problem for appropriately chosen distances. This approach allows us to give a solution of the so-called computer tomography paradox. (c) The relation of quantum mechanics to computer tomography. An intriguing method for ‘measuring' wavefunctions by tomographic methods (CAT scans) opens a new approach to various problems in quantum mechanics. Using the method outlined for the solution of the computer tomography paradox, we derive inequalities that estimate the amount of information on the wavefunctions resulting from real CAT scans, i.e. CAT scans based on the finite number of measured marginals (projections) of the Wigner distributions. In conclusion, we propose a new version of the mathematical justification of CAT scans.

scholarly journals “Artificial Wood” Lignocellulosic Membranes: Influence of Kraft Lignin on the Properties and Gas Transport in Tunicate-Based Nanocellulose Composites

Membranes ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 204
Author(s):  
Ievgen Pylypchuk ◽  
Roman Selyanchyn ◽  
Tetyana Budnyak ◽  
Yadong Zhao ◽  
Mikael Lindström ◽  
...  
Keyword(s):  
Knudsen Diffusion ◽  
Cellulose Nanofibers ◽  
Kraft Lignin ◽  
Separation Processes ◽  
New Approach ◽  
Future Studies ◽  
Different Types ◽  
Molecular Sizes ◽  
Fast Transport ◽  
Cellulose Membranes

Nanocellulose membranes based on tunicate-derived cellulose nanofibers, starch, and ~5% wood-derived lignin were investigated using three different types of lignin. The addition of lignin into cellulose membranes increased the specific surface area (from 5 to ~50 m2/g), however the fine porous geometry of the nanocellulose with characteristic pores below 10 nm in diameter remained similar for all membranes. The permeation of H2, CO2, N2, and O2 through the membranes was investigated and a characteristic Knudsen diffusion through the membranes was observed at a rate proportional to the inverse of their molecular sizes. Permeability values, however, varied significantly between samples containing different lignins, ranging from several to thousands of barrers (10−10 cm3 (STP) cm cm−2 s−1 cmHg−1cm), and were related to the observed morphology and lignin distribution inside the membranes. Additionally, the addition of ~5% lignin resulted in a significant increase in tensile strength from 3 GPa to ~6–7 GPa, but did not change thermal properties (glass transition or thermal stability). Overall, the combination of plant-derived lignin as a filler or binder in cellulose–starch composites with a sea-animal derived nanocellulose presents an interesting new approach for the fabrication of membranes from abundant bio-derived materials. Future studies should focus on the optimization of these types of membranes for the selective and fast transport of gases needed for a variety of industrial separation processes.

LOCAL ANALYSIS BY WAVELETS VERSUS NONLOCAL FOURIER ANALYSIS

2007 ◽  
Vol 05 (01n02) ◽  
pp. 89-95
Author(s):  
J. R. CROCA
Keyword(s):  
Quantum Mechanics ◽  
Fourier Analysis ◽  
Quantum Physics ◽  
Plane Waves ◽  
Local Analysis ◽  
Mathematical Tool ◽  
Space Harmonic ◽  
New Approach ◽  
Spatial Frequencies ◽  
Temporal And Spatial

Orthodox quantum mechanics has another implicit postulate stating that temporal and spatial frequencies of the Planck–Einstein and de Broglie formulas can only be linked with the infinite, in time and space, harmonic plane waves of Fourier analysis. From this assumption, nonlocality either in space and time follows directly. This is what is called Fourier Ontology. In order to build nonlinear causal and local quantum physics, it is necessary to reject Fourier ontology and accept that in certain cases a finite wave may have a well defined frequency. Now the mathematical tool to describe this new approach is wavelet local analysis. This more general nonlinear local and causal quantum physics, in the limit of the linear approximation, contains formally orthodox quantum mechanics as a particular case.

scholarly journals The Sum and Difference of Two Lognormal Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Stochastic Process ◽  
Probability Distributions ◽  
Operator Splitting ◽  
Splitting Method ◽  
Unified Approach ◽  
New Approach ◽  
Numerical Examples ◽  
Operator Splitting Method ◽  
Approximate Probability ◽  
Analytical Series

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum ofNlognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion.

scholarly journals An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

2021 ◽  
Vol 9 (10) ◽  
pp. 74-79
Author(s):  
Anurag Chapagain
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stability Problem ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Degree Of Stability ◽  
The Stability ◽  
Heisenberg's Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

scholarly journals Urban, industrial and technological risks. Synthesis of the elements of vulnerability of the city of Hassi-Messaoud

2020 ◽  
Vol 12 ◽  
Author(s):  
Lahcene Bouzouaid ◽  
Moussadek Benabbas
Keyword(s):  
Urban Space ◽  
Job Search ◽  
Population Distribution ◽  
Risk Assessments ◽  
Demographic Development ◽  
New Approach ◽  
Different Types ◽  
Specific Factors ◽  
The City

Abstract Today, Algeria is one of the developing countries that are engaging seriously into a new approach consisting of all kinds of combined risk assessments for better prevention them. Note that, this is a fairly important parameter, that is, the safety of people and property. However, the magnitude of the risk, of whatever nature, affects a variety of diversified aspects (Human, economic, technical and environmental). This study presented a case study, which is sometimes paradoxical, seeing that it is the result of the combination of all risk factors and specific factors related to them connected to a fragile urban environment: Hassi-Messaoud. It is well known that Hassi-Messaoud is one of the most important city for Algeria's economy; in which the demographic development is mainly known by incessant flows of immigrants, motivated essentially by job search. This arbitrary of population distribution exposes this city to a certain danger; especially as Hassi-Messaoud is in a zone subject to a probable risk expressed here by being characteristic of an oil zone. Thus, this article aimed to provide elements of risk assessment related to oil activity. This approach could conclude that, through a schematic scale, the different types and levels of exposure and vulnerability could be identified, that is, characteristics of the urban space in question.

scholarly journals Putting resilient sustainability into strategy decisions – case studies

2018 ◽  
Vol 56 (7) ◽  
pp. 1598-1612 ◽  
Author(s):  
Julie Winnard ◽  
Jacquetta Lee ◽  
David Skipp
Keyword(s):  
Case Studies ◽  
Real World ◽  
Design Methodology ◽  
Strategic Decision ◽  
New Approach ◽  
Content Type ◽  
Industrial Companies ◽  
Different Types ◽  
Strategic Decision Support ◽  
Practical Implications

Purpose The purpose of this paper is to report the results of testing a new approach to strategic sustainability and resilience – Sustainable Resilient Strategic Decision-Support (SuReSDS™). Design/methodology/approach The approach was developed and tested using action-research case studies at industrial companies. It successfully allowed the participants to capture different types of value affected by their choices, optimise each strategy’s resilience against different future scenarios and compare the results to find a “best” option. Findings SuReSDS™ enabled a novel integration of environmental and social sustainability into strategy by considering significant risks or opportunities for an enhanced group of stakeholders. It assisted users to identify and manage risks from different kinds of sustainability-related uncertainty by applying resilience techniques. Users incorporated insights into real-world strategies. Research limitations/implications Since the case studies and test organisations are limited in number, generalisation from the results is difficult and requires further research. Practical implications The approach enables companies to utilise in-house and external experts more effectively to develop sustainable and resilient strategies. Originality/value The research described develops theories linking sustainability and resilience for organisations, particularly for strategy, to provide a new consistent, rigorous and flexible approach for applying these theories. The approach has been tested successfully and benefited real-world strategy decisions.

scholarly journals Building SMARTER Communities of Resistance and Solidarity

2018 ◽  
Vol 10 (2) ◽  
pp. 99-118
Author(s):  
Andre Oboler ◽  
Karen Connelly
Keyword(s):  
Online Communities ◽  
Community Resilience ◽  
New Work ◽  
New Approach ◽  
Different Types ◽  
Future Work

The Cyber-Racism and Community Resilience (CRaCR) project included an examination into features of online communities of resistance and solidarity. This work formed a key part of the project’s focus on resilience and produced a deeper understanding of a range of types of actors working in this space and how they might individually contribute effectively to creating resilience. The need for new synergies between different types of stakeholders and approaches was highlighted as an area of future work. This paper explores a design for that future work that builds and supports online communities of resistance and solidarity by drawing on the lessons from the earlier research and extending them. This new work both presents a model for cooperation and explains how different stakeholders can positively engage under the model in a smarter way. That is, through a system which facilitates Solidarity in Moving Against Racism Together while Enabling Resilience. This new approach draws on the strengths of individuals actors, but also seeks to turn points of weakness for one actor into opportunities for cooperation that strengthen the system as a whole.

Sensor and Actuator Intrusion Detection for Cyber-Physical Systems via Adaptive Estimation Algorithm

2020 ◽  
Author(s):  
Jiayi Su ◽  
Yuqin Weng ◽  
Susan C. Schneider ◽  
Edwin E. Yaz
Keyword(s):  
Kalman Filters ◽  
Adaptive Estimation ◽  
Estimation Algorithm ◽  
Cyber Physical Systems ◽  
Motor Speed ◽  
New Approach ◽  
Physical Systems ◽  
Unknown Type ◽  
Different Types ◽  
Conditional State

Abstract In this work, a new approach to detect sensor and actuator intrusion for Cyber-Physical Systems using a bank of Kalman filters is presented. The case where the unknown type of the intrusion signal is considered first, using two Kalman filters in a bank to provide the conditional state estimates, then the unknown type of intrusion signal can be detected properly via the adaptive estimation algorithm. The case where the target (either sensor or actuator) of the intrusion signal is unknown is also considered, using four Kalman filters in a bank designed to detect if the intrusion signal is about to affect healthy sensor or actuator signal. To test these methods, a DC motor speed control system subject to attack by different types of sensor and actuator signals is simulated. Simulations show that different types of sensor and actuator intrusion signals can be detected properly without the knowledge of the nature and the type of these signals.

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