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2021 ◽  
pp. 1-34
Author(s):  
Jannik Dreier ◽  
Jean-Guillaume Dumas ◽  
Pascal Lafourcade ◽  
Léo Robert

In 1968, Liu described the problem of securing documents in a shared secret project. In an example, at least six out of eleven participating scientists need to be present to open the lock securing the secret documents. Shamir proposed a mathematical solution to this physical problem in 1979, by designing an efficient k-out-of-n secret sharing scheme based on Lagrange’s interpolation. Liu and Shamir also claimed that the minimal solution using physical locks is clearly impractical and exponential in the number of participants. In this paper we relax some implicit assumptions in their claim and propose an optimal physical solution to the problem of Liu that uses physical padlocks, but the number of padlocks is not greater than the number of participants. Then, we show that no device can do better for k-out-of-n threshold padlock systems as soon as k ⩾ 2 n , which holds true in particular for Liu’s example. More generally, we derive bounds required to implement any threshold system and prove a lower bound of O ( log ( n ) ) padlocks for any threshold larger than 2. For instance we propose an optimal scheme reaching that bound for 2-out-of-n threshold systems and requiring less than 2 log 2 ( n ) padlocks. We also discuss more complex access structures, a wrapping technique, and other sublinear realizations like an algorithm to generate 3-out-of-n systems with 2.5 n padlocks. Finally we give an algorithm building k-out-of-n threshold padlock systems with only O ( log ( n ) k − 1 ) padlocks. Apart from the physical world, our results also show that it is possible to implement secret sharing over small fields.


Abstract In the first and second chapter the article provides an overview of the currently used energy sources in Hungary and the most popular renewable energies. In addition, the Weibull estimation is presented, too. The subsequent chapter looks at some of the research results about the solar energy optimization with Weibull distribution. The study presented is a mathematical solution of the solar energy optimization with distribution. The final chapter contains a brief explanation of the results. This publication briefly summarizes a prototype solution for an estimation and forecast of solar energy and yield with Weibull distribution.


2021 ◽  
pp. 1-28
Author(s):  
Jesse Lopes ◽  
Chris Byron

Abstract We argue in this article that Marx’s scientific method coupled with his analysis of the phenomenological consciousness of agents trapped within the capitalist mode of production provides a sufficient solution to the transformation problem. That is, Marx needs no amending – mathematical, philosophical, or otherwise – and the tools he uses to demonstrate and resolve the problem – science and phenomenology – were already clearly spelled out in his texts. Critics of Marx either fail to understand his scientific method, or are themselves trapped within a non-scientific capitalist phenomenology. Similarly, Marxists that mathematically resolve the transformation problem fail to realise that Marx’s scientific analysis alone demonstrates that a mathematical solution to the transformation problem is a misapprehension of the relation between Marx’s abstract theory and concrete phenomena. Consequently, we also criticise the monetary theorists who try to dismiss the problem as pointless by claiming that Marx was not a pre-monetary theorist.


Philosophies ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 96
Author(s):  
Maria Antonietta Salamone

In this article, I interpret Book V of the Nicomachean Ethics in which Aristotle presents a geometrical problem to explain which is the Best Criterion for the Distribution of Political and Economic Rights and Duties among Citizens, starting from the empirical evidence that there are three opposing opinions on which is the fairest distribution criterion: for some it is Freedom (Democrats), for others Wealth (Oligarchs), and for others Virtue (Aristocrats). Against the almost unique and most quoted interpretation of the geometrical problem, I present my mathematical solution, which I arrived at thanks to the Doctrine of the Four Causes and the Theory of the Mean. My thesis is that the Mean Term of Distributive Justice is the Golden Ratio between the opposite criteria of distribution, and the unjust distribution is the one that violates this ratio. This solution allows us to understand what is the Rational Principle at the basis of just distribution: that is, Geometrical Equality as opposed to Arithmetical Equality. Indeed, by applying the geometric figure of the Golden Triangle to the different political constitutions, I show, in line with Politics, that the Best Form of Government is the Aristocratic Politeia, i.e., a mixture of Democracy, Oligarchy and Aristocracy.


2021 ◽  
Vol 48 (2) ◽  
Author(s):  
Nicolás Oliveras

Measuring the carbon dioxide (CO2) mass flux in a volcanic environment is necessary for volcanic monitoring. CO2 mass flux must be measured continuously and telemetrically to get, almost in real-time, a better understanding of the dynamics of the volcanic degassing processes, contributing to the building, together with other monitoring technics, of a volcano behavior model. This study presents two analytical solutions, 1) a simple diffuse solution and 2) an advective-diffusive solution, which both implement NDIR (Non-Dispersive Infrared Emitter) sensor arrays in an open chamber (diffusion chimney) and an exchange chamber (gas interchanger). The first system, for which the gas speed is negligible, despite being basic (with values reflected in the slope of an equation line), introduces mass flux calculations with a single sensor NDIR. For the second system, where the gas speed is part of the equation, another mathematical solution and three measuring points are required, which demands the system to include a se­cond NDIR sensor for the correct mathematical solution of the equations system. In addition, an embedded system can automate the method by calibrating, controlling an agitation fan, and recording temperature, pressure, and mass flux in volcanic soils at the surface. Since this theoretically proposed method needs to be tested, experimental data are expected to validate the measurement of CO2 mass flux, which will be used as a helpful tool for volcanic monitoring.


Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1865
Author(s):  
Daniel Caballero-Julia ◽  
Philippe Campillo

In the era of big data, the capacity to produce textual documents is increasing day by day. Our ability to generate large amounts of information has impacted our lives at both the individual and societal levels. Science has not escaped this evolution either, and it is often difficult to quickly and reliably “stand on the shoulders of giants”. Text mining is presented as a promising mathematical solution. However, it has not yet convinced qualitative analysts who are usually wary of mathematical calculation. For this reason, this article proposes to rethink the epistemological principles of text mining, by returning to the qualitative analysis of its meaning and structure. It presents alternatives, applicable to the process of constructing lexical matrices for the analysis of a complex textual corpus. At the same time, the need for new multivariate algorithms capable of integrating these principles is discussed. We take a practical example in the use of text mining, by means of Multivariate Analysis of Variance Biplot (MANOVA-Biplot) when carrying out a systematic review of the literature. The article will show the advantages and disadvantages of exploring and analyzing a large set of publications quickly and methodically.


2021 ◽  
Author(s):  
Lingfei Zeng ◽  
Hongmei Zhang ◽  
Zhipeng Lai ◽  
Yuesong Chen

Author(s):  
Cao Wang

AbstractThe performance of civil infrastructure systems is vital in supporting a community’s functionalities. Reliability assessment of these systems is a powerful approach to evaluate whether the system performance is desirably safe under the impacts of resistance degradation and non-stationary loads. A k-out-of-n system is a widely-used logic model for a system with n components, which survives (works) if at least k components work. Its special cases include a series or a parallel system. Furthermore, a weighted k-out-of-n system has components with positive integer weights and the system survives if the total weight of working components reaches the predefined threshold k. This paper proposes a method for estimating the time-dependent reliability of both ordinary and weighted k-out-of-n systems, taking into account the effects of resistance deterioration, resistance correlation and load non-stationarity, for which a mathematical solution is derived. The applicability of the proposed method is illustrated through reliability evaluation of a representative k-out-of-n system.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Xinran Zheng ◽  
Mingqi Huang ◽  
Dongqi An ◽  
Chao Zhou ◽  
Rui Li

AbstractNew analytic bending, buckling, and free vibration solutions of rectangular nanoplates with combinations of clamped and simply supported edges are obtained by an up-to-date symplectic superposition method. The problems are reformulated in the Hamiltonian system and symplectic space, where the mathematical solution framework involves the construction of symplectic eigenvalue problems and symplectic eigen expansion. The analytic symplectic solutions are derived for several elaborated fundamental subproblems, the superposition of which yields the final analytic solutions. Besides Lévy-type solutions, non-Lévy-type solutions are also obtained, which cannot be achieved by conventional analytic methods. Comprehensive numerical results can provide benchmarks for other solution methods.


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