Modeling and Exact Reliability for a Consecutive Linear (k1,k2,…,kn−r+1)-Out-of-r-from-n: F System and Consecutive Circular (k1,k2,…,kn)-Out-of-r-from-n: F System

2021 ◽  
pp. 2150029
Author(s):  
Y. Amirian ◽  
A. Khodadadi
Keyword(s):  
Linear System ◽  
Order Statistic ◽  
Failed State ◽  
Time Modeling ◽  
Linear Formula ◽  
State Formula ◽  
Extensive Class ◽  
Circular System ◽  
First Time ◽  
F System

The consecutive linear [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]:F system consists of [Formula: see text] linear ordered components and the consecutive circular [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]:F system consists of [Formula: see text] circular ordered components. In this paper, we suggest, for the first time, modeling and exact reliability for these models. The linear system fails if and only if there exists a [Formula: see text]-order statistic of [Formula: see text]-consecutive [Formula: see text] [Formula: see text] of components in the failed state, [Formula: see text], [Formula: see text]; and the circular system fails if and only if there exists a [Formula: see text]-order statistic of [Formula: see text]-consecutive [Formula: see text] [Formula: see text] of components in the failed state, [Formula: see text], [Formula: see text]. In this paper, we designed an innovative algorithm to obtain the exact reliability for an extensive class of consecutive linear and circular systems. In continuation, there are the MATLAB Programs of exact reliability for consecutive linear and circular systems. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.

scholarly journals Power-to-Syngas: A Parareal Optimal Control Approach

2021 ◽  
Vol 9 ◽  
Author(s):  
Andrea Maggi ◽  
Dominik Garmatter ◽  
Sebastian Sager ◽  
Martin Stoll ◽  
Kai Sundmacher
Keyword(s):  
Optimal Control ◽  
Water Gas Shift ◽  
Control Approach ◽  
Renewable Power ◽  
Reverse Water Gas Shift ◽  
Time Modeling ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint ◽  
Water Gas ◽  
First Time

A chemical plant layout for the production of syngas from renewable power, H2O and biogas, is presented to ensure a steady productivity of syngas with a constant H2-to-CO ratio under time-dependent electricity provision. An electrolyzer supplies H2 to the reverse water-gas shift reactor. The system compensates for a drop in electricity supply by gradually operating a tri-reforming reactor, fed with pure O2 directly from the electrolyzer or from an intermediate generic buffering device. After the introduction of modeling assumptions and governing equations, suitable reactor parameters are identified. Finally, two optimal control problems are investigated, where computationally expensive model evaluations are lifted viaparareal and necessary objective derivatives are calculated via the continuous adjoint method. For the first time, modeling, simulation, and optimal control are applied to a combination of the reverse water-gas shift and tri-reforming reactor, exploring a promising pathway in the conversion of renewable power into chemicals.

scholarly journals GLOBAL MONOPOLES AND SCALAR FIELDS AS THE ELECTROGRAVITY DUAL OF SCHWARZSCHILD SPACE–TIME

2001 ◽  
Vol 16 (18) ◽  
pp. 1193-1200 ◽  
Author(s):  
NARESH DADHICH ◽  
NARAYAN BANERJEE
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Scalar Fields ◽  
Flat Space ◽  
Space Time ◽  
Global Monopole ◽  
Schwarzschild Solution ◽  
State Formula ◽  
Global Monopoles ◽  
First Time

We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, [Formula: see text]. This property was however known for the global monopole space–time while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos–Zannias scalar field solution is dual to flat space.

The T Optimal Maintenance Time of Consecutive Linear k-out-of-r-from-n: F System and Consecutive Circular k-out-of-r-from-n: F System

2020 ◽  
pp. 2150008
Author(s):  
Y. Amirian ◽  
A. Khodadadi
Keyword(s):  
Real World ◽  
Preventive Maintenance ◽  
Corrective Maintenance ◽  
Integrated Strategy ◽  
Maintenance Time ◽  
Circular Component ◽  
Time Optimal ◽  
Optimal Maintenance ◽  
First Time ◽  
F System

A consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: [Formula: see text] system consists of [Formula: see text] linear (circular) ordered components such that the system fails if and only if there exist a set of [Formula: see text] consecutive linear (circular) component that contains at least [Formula: see text] failed components. The optimal maintenance of the consecutive [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: [Formula: see text] system to linear and circular states is investigated in this paper. First, an integrated strategy of corrective maintenance and preventive maintenance is introduced. Then, for first time, optimal maintenance has been applied to these systems, and optimum maintenance time has been achieved with this strategy. Also, real-world practical examples for this system have been presented.

scholarly journals Power-like potentials: From the Bohr–Sommerfeld energies to exact ones

2021 ◽  
Author(s):  
J. C. del Valle ◽  
Alexander V. Turbiner
Keyword(s):  
Quantum Number ◽  
Ground State ◽  
Analytic Form ◽  
Negative Parity ◽  
Quantization Condition ◽  
Linear Formula ◽  
Order Of Magnitude ◽  
Number Formula ◽  
The Right ◽  
First Time

For one-dimensional power-like potentials [Formula: see text], [Formula: see text], the Bohr–Sommerfeld energies (BSE) extracted explicitly from the Bohr–Sommerfeld quantization condition are compared with the exact energies. It is shown that for the ground state as well as for all positive parity states the BSE are always above the exact ones as opposed to the negative parity states where the BSE remain above the exact ones for [Formula: see text] but below them for [Formula: see text]. The ground state BSE as function of [Formula: see text] are of the same order of magnitude as the exact energies for linear [Formula: see text], quartic [Formula: see text] and sextic [Formula: see text] oscillators but their relative deviation grows with [Formula: see text], reaching the value 4 at [Formula: see text]. For physically important cases [Formula: see text], for the 100th excited state BSE coincide with exact ones in 5–6 figures. It is demonstrated that by modifying the right-hand side of the Bohr–Sommerfeld quantization condition by introducing the so-called WKB correction [Formula: see text] (coming from the sum of higher-order WKB terms taken at the exact energies or from the accurate boundary condition at turning points) to the so-called exact WKB condition one can reproduce the exact energies. It is shown that the WKB correction is a small, bounded function [Formula: see text] for all [Formula: see text]. It grows slowly with increasing [Formula: see text] for fixed quantum number [Formula: see text], while it decays with quantum number growth at fixed [Formula: see text]. It is the first time when for quartic and sextic oscillators the WKB correction and energy spectra (and eigenfunctions) are found in explicit analytic form with a relative accuracy of [Formula: see text] (and [Formula: see text]).

scholarly journals Multi-resolution Bayesian CMB component separation through Wiener filtering with a pseudo-inverse preconditioner

2019 ◽  
Vol 627 ◽  
pp. A98 ◽  
Author(s):  
D. S. Seljebotn ◽  
T. Bærland ◽  
H. K. Eriksen ◽  
K.-A. Mardal ◽  
I. K. Wehus
Keyword(s):  
Linear System ◽  
Computer Code ◽  
Coefficient Matrix ◽  
Component Separation ◽  
Wiener Filtering ◽  
Microwave Background ◽  
Data Set ◽  
Full Resolution ◽  
First Time ◽  
Pseudo Inverse

We present a Bayesian model for multi-resolution component separation for cosmic microwave background (CMB) applications based on Wiener filtering and/or computation of constrained realizations, extending a previously developed framework. We also develop an efficient solver for the corresponding linear system for the associated signal amplitudes. The core of this new solver is an efficient preconditioner based on the pseudo-inverse of the coefficient matrix of the linear system. In the full sky coverage case, the method gives an increased speed of the preconditioner, and it is easier to implement in terms of practical computer code. In the case where a mask is applied and prior-driven constrained realization is sought within the mask, this is the first time full convergence has been achieved at the full resolution of the Planck data set.

scholarly journals Pedagogical Giftedness as a Key Prerequisite for Efficient Modern Educational System

2019 ◽  
pp. 37-49
Author(s):  
Vladimir A. Mazilov ◽  
Yuriy N. Slepko
Keyword(s):  
Teacher Training ◽  
Professional Activity ◽  
Teaching Staff ◽  
Professional Activities ◽  
Functional Methods ◽  
Time Modeling ◽  
Study Results ◽  
Psychological Structure ◽  
Professional Self ◽  
First Time

Introduction. The paper represents the analysis of the ability to teach within the context of the study of the phenomenon of giftedness and psychological structure of a teacher’s professional activities. The objective of the paper is to analyze key areas of the development of the concept of teacher giftedness. This approach allows to describe the basic qualities of the efficient pedagogical activity at the stage of training teachers at higher school. Materials and Methods. Description of key areas of the concept of pedagogical giftedness is based on the ability theory, proposed by V. D. Shadrikov. At the same time, modeling processes of goal-oriented development of pedagogical giftedness is based on a set of modern research psychological methods of structuralfunctional analysis allowing for prediction of properties of the pedagogical system of a teacher, which has such characteristics as varying degrees of success. Organizational methods (first of all, comparative) open up possibilities for assessing the effectiveness of giftedness-in-training development at different stages of teacher training – pre-university, undergraduate and post-graduate. The choice of empirical methods is substantiated by the results of theoretically modeling the structure and ways of development of pedagogical giftedness at the stage of professional self-determination at school, under conditions of educational and independent professional activity. Out of interpretative methods, the most significant (in the context of planned results) are genetic, structural and functional methods . Results. Based on the analysis of the theory of abilities, taking into account the progress in the activitybased approach, a new understanding of the object of psychological sciences as the inner personal world, the methodological validity of the concept of goal-oriented development of pedagogical gift under conditions of teacher training is substantiated. The results obtained make it possible to get a fresh look at the problem of the teacher’s professionally valuable qualities and translate its solution from analytical to systemic research methodology. In the concept proposed by the authors first time ever, the phenomenon of giftedness is considered within the context of its formation in teacher college student, while the subject of the bulk of contemporary research is the object of pedagogical influence. Discussion and Conclusion. The practical application of the study results can significantly modernize the process of teacher training in pedagogical colleges and universities. They will be useful for the teaching staff of pedagogical universities, secondary vocational education institutions, and departments of continuing education.

scholarly journals Reliability and failure functions of some weighted systems

2017 ◽  
Vol 6 (1) ◽  
pp. 7 ◽  
Author(s):  
Imad Nashwan
Keyword(s):  
Failure State ◽  
Main Factors ◽  
Circular System ◽  
F System

In modern systems, not only the number and the position of the functioning or the failed components are the main factors that keep the system into the functioning state or transform it into failure state, but the contribution or the working probability of the component is also a very important one. This contribution is usually called the component weight. In this paper, the reliability and the failure functions of the consecutive weighted k-out-of-n: F linear and circular system, the weighted f-out-of-n: F system, the weighted  (n,f,k) linear and circular system and the weighted  linear and circular system are obtained.

Exact Reliability for a Consecutive Circular k-out-of-r-from-n: F System with Equal and Unequal Component Probabilities

2019 ◽  
Vol 27 (01) ◽  
pp. 2050003 ◽  
Author(s):  
Y. Amirian ◽  
A. Khodadadi ◽  
O. Chatrabgoun
Keyword(s):  
Closed Form ◽  
Reliability Analysis ◽  
Numerical Results ◽  
Innovative Program ◽  
Circular Component ◽  
Extensive Class ◽  
Exact Amount ◽  
F System

A consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F system consists of [Formula: see text] linear (circular)-ordered components such that the system fails if and only if there exists a set of [Formula: see text] consecutive linear (circular) component that contains at least [Formula: see text] failed components. Consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F systems attract tremendous attention for researchers of reliability analysis. Recent efforts in this area have focused on simple situations or approximation bands for their reliability but closed form and exact amount not gained. In this paper, we designed an innovative algorithm and an innovative program to obtain the exact reliability for an extensive class of consecutive circular [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F system with particular emphasis for equal and unequal component probabilities. Finally, we reviewed an applied example and applied comparative and numerical results and calculated the exact reliability of this strategic system.

Fragment of a Byzantine Musical Handbook in the Monastery of Laura on Mt. Athos

1913 ◽  
Vol 19 ◽  
pp. 95-117
Author(s):  
H. J. W. Tillyard
Keyword(s):  
Linear System ◽  
Thirteenth Century ◽  
Musical Notation ◽  
Single Leaf ◽  
First Time

The musical Notation of the Greek Church is decipherable as far back as the beginning of the Round System in the thirteenth century. Some examples of this were given in my article in last year's Annual. But before the invention of the Round System another kind of notation was in use, called for convenience the Linear System, the rules of which are very obscure. The reading of the Round System was made easy by the familiar little treatise called the Papadike, which occurs in many MSS., and explains the main principles of the notation. Nothing of the kind seems to have been known dealing with the Linear System. But the fragment which I am now to place before the reader may be expected to throw some light upon it. I photographed this fragment on my visit to the Monastery of Laura in 1912: and so far as I know, this is the first time that anything has been written about it.The fragment is a single leaf of parchment bound up with the MS. Laura Γ 67, a small quarto codex containing some of the Stichera of the Triodium and Pentescostarium, i.e. the original hymns (excluding Canons and words set to tunes not specially composed for them) sung at the movable days in Lent, Holy Week and Eastertide. The manuscript is written in a bold well-formed hand, the text in black, the notes in red.

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