Application of symmetric analytic functions to spectra of linear operators

The paper is devoted to extension of the theory of symmetric analytic functions on Banach sequence spaces to the spaces of nuclear and $p$-nuclear operators on the Hilbert space. We introduced algebras of symmetric polynomials and analytic functions on spaces of $p$-nuclear operators, described algebraic bases of such algebras and found some connection with the Fredholm determinant of a nuclear operator. In addition, we considered cases of compact and bounded normal operators on the Hilbert space and discussed structures of symmetric polynomials on corresponding spaces.

Biosignal-Based Attention Monitoring to Support Nuclear Operator Safety-Relevant Tasks

In the main control room (MCR) of a nuclear power plant (NPP), the quality of an operator's performance can depend on their level of attention to the task. Insufficient operator attention accounted for more than 26% of the total causes of human errors and is the highest category for errors. It is therefore necessary to check whether operators are sufficiently attentive either as supervisors or peers during reactor operation. Recently, digital control technologies have been introduced to the operating environment of an NPP MCR. These upgrades are expected to enhance plant and operator performance. At the same time, because personal computers are used in the advanced MCR, the operators perform more cognitive works than physical work. However, operators may not consciously check fellow operators' attention in this environment indicating potentially higher importance of the role of operator attention. Therefore, remote measurement of an operator's attention in real time would be a useful tool, providing feedback to supervisors. The objective of this study is to investigate the development of quantitative indicators that can identify an operator's attention, to diagnose or detect a lack of operator attention thus preventing potential human errors in advanced MCRs. To establish a robust baseline of operator attention, this study used two of the widely used biosignals: electroencephalography (EEG) and eye movement. We designed an experiment to collect EEG and eye movements of the subjects who were monitoring and diagnosing nuclear operator safety-relevant tasks. There was a statistically significant difference between biosignals with and without appropriate attention. Furthermore, an average classification accuracy of about 90% was obtained by the k-nearest neighbors and support vector machine classifiers with a few EEG and eye movements features. Potential applications of EEG and eye movement measures in monitoring and diagnosis tasks in an NPP MCR are also discussed.

Nuclear operators on Banach function spaces

Let X be a Banach space and E be a perfect Banach function space over a finite measure space $$(\Omega ,\Sigma ,\lambda )$$ ( Ω , Σ , λ ) such that $$L^\infty \subset E\subset L^1$$ L ∞ ⊂ E ⊂ L 1 . Let $$E'$$ E ′ denote the Köthe dual of E and $$\tau (E,E')$$ τ ( E , E ′ ) stand for the natural Mackey topology on E. It is shown that every nuclear operator $$T:E\rightarrow X$$ T : E → X between the locally convex space $$(E,\tau (E,E'))$$ ( E , τ ( E , E ′ ) ) and a Banach space X is Bochner representable. In particular, we obtain that a linear operator $$T:L^\infty \rightarrow X$$ T : L ∞ → X between the locally convex space $$(L^\infty ,\tau (L^\infty ,L^1))$$ ( L ∞ , τ ( L ∞ , L 1 ) ) and a Banach space X is nuclear if and only if its representing measure $$m_T:\Sigma \rightarrow X$$ m T : Σ → X has the Radon-Nikodym property and $$|m_T|(\Omega )=\Vert T\Vert _{nuc}$$ | m T | ( Ω ) = ‖ T ‖ nuc (= the nuclear norm of T). As an application, it is shown that some natural kernel operators on $$L^\infty $$ L ∞ are nuclear. Moreover, it is shown that every nuclear operator $$T:L^\infty \rightarrow X$$ T : L ∞ → X admits a factorization through some Orlicz space $$L^\varphi $$ L φ , that is, $$T=S\circ i_\infty $$ T = S ∘ i ∞ , where $$S:L^\varphi \rightarrow X$$ S : L φ → X is a Bochner representable and compact operator and $$i_\infty :L^\infty \rightarrow L^\varphi $$ i ∞ : L ∞ → L φ is the inclusion map.

Tort law makes a quantum leap: a review of the civil liability regime for nuclear operators in UAE law

Purpose This study aims to illustrate the special liability regime applying to a nuclear operator for damage caused to individuals, property and natural resources, after the United Arab Emirates (UAE) implemented the Vienna Convention on Civil Liability for Nuclear Damage of 1963 through Federal Law No. 4 of 2012. This paper contrasts this special regime with the default regime of civil liability set out in the UAE Civil Code. The comparison helps clarify the legal nature of nuclear operator liability, the extent of protection it affords to the parties injured in a nuclear incident, the conditions under which it obtains, as well as the different damage headings it allows. Design/methodology/approach This paper is a desk-based legal research. Findings The main novelties enshrined in the special liability regime for nuclear facility operators are the adoption of an objective approach (strict liability) and the introduction of exceptions different from those contemplated in the default regime spelled out in the UAE Civil Code, thereby affording greater protection to victims of nuclear leakages. Originality/value This paper is a first in-depth commentary of UAE Federal Law No. 4 of 2012 Concerning Civil Liability for Nuclear Damage. Considering the UAE’s dualistic approach to the implementation of international obligations, and the present lack of reliable alternative avenues towards compensation beyond private operator liability, the overview provided here will be of value to regional and international practitioners – including from neighbouring countries to the UAE (Oman, Qatar, Bahrain) – that are not currently signatories to any convention on nuclear liability.

On the Existence of Eigenvalues of a Boundary Value Problem with Transmitting Condition of the Integral Form for a Parabolic-Hyperbolic Equation

In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered problem has been proved and integral representation of the solution is obtained in a functional space. Using Lidskii Theorem on coincidences of matrix and spectral traces of nuclear operator and Gaal’s formula for evaluating traces of nuclear operator, which is represented as a product of two Hilbert-Schmidt operators, we prove the existence of eigenvalues of the considered problem.

The space of operator valued functions seen as Hilbert H*-module

Let M be a space of weakly*-measurable functions F : ? ? B(H) on measure space (?,?,?), for which the function F*F is Gel'fand integrable and Gel'fand integral ? ? F*F d? is a nuclear operator on Hilbert space H. We show that M is Hilbert H*-module which contains an orthonormal basis.

Operators constructed by means of basic sequences and nuclear matrices

In this work, we establish an approach to constructing compact operators between arbitrary infinite-dimensional Banach spaces without a Schauder basis. For this purpose, we use a countable number of basic sequences for the sake of verifying the result of Morrell and Retherford. We also use a nuclear operator, represented as an infinite-dimensional matrix defined over the space $\ell _{1}$ℓ1 of all absolutely summable sequences. Examples of nuclear operators over the space $\ell _{1}$ℓ1 are given and used to construct operators over general Banach spaces with specific approximation numbers.

Main Evolutions of the RCC-C Design and Construction Code for Fuel Assemblies Since 2015

AFCEN is a French Standard Development Organization which publishes codes for design, construction and in-service inspection rules for Pressurized Water Reactors. The fields covered by theses codes are mechanical components, in-service surveillance of mechanical components, electrical equipments, nuclear fuel, civil works and fire protection. AFCEN was initially founded by electric utility EDF and nuclear steam supply system manufacturer FRAMATOME. AFCEN has more than 60 institutional members, representing more than 650 experts who contribute to the development and continuous improvement of codes. The RCC-C code, which is dedicated to PWR fuel assemblies and associated core components, set forth generic requirements to be fulfilled by the suppliers and by the manufacturers for the design justifications and for the manufacturing and inspection operations of PWR fuel assemblies and rod cluster control assemblies. The RCC-C is intended to be used in the frame of contractual relations between a customer (nuclear operator) and a nuclear fuel supplier. The first edition was published in 1981. Over the years, many changes have been made to the original text but the structure hasn’t been much modified. Because of this, the text was becoming less coherent for the users and was lacking also minimal explanations. A redesign of the code was scheduled for the 2015 edition to address those problems. With the involvement of fuel vendors FRAMATOME, WESTINGHOUSE, and French nuclear operator EDF, the text was restructured and clarified. New requirements were implemented and the set of both design and manufacturing rules was strengthened to reflect fuel vendors’ practices and operator expectations. This article explains the main modifications that were implemented since the 2015 edition, and also outlines the prospects for future changes taking into account the latest regulatory requirements and evolutions of the industrial practices.

A Statistical Method for Benchmarking Nuclear Plant Models, Using ACAP

One of the requirements for validating nuclear reactor plant models is to benchmark the predicted results of selected transients against measured plant data or another qualified code. A major challenge with benchmarking is the criteria for validating a model are not always well defined and rely heavily on human judgment, thus introducing the possibility of human bias or inconsistent conclusions. The validation process can also be time consuming. A new method is presented to aid in the validation of nuclear reactor plant models, using the Automated Code Assessment Program (ACAP), which is a tool developed at Pennsylvania State University under contract by the U. S. Nuclear Regulatory Commission (NRC). The proposed method was developed specifically for real-time best-estimate nuclear operator training simulator transients. However, the tool can be easily customized for most applications (e.g., design models, steady state data). Four distinct statistical metrics and weightings were chosen, as deemed appropriate for transient nuclear operator training simulator applications. The metrics account for errors in magnitude and trend, and incorporate an experimental uncertainty. The four metrics are then combined into a single Figure of Merit (i.e., a statistical level of agreement between the predicted and benchmarking data sets). The use of ACAP for benchmarking is demonstrated by comparing experimental data from the Loss-of-Fluid-Test (LOFT) facility Large Break Loss-of-Coolant Experiment L2-5 with code predictions from a RELAP5-3D (Version 2.9.3+) model previously developed and published by Idaho National Laboratories. The proposed method is shown to have several advantages over conventional validation methods, in that it greatly reduces the possibility of human bias, generates reproducible results, can be easily automated to improve efficiency, and can be easily documented. After the initial validation, the tool can also be used to re-validate models after computer hardware changes, model changes, tool upgrades, and operating system upgrades.