Technique of operator algebras in quantum structures

Katedra matematik

Welsh Women's Industrial Fiction 1880–1910

From the beginning of the genre, women writers have made a major contribution to the development of industrial writing. Although prevented from gaining first-hand experience of the coalface, Welsh women writers were amongst the first to try to fictionalize those heavy industries—coal and metal in the south, and slate in the north—which dominated the lives of the majority of the late nineteenth-century Welsh population. Treatment of industrial matter is generally fragmentary in this early women’s writing; industrial imagery and metaphor may be used in novels that are not primarily “about” industry at all. Yet from c. 1880–1910, Welsh women writers made a significant—and hitherto critically neglected—attempt to make sense in literature of contemporary industrial Wales in powerful and innovative ways. This essay maps their contribution and considers anglophone Welsh women writers’ adaptations and innovations of form (particularly romance) as they try to find a way of representing industrial landscapes, communities and the daily realities of industrial labour. It identifies the genesis in women’s writing of tropes that would become central to later industrial fiction, including depictions of industrial accident, injury, death and disability. And it explores the representation of social relations (class, gender, ethnicity, sexuality) and conflict on this tumultuous, dangerous new stage

Experimental and Analytical Investigations of an Optically Pre-Amplified FSO-MIMO System With Repetition Coding Over Non-Identically Distributed Correlated Channels

This paper presents theoretical and experimental bit error rate (BER) results for a freespace optical (FSO) multiple-input-multiple-output system over an arbitrarily correlated turbulence channel. We employ an erbium-doped fiber amplifier at the receiver (Rx), which results in an improved Rx’s sensitivity at the cost of an additional non-Gaussian amplified spontaneous emission noise. Repetition coding is used to combat turbulence and to improve the BER performance of the FSO links. A mathematical framework is provided for the considered FSO system over a correlated non-identically distributed Gamma-Gamma channel; and analytical BER results are derived with and without the pre-amplifier for a comparative study. Moreover, novel closed-form expressions for the asymptotic BER are derived; a comprehensive discussion about the diversity order and coding gain is presented by performing asymptotic analysis at high signal-tonoise ratio (SNR). To verify the analytical results, an experimental set-up of a 2 × 1 FSO-multiple-inputsingle-output (MISO) system with pre-amplifier at the Rx is developed. It is shown analytically that, both correlation and pre-amplification do not affect the diversity order of the system, however, both factors have contrasting behaviour with respect to coding gain. Further, to achieve the target forward error correction BER limit of 3.8 × 10−3 , a 2 × 1 FSO-MISO system with a pre-amplifier requires 6.5 dB lower SNR compared with the system with no pre-amplifier. Moreover, an SNR penalty of 2.5 dB is incurred at a higher correlation level for the developed 2×1 experimental FSO set-up, which is in agreement with the analytical findings

Impact of Channel Correlation on Different Performance Metrics of OSSK-Based FSO System

In this paper, we study the impact of correlation on the bit error rate (BER) and the channel capacity of a free-space optical (FSO) multiple-input-multiple-output (MIMO) system employing optical space shift keying (OSSK) over a fading channel. In order to study a practical correlated channel, we consider the effect of channel correlation due to both small-and large-scale eddies and show that the use of OSSK over correlated FSO channel can lead to an improved system performance with increasing correlation level of upto 0.9. In this work, we first develop an analytical framework for different performance metrics of the OSSK multiple-input single-output system with correlation and then extend our investigation by proposing an asymptotically accurate mathematical framework for MIMO. We also validate all the analytical results using MATLAB simulations. Finally, we develop an experimental setup of FSO with two correlated links to study the throughput and latency of the links at different turbulence levels

Technika operátorových algeber v kvantových strukturách

Název práce: Technika operátorových algeber v kvantových strukturách Autor: Mgr. Martin Bohata Instituce: Katedra matematiky, Fakulta elektrotechnická, České vysoké učení technické v Praze Vedoucí disertační práce: Prof. RNDr. Jan Hamhalter, CSc. Abstrakt: Disertační práce se zabývá Bellovými nerovnostmi a částečným uspořádáním nazývaným *-uspořádání. Tyto dvě struktury jsou zkoumány pomocí teorie operátorových algeber. Studium Bellových nerovností je zaměřeno na CHSH verzi Bellovy nerov- nosti a její kvantovou formu nazývanou Cirel'sonova nerovnost. Cirel'sonova nerovnost je zobecněna do reálných a komplexních lineárních prostorů s pseu- doskalárním součinem. Výsledky obdržené na této abstraktní úrovni jsou aplikovány na studium maximálního narušení (CHSH verze) Bellovy nerov- nosti formulované v matematickém rámci *-algeber. Je ukázáno, že prvky maximálně narušující Bellovu nerovnost úzce souvisí s Pauliho spinovými maticemi. Tyto výsledky jsou také zobecněny do neasociativního případu Jordanových algeber. Další oblastí našeho zájmu je *-uspořádání. Toto částečné uspořádání je uvažováno na vhodných *-algebrách. Jako důsledek naší analýzy *-uspořádání na částečných izometriích...Title: Technique of operator algebras in quantum structures Author: Mgr. Martin Bohata Institution: Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague Supervisor: Prof. RNDr. Jan Hamhalter, CSc. Abstract: The thesis deals with Bell inequalities and a partial order called star order. These two structures are investigated by means of the theory of operator algebras. The study of Bell inequalities is focused on the CHSH version of Bell inequality and its quantum version called Cirel'son inequality. The Cirel'son inequality is generalized to real and complex linear spaces with a pseudo inner product. The results obtained on this abstract level are applied to the study of maximal violation of the (CHSH version of) Bell inequality formulated in the mathematical framework of *-algebras. It is shown that elements maximally violated the Bell inequality are closely related to Pauli spin matrices. These results are also generalized to the nonassociative case of Jordan algebras. The next field of our interest is the star order. This partial order is considered on certain *-algebras. As a consequence of our analysis of the star order on partial isometries, we obtain a new characterization of infinite C*-algebras. Then we investigate the infimum and supremum problem for the...Katedra matematické analýzyDepartment of Mathematical AnalysisFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult