A non-hyponormal operator generating Stieltjes moment sequences

A linear operator $S$ in a complex Hilbert space \hh for which the set \dzn{S} of its $C^\infty$-vectors is dense in \hh and $\{\|S^n f\|^2\}_{n=0}^\infty$ is a Stieltjes moment sequence for every f \in \dzn{S} is said to generate Stieltjes moment sequences. It is shown that there exists a closed non-hyponormal operator $S$ which generates Stieltjes moment sequences. What is more, \dzn{S} is a core of any power $S^n$ of $S$. This is established with the help of a weighted shift on a directed tree with one branching vertex. The main tool in the construction comes from the theory of indeterminate Stieltjes moment sequences. As a consequence, it is shown that there exists a non-hyponormal composition operator in an $L^2$-space (over a $\sigma$-finite measure space) which is injective, paranormal and which generates Stieltjes moment sequences. In contrast to the case of abstract Hilbert space operators, composition operators which are formally normal and which generate Stieltjes moment sequences are always subnormal (in fact normal). The independence assertion of Barry Simon's theorem which parameterizes von Neumann extensions of a closed real symmetric operator with deficiency indices $(1,1)$ is shown to be false

Track clustering with a quantum annealer for primary vertex reconstruction at hadron colliders

Clustering of charged particle tracks along the beam axis is the first step in reconstructing the positions of hadronic interactions, also known as primary vertices, at hadron collider experiments. We use a 2036 qubit D-Wave quantum annealer to perform track clustering in a limited capacity on artificial events where the positions of primary vertices and tracks resemble those measured by the Compact Muon Solenoid experiment at the Large Hadron Collider. The algorithm, which is not a classical-quantum hybrid but relies entirely on quantum annealing, is tested on a variety of event topologies from 2 primary vertices and 10 tracks up to 5 primary vertices and 15 tracks. It is benchmarked against simulated annealing executed on a commercial CPU constrained to the same processor time per anneal as time in the physical annealer, and performance is found to be comparable for small numbers of vertices with an intriguing advantage noted for 2 vertices and 16 tracks

Ferromagnetic Domain Structure of La0.78Ca0.22MnO3 Single Crystals

The magneto-optical technique has been employed to observe spontaneous ferromagnetic domain structures in La0.78Ca0.22MnO3 single crystals. The magnetic domain topology was found to be correlated with the intrinsic twin structure of the investigated crystals. With decreasing temperature the regular network of ferromagnetic domains undergoes significant changes resulting in apparent rotation of the domain walls in the temperature range of 70-150 K. The apparent rotation of the domain walls can be understood in terms of the Jahn-Teller deformation of the orthorhombic unit cell, accompanied by additional twinning.Comment: 7 pages, 5 figures, to be published in PR

On the distribution of career longevity and the evolution of home run prowess in professional baseball

Statistical analysis is a major aspect of baseball, from player averages to historical benchmarks and records. Much of baseball fanfare is based around players exceeding the norm, some in a single game and others over a long career. Career statistics serve as a metric for classifying players and establishing their historical legacy. However, the concept of records and benchmarks assumes that the level of competition in baseball is stationary in time. Here we show that power-law probability density functions, a hallmark of many complex systems that are driven by competition, govern career longevity in baseball. We also find similar power laws in the density functions of all major performance metrics for pitchers and batters. The use of performance-enhancing drugs has a dark history, emerging as a problem for both amateur and professional sports. We find statistical evidence consistent with performance-enhancing drugs in the analysis of home runs hit by players in the last 25 years. This is corroborated by the findings of the Mitchell Report [1], a two-year investigation into the use of illegal steroids in major league baseball, which recently revealed that over 5 percent of major league baseball players tested positive for performance-enhancing drugs in an anonymous 2003 survey.Comment: 5 pages, 5 figures, 2-column revtex4 format. Revision has change of title, a figure added, and minor changes in response to referee comment

Quantum and classical echoes in scattering systems described by simple Smale horseshoes

We explore the quantum scattering of systems classically described by binary and other low order Smale horseshoes, in a stage of development where the stable island associated with the inner periodic orbit is large, but chaos around this island is well developed. For short incoming pulses we find periodic echoes modulating an exponential decay over many periods. The period is directly related to the development stage of the horseshoe. We exemplify our studies with a one-dimensional system periodically kicked in time and we mention possible experiments.Comment: 7 pages with 6 reduced quality figures! Please contact the authors ([email protected]) for an original good quality pre-prin

From patriarchal socialism to grassroots capitalism: The role of female entrepreneurs in the transition of North Korea

© 2018 Elsevier Ltd Since the collapse of North Korea's command economy in the 1990s, a large number of women have become entrepreneurs. This remarkable feature of North Korean marketisation cannot be adequately explained by female entrepreneur (FE) deficit premises, which highlight women's supposed shortcomings in what is considered a male enterprise. Based on in-depth interviews with female North Korean defectors, and viewing entrepreneurship as a catalyst for socio-cultural change, this paper questions how FEs emerged in North Korea and whether women's market participation influences gender relations, or attitudes toward the North Korean regime. There have been noticeable changes in gender roles, son preference and choice of marriage partners. Our findings suggest that female entrepreneurship has the potential to both challenge and support the North Korean system. This research significantly advances scholarship on gender and entrepreneurship by adopting a constructionist approach to gender and transcending the prevalence of descriptive analysis of gendered entrepreneurial practices