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Characteristic, C-characteristic and positive cones in hyperfields
Dawid Edmund Kędzierski, Alessandro Linzi, Hanna Stojałowska, 2023, original scientific article

Abstract: We study the notions of positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We show how these interact in order to produce interesting results in the theory of hyperfields. For instance, we give a criterion for deciding whether certain hyperfields cannot be obtained via Krasner's quotient construction. We prove that any positive integer (larger than 1) can be realized as the characteristic of some infinite hyperfield and an analogous result for C-characteristic. Finally, we study the (directed) graph associated to the strict partial order induced by a positive cone in a hyperfield in various examples.
Keywords: hyperfield, order, characteristic, positive cone
Published in RUNG: 13.02.2023; Views: 1108; Downloads: 3
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Measuring free word order: Some empirical and modeling perspectives
Arthur Stepanov, invited lecture at foreign university

Abstract: Languages manifesting flexibility of word order (within the sentence's compositional meaning) have always presented a challenge for modern theories of syntax requiring any deviation from the canonical word order to be grammatically motivated. Parasyntactic motivations such as information structural or stylistic requirements may account for some portion of this flexibility, but not all of it. In addition, native speakers do not necessarily accept canonical and non-canonical word orders to an equal extent. In fact, the latter typically receive lower acceptability scores than the former, albeit above the subjective threshold for what would count as "ungrammatical". Some of the combinatorially possible word orders are not acceptable at all. In this experimental study we scrutinize different word order sequences in a free word order language (Serbo-Croatian) and attempt to isolate independent displacement factors responsible for various elements of the sentence appearing away from their canonical structural positions. We explore differential and cumulative effects of these independent factors to predict speakers' acceptability scores.
Keywords: Free word order, experimental syntax, Serbo-Croatian, sentence acceptability task
Published in RUNG: 11.02.2021; Views: 2633; Downloads: 0
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Advantages and disadvantages of experiments with ultrashort two-color pulses
Matija Stupar, 2020, doctoral dissertation

Abstract: Advances in the development of lasers have led to a new class of radiation sources generating coherent, tunable, ultrashort light pulses in the spectral region ranging from infrared to soft X-rays. This includes high-order harmonics generation in gas (HHG), on which relies the CITIUS facility at University of Nova Gorica (Slovenia), and free-electron lasers (FELs), such as the facility FERMI at Elettra-Sincrotrone Trieste (Italy). The distinctive structure of HHG and FEL radiation paved the way to time-resolved experiments, which are performed to investigate events occurring on a short, or very short, temporal scale, from picoseconds to femtoseconds. This work focuses on the advantages and disadvantages of some experimental techniques based on using these novel light sources to investigate the microscopic and/or ultrafast dynamics of matter samples, which have been previously driven out of equilibrium. Advantages rely on the implementation of various applications based on two-color schemes and, more specifically, include the possibility of acquiring two-dimensional frequency maps, measuring electrons’ effective masses, or investigating electronic properties decoupled from the influence of the lattice. Particular focus will be put on experimental methods relying on photoelectric effect and photoelectron spectroscopy. In all experiments, we took advantage of one or more specific properties of HHG and FEL sources, such as controllable chirp, to study laser dressed states in helium, variable polarization, to study electronic properties of iron-based pnictides and ultrashort pulses (< 10 fs) to study the purely electronic dynamics in transition metal dichalcogenides. On the other hand, the study of the interface between a molecule and a topological insulator revealed some intrinsic limitations and physical drawbacks of the technique, such as spurious effects originating from the high power pulses, like multiphoton absorption and the space charge effect, or the reduction of experimental resolution when pushing for shorter and shorter pulse durations. Some disadvantages are also connected to the current state-of-the-art in the field of ultrashort laser systems, where a trade-off needs to be found between repetition rate and laser power. Finally, state-of-the-art experiments based on the ability to generate ultrashort pulses carrying orbital angular momentum in visible, near-infrared as well as extreme UV range will be presented. The use of these pulses opens the door to the investigation of new physical phenomena, such as probing magnetic vortices using extreme ultraviolet light from a free-electron laser or imprinting the spatial distribution of an ultrashort infrared pulse carrying orbital angular momentum onto a photoelectron wave packet.
Keywords: ultrafast lasers, two-color experiments, photoemission, high-order harmonic generation, free-electron lasers, hot-electrons dynamics, surface science, pump-probe photoemission, ultraviolet photoemission, orbital angular momentum
Published in RUNG: 02.12.2020; Views: 3996; Downloads: 121
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Al Tahan, M.; Davvaz, B. , On Corsini hypergroups and their productional hypergroups. (Englishsummary)
Irina Elena Cristea, 2019, review, book review, critique

Keywords: hypergroup, productional hypergroup, order
Published in RUNG: 18.12.2019; Views: 2578; Downloads: 0
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