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"Gray, Robert"
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Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups
We prove the following results: (1) There is a one-relator inverse monoid Inv⟨A|w=1⟩ with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The second of these results is proved by showing that for any finite forest the associated right-angled Artin group embeds into a one-relator group. Combining this with a result of Lohrey and Steinberg (J Algebra 320(2):728–755, 2008), we use this to prove that there is a one-relator group containing a fixed finitely generated submonoid in which the membership problem is undecidable. To prove (1) a new construction is introduced which uses the one-relator group and submonoid in which membership is undecidable from (2) to construct a one-relator inverse monoid Inv⟨A|w=1⟩ with undecidable word problem. Furthermore, this method allows the construction of an E-unitary one-relator inverse monoid of this form with undecidable word problem. The results in this paper answer a problem originally posed by Margolis et al. (in: Semigroups and their applications, Reidel, Dordrecht, pp. 99–110, 1987).
Journal Article
Adam of the road
The adventures of eleven-year-old Adam as he travels the open roads of thirteenth-century England searching for his missing father, a minstrel, and his stolen red spaniel, Nick.
BOOK
Composition and Properties of Drilling and Completion Fluids (6th Edition)
In its Sixth Edition, this book has been updated and revised to incorporate new information on technology, economic, and political issues that have impacted the use of fluids to drill and complete oil and gas wells. With updated content on completion fluids and reservoir drilling fluids; health, safety and environment; drilling fluid systems and products; new fluid systems and additives from both chemical and engineering perspectives; wellbore stability, adding the new R&D on water-based muds; and equipment and procedures for evaluating drilling fluid performance in light of the advent of digital technology and better manufacturing techniques, this book has been thoroughly updated to meet the drilling and completion engineer's needs.
eBook
Femtojoule femtosecond all-optical switching in lithium niobate nanophotonics
Optical nonlinear functions are crucial for various applications in integrated photonics, including all-optical information processing1, photonic neural networks2,3 and on-chip ultrafast light sources4,5. However, the weak native nonlinearity of most nanophotonic platforms has imposed barriers for such functions by necessitating large driving energies, high-Q cavities or integration with other materials with stronger nonlinearity. Here we effectively utilize the strong and instantaneous quadratic nonlinearity of lithium niobate nanowaveguides for the realization of cavity-free all-optical switching. By simultaneous engineering of the dispersion and quasi-phase matching, we design and demonstrate a nonlinear splitter that can achieve ultralow switching energies down to 80 fJ, featuring a fastest switching time of ~46 fs and a lowest energy–time product of 3.7 × 10−27 J s in integrated photonics. Our results can enable on-chip ultrafast and energy-efficient all-optical information processing, computing systems and light sources.Researchers exploit the quadratic nonlinearity of lithium niobate nanowaveguides and demonstrate cavity-free all-optical switching. Switching energies down to 80 fJ, switching times down to ~46 fs and energy–time products of 3.7 × 10−27 J s are shown.
Journal Article
Adam of the road
The adventures of eleven-year-old Adam as he travels the open roads of thirteenth-century England searching for his missing father, a minstrel, and his stolen red spaniel, Nick.
BOOK
Mid-infrared cross-comb spectroscopy
Dual-comb spectroscopy has been proven beneficial in molecular characterization but remains challenging in the mid-infrared region due to difficulties in sources and efficient photodetection. Here we introduce cross-comb spectroscopy, in which a mid-infrared comb is upconverted via sum-frequency generation with a near-infrared comb of a shifted repetition rate and then interfered with a spectral extension of the near-infrared comb. We measure CO
2
absorption around 4.25 µm with a 1-µm photodetector, exhibiting a 233-cm
−1
instantaneous bandwidth, 28000 comb lines, a single-shot signal-to-noise ratio of 167 and a figure of merit of 2.4 × 10
6
Hz
1/2
. We show that cross-comb spectroscopy can have superior signal-to-noise ratio, sensitivity, dynamic range, and detection efficiency compared to other dual-comb-based methods and mitigate the limits of the excitation background and detector saturation. This approach offers an adaptable and powerful spectroscopic method outside the well-developed near-IR region and opens new avenues to high-performance frequency-comb-based sensing with wavelength flexibility.
The authors introduce and demonstrate cross-comb spectroscopy in the mid-infrared as a variant of dual-comb spectroscopy. It provides enhanced performance and allows mid-infrared spectral information to be obtained by near-infrared detection.
Journal Article
Enhanced sensitivity via non-Hermitian topology
Sensors are indispensable tools of modern life that are ubiquitously used in diverse settings ranging from smartphones and autonomous vehicles to the healthcare industry and space technology. By interfacing multiple sensors that collectively interact with the signal to be measured, one can go beyond the signal-to-noise ratios (SNR) attainable by the individual constituting elements. Such techniques have also been implemented in the quantum regime, where a linear increase in the SNR has been achieved via using entangled states. Along similar lines, coupled non-Hermitian systems have provided yet additional degrees of freedom to obtain better sensors via higher-order exceptional points. Quite recently, a new class of non-Hermitian systems, known as non-Hermitian topological sensors (NTOS) has been theoretically proposed. Remarkably, the synergistic interplay between non-Hermiticity and topology is expected to bestow such sensors with an enhanced sensitivity that grows exponentially with the size of the sensor network. Here, we experimentally demonstrate NTOS using a network of photonic time-multiplexed resonators in the synthetic dimension represented by optical pulses. By judiciously programming the delay lines in such a network, we realize the archetypal Hatano-Nelson model for our non-Hermitian topological sensing scheme. Our experimentally measured sensitivities for different lattice sizes confirm the characteristic exponential enhancement of NTOS. We show that this peculiar response arises due to the combined synergy between non-Hermiticity and topology, something that is absent in Hermitian topological lattices. Our demonstration of NTOS paves the way for realizing sensors with unprecedented sensitivities.
Journal Article