Abstract
The classical uncertainty principle works for smooth signal functions. In our work, we apply the Fourier transform derivatives for the study of uncertainty principle, so that the smoothness ...condition for the signal functions is not required. At first, the amplitude and phase derivatives of vector-valued signal functions based on the Fourier transform are defined. Then we obtain a strong form of the uncertainty principle.
We develop a systematic study of the superpositions of elliptic operators with different orders, mixing classical and fractional scenarios. For concreteness, we focus on the sum of the Laplacian and ...the fractional Laplacian, and we provide structural results, including existence, maximum principles (both for weak and classical solutions), interior Sobolev regularity and boundary regularity of Lipschitz type.
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BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
The phase transition between λ-Ti3O5and β-Ti3O5is an intriguing process that can be driven in multiple ways. However, the phase transition has not been reasonably and universally analyzed in ...atomic-scale, because it is limited by experimental inaccessibility. Here, the nudged elastic band method, crystal orbital Hamiltonian population integral calculation, phonon calculation, and electron (or hole) doping calculation are used to investigate the phase transition between λ-Ti3O5and β-Ti3O5. The atomic displacement mode in the phase transition between the β-Ti3O5and λ-Ti3O5is provided, and a theory that the coupling between the lattice and excited electrons (or holes) is responsible for the phase transition between λ-Ti3O5and β-Ti3O5is established.
Water in nanoscale cavities is ubiquitous and of central importance to everyday phenomena in geology and biology. However, the properties of nanoscale water can be substantially different from those ...of bulk water, as shown, for example, by the anomalously low dielectric constant of water in nanochannels
, near frictionless water flow
or the possible existence of a square ice phase
. Such properties suggest that nanoconfined water could be engineered for technological applications in nanofluidics
, electrolyte materials
and water desalination
. Unfortunately, challenges in experimentally characterizing water at the nanoscale and the high cost of first-principles simulations have prevented the molecular-level understanding required to control the behaviour of water. Here we combine a range of computational approaches to enable a first-principles-level investigation of a single layer of water within a graphene-like channel. We find that monolayer water exhibits surprisingly rich and diverse phase behaviour that is highly sensitive to temperature and the van der Waals pressure acting within the nanochannel. In addition to multiple molecular phases with melting temperatures varying non-monotonically by more than 400 kelvins with pressure, we predict a hexatic phase, which is an intermediate between a solid and a liquid, and a superionic phase with a high electrical conductivity exceeding that of battery materials. Notably, this suggests that nanoconfinement could be a promising route towards superionic behaviour under easily accessible conditions.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Abstract In the last two academical years, as part of the Italian Ministry plan PLS – “Piano Lauree Scientifiche” (Scientific Degree Plan), two courses for high school students and teachers ...consisting in some interdisciplinary and transversal online meetings have been proposed. They regarded the three principles of dynamics, the law of universal gravitation and Maxwell’s equations. “Variations” around these topics were also presented – of historical, philosophical and also of musical nature – to make the cultural setting of what has been discussed deeper and make it meaningful in the present. At the end of each course, students produced a video of few minutes with a personal reworking and rethinking of the meaning of one of the topics discussed.
In this paper, we define the two‐sided fractional Clifford–Fourier transform (FrCFT). Using its properties, we get some uncertainty principles of the FrCFT. Two parts are obtained. One part is a ...modified uncertainty principle. The uncertainty principle states a lower bound on the spreads of two specific transform domains. It is shown that only a Gaussian‐type signal minimizes the uncertainty. We also give a Heisenberg‐type uncertainty principle. The other part is a logarithmic uncertainty principle, which may be obtained from a sharp of Pitt's inequality.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
Courtesy Lucy Caldicott/Photo Alan Hassey Psychiatrist and UK leader in health information governance. A second appropriation of Caldicott's name stemmed from one of the 16 recommendations of her ...report: that every National Health Service (NHS) organisation dealing with such requests should appoint a senior person, preferably a health professional, to act as a guardian of the confidentiality of patient information. In 2011, she became Chair of the National Information Governance Board and subsequently the National Data Guardian for Health and Social Care.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
We develop a theory of monotone comparative statics for models with adjustment costs. We show that comparative-statics conclusions may be drawn under the usual ordinal complementarity assumptions on ...the objective function, assuming very little about costs: only a mild monotonicity condition is required. We use this insight to prove a general le Chatelier principle: under the ordinal complementarity assumptions, if short-run adjustment is subject to a monotone cost, then the long-run response to a shock is greater than the short-run response. We extend these results to a fully dynamic model of adjustment over time: the le Chatelier principle remains valid, and under slightly stronger assumptions, optimal adjustment follows a monotone path. We apply our results to models of saving, production, pricing, labor supply and investment.
Concerns about secondary use of data and limited opportunities for benefit-sharing have focused attention on the tension that Indigenous communities feel between (1) protecting Indigenous rights and ...interests in Indigenous data (including traditional knowledges) and (2) supporting open data, machine learning, broad data sharing, and big data initiatives. The International Indigenous Data Sovereignty Interest Group (within the Research Data Alliance) is a network of nation-state based Indigenous data sovereignty networks and individuals that developed the 'CARE Principles for Indigenous Data Governance' (Collective Benefit, Authority to Control, Responsibility, and Ethics) in consultation with Indigenous Peoples, scholars, non-profit organizations, and governments. The CARE Principles are people- and purpose-oriented, reflecting the crucial role of data in advancing innovation, governance, and self-determination among Indigenous Peoples. The Principles complement the existing data-centric approach represented in the 'FAIR Guiding Principles for scientific data management and stewardship' (Findable, Accessible, Interoperable, Reusable). The CARE Principles build upon earlier work by the Te Mana Raraunga Maori Data Sovereignty Network, US Indigenous Data Sovereignty Network, Maiam nayri Wingara Aboriginal and Torres Strait Islander Data Sovereignty Collective, and numerous Indigenous Peoples, nations, and communities. The goal is that stewards and other users of Indigenous data will 'Be FAIR and CARE.' In this first formal publication of the CARE Principles, we articulate their rationale, describe their relation to the FAIR Principles, and present examples of their application. Keywords: Indigenous, data sovereignty, data governance, data principles, FAIR principles
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