Phase-Sensitive Vibrational Sum and Difference Frequency-Generation Spectroscopy Enabling Nanometer-Depth Profiling at Interfaces

The unique physical and chemical properties of interfaces are governed by a finite depth that describes the transition from the topmost atomic layer to the properties of the bulk material. Thus, understanding the physical nature of interfaces requires detailed insight into the different structures, chemical compositions, and physical processes that form this interfacial region. Such insight has traditionally been difficult to obtain from experiments, as it requires a combination of structural and chemical sensitivity with spatial depth resolution on the nanometer scale. In this contribution, we present a vibrational spectroscopic approach that can overcome these limitations. By combining phase-sensitive sum and difference frequency-generation (SFG and DFG, respectively) spectroscopy and by selectively determining different nonlinear interaction pathways, we can extract precise depth information and correlate these to specific vibrationally resonant modes of interfacial species. We detail the mathematical framework behind this approach and demonstrate the performance of this technique in two sets of experiments on selected model samples. An analysis of the results shows an almost perfect match between experiment and theory, confirming the practicability of the proposed concept under realistic experimental conditions. Furthermore, in measurements with self-assembled monolayers of different chain lengths, we analyze the spatial accuracy of the technique and find that the precision can even reach the sub-nanometer regime. We also discuss the implications and the information content of such depth-sensitive measurements and show that the concept is very general and goes beyond the analysis of the depth profiles. The presented SFG/DFG technique offers new perspectives for spectroscopic investigations of interfaces in various material systems by providing access to fundamental observables that have so far been inaccessible by experiments. Here, we set the theoretical and experimental basis for such future investigations

Zermelo Navigation and a Speed Limit to Quantum Information Processing

We use a specific geometric method to determine speed limits to the implementation of quantum gates in controlled quantum systems that have a specific class of constrained control functions. We achieve this by applying a recent theorem of Shen, which provides a connection between time optimal navigation on Riemannian manifolds and the geodesics of a certain Finsler metric of Randers type. We use the lengths of these geodesics to derive the optimal implementation times (under the assumption of constant control fields) for an arbitrary quantum operation (on a finite dimensional Hilbert space), and explicitly calculate the result for the case of a controlled single spin system in a magnetic field, and a swap gate in a Heisenberg spin chain

Extendibility of bilinear forms on banach sequence spaces

[EN] We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c(0) in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to any superspace.The second author was supported by MICINN Project MTM2011-22417.DANIEL CARANDO; Sevilla Peris, P. (2014). Extendibility of bilinear forms on banach sequence spaces. Israel Journal of Mathematics. 199(2):941-954. https://doi.org/10.1007/s11856-014-0003-9S9419541992F. Albiac and N. J. Kalton, Topics in Banach Space Theory, Graduate Texts in Mathematics, Vol. 233, Springer, New York, 2006.R. Arens, The adjoint of a bilinear operation, Proceedings of the American Mathematical Society 2 (1951), 839–848.R. Arens, Operations induced in function classes, Monatshefte für Mathematik 55 (1951), 1–19.R. M. Aron and P. D. Berner, A Hahn-Banach extension theorem for analytic mappings, Bulletin de la Société Mathématique de France 106 (1978), 3–24.S. Banach, Sur les fonctionelles linéaires, Studia Mathematica 1 (1929), 211–216.S. Banach, Théorie des opérations linéaires, (Monogr. Mat. 1) Warszawa: Subwncji Funduszu Narodowej. VII, 254 S., Warsaw, 1932.D. Carando, Extendible polynomials on Banach spaces, Journal of Mathematical Analysis and Applications 233 (1999), 359–372.D. Carando, Extendibility of polynomials and analytic functions on l p, Studia Mathematica 145 (2001), 63–73.D. Carando, V. Dimant and P. Sevilla-Peris, Limit orders and multilinear forms on lp spaces, Publications of the Research Institute for Mathematical Sciences 42 (2006), 507–522.J. M. F. Castillo, R. García, A. Defant, D. Pérez-García and J. Suárez, Local complementation and the extension of bilinear mappings, Mathematical Proceedings of the Cambridge Philosophical Society 152 (2012), 153–166.J. M. F. Castillo, R. García and J. A. Jaramillo, Extension of bilinear forms on Banach spaces, Proceedings of the American Mathematical Society 129 (2001), 3647–3656.P. Cembranos and J. Mendoza, The Banach spaces ℓ ∞(c 0) and c 0(ℓ ∞) are not isomorphic, Journal of Mathematical Analysis and Applications 367 (2010), 461–463.A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Mathematics Studies, Vol. 176, North-Holland Publishing Co., Amsterdam, 1993.A. Defant and C. Michels, Norms of tensor product identities, Note di Matematica 25 (2005/06), 129–166.J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, Vol. 43, Cambridge University Press, Cambridge, 1995.D. J. H. Garling, On symmetric sequence spaces, Proceedings of the London Mathematical Society (3) 16 (1966), 85–106.A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1953), 1–79.H. Hahn, Über lineare Gleichungssysteme in linearen Räumen, Journal für die Reine und Angewandte Mathematik 157 (1927), 214–229.R. C. James, Bases and reflexivity of Banach spaces, Annals of Mathematics (2) 52 (1950), 518–527.H. Jarchow, C. Palazuelos, D. Pérez-García and I. Villanueva, Hahn-Banach extension of multilinear forms and summability, Journal of Mathematical Analysis and Applications 336 (2007), 1161–1177.W. B. Johnson and L. Tzafriri, On the local structure of subspaces of Banach lattices, Israel Journal of Mathematics 20 (1975), 292–299.P. Kirwan and R. A. Ryan, Extendibility of homogeneous polynomials on Banach spaces, Proceedings of the American Mathematical Society 126 (1998), 1023–1029.J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in Lp-spaces and their applications, Studia Mathematica 29 (1968), 275–326.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], Vol. 97, Springer-Verlag, Berlin, 1979. Function spaces.G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conference Series in Mathematics, Vol. 60, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1986.M. Fernndez-Unzueta and A. Prieto, Extension of polynomials defined on subspaces, Mathematical Proceedings of the Cambridge Philosophical Society 148 (2010), 505–518.W. L. C. Sargent, Some sequence spaces related to the lp spaces, Journal of the London Mathematical Society 35 (1960), 161–171.N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 38, Longman Scientific & Technical, Harlow, 1989

Low-density star cluster formation: Discovery of a young faint fuzzy on the outskirts of the low-mass spiral galaxy NGC 247

The classical globular clusters found in all galaxy types have half-light radii of rh ~2-4 pc, which have been tied to formation in the dense cores of giant molecular clouds. Some old star clusters have larger sizes, and it is unclear if these represent a fundamentally different mode of low-density star cluster formation. We report the discovery of a rare, young \u27faint fuzzy\u27 star cluster, NGC 247-SC1, on the outskirts of the low-mass spiral galaxy NGC 247 in the nearby Sculptor group, and measure its radial velocity using Keck spectroscopy. We use Hubble Space Telescope imaging to measure the cluster half-light radius of rh ≃ 12 pc and a luminosity of LV ≃ 4 × 105Lθ. We produce a colour-magnitude diagram of cluster stars and compare to theoretical isochrones, finding an age of ≃300 Myr, a metallicity of [Z/H] ~-0.6 and an inferred mass of M∗ ≃ 9 × 104Mθ. The narrow width of blue-loop star magnitudes implies an age spread of ≲50 Myr, while no old red-giant branch stars are found, so SC1 is consistent with hosting a single stellar population, modulo several unexplained bright \u27red straggler\u27 stars. SC1 appears to be surrounded by tidal debris, at the end of an ∼2 kpc long stellar filament that also hosts two low-mass, low-density clusters of a similar age. We explore a link between the formation of these unusual clusters and an external perturbation of their host galaxy, illuminating a possible channel by which some clusters are born with large sizes

No differences in in vivo kinematics between six different types of knee prostheses

Purpose: The aim of this study was to compare a broad range of total knee prostheses with different design parameters to determine whether in vivo kinematics was consistently related to design. The hypothesis was that there are no clear recognizable differences in in vivo kinematics between different design parameters or prostheses. Methods: At two sites, data were collected by a single observer on 52 knees (49 subjects with rheumatoid arthritis or osteoarthritis). Six different total knee prostheses were used: multi-radius, single-radius, fixed-bearing, mobilebearing, posterior-stabilized, cruciate retaining and cruciate sacrificing. Knee kinematics was recorded using fluoroscopy as the patients performed a step-up motion. Results: There was a significant effect of prosthetic design on all outcome parameters; however, post hoc tests showed that the NexGen group was responsible for 80% of the significant values. The range of knee flexion was much smaller in this group, resulting in smaller anterior-posterior translations and rotations. Conclusion: Despite kinematics being generally consistent with the kinematics intended by their design, there were no clear recognizable differences in in vivo kinematics between different design parameters or prostheses. Hence, the differences in design parameters or prostheses are not distinct enough to have an effect on clinical outcome of patients.Biomechanical EngineeringMechanical, Maritime and Materials Engineerin

Parental perceptions of barriers and facilitators to preventing child unintentional injuries within the home: a qualitative study

Background Childhood unintentional injury represents an important global health problem. Most of these injuries occur at home, and many are preventable. The main aim of this study was to identify key facilitators and barriers for parents in keeping their children safe from unintentional injury within their homes. A further aim was to develop an understanding of parents’ perceptions of what might help them to implement injury prevention activities. Methods Semi-structured interviews were conducted with sixty-four parents with a child aged less than five years at parent’s homes. Interview data was transcribed verbatim, and thematic analysis was undertaken. This was a Multi-centre qualitative study conducted in four study centres in England (Nottingham, Bristol, Norwich and Newcastle). Results Barriers to injury prevention included parents’ not anticipating injury risks nor the consequences of some risk-taking behaviours, a perception that some injuries were an inevitable part of child development, interrupted supervision due to distractions, maternal fatigue and the presence of older siblings, difficulties in adapting homes, unreliability and cost of safety equipment and provision of safety information later than needed in relation to child age and development. Facilitators for injury prevention included parental supervision and teaching children about injury risks. This included parents’ allowing children to learn about injury risks through controlled risk taking, using “safety rules” and supervising children to ensure that safety rules were adhered to. Adapting the home by installing safety equipment or removing hazards were also key facilitators. Some parents felt that learning about injury events through other parents’ experiences may help parents anticipate injury risks. Conclusions There are a range of barriers to, and facilitators for parents undertaking injury prevention that would be addressable during the design of home safety interventions. Addressing these in future studies may increase the effectiveness of interventions