24,497,072 research outputs found

    Complexity and integrability in 4D bi-rational maps with two invariants

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    In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most quadratic growth. Cubic growth may reflect the existence of non-elliptic fibrations of invariants, whereas we conjecture that the exponentially growing cases lack the necessary conditions for the applicability of the discrete Liouville theorem.Comment: 16 pages, 2 figure

    A multiple scales approach to maximal superintegrability

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    In this paper we present a simple, algorithmic test to establish if a Hamiltonian system is maximally superintegrable or not. This test is based on a very simple corollary of a theorem due to Nekhoroshev and on a perturbative technique called multiple scales method. If the outcome is positive, this test can be used to suggest maximal superintegrability, whereas when the outcome is negative it can be used to disprove it. This method can be regarded as a finite dimensional analog of the multiple scales method as a way to produce soliton equations. We use this technique to show that the real counterpart of a mechanical system found by Jules Drach in 1935 is, in general, not maximally superintegrable. We give some hints on how this approach could be applied to classify maximally superintegrable systems by presenting a direct proof of the well-known Bertrand's theorem.Comment: 30 pages, 4 figur

    Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

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    In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations.Comment: 27 page

    Darboux integrability of trapezoidal H4H^{4} and H6H^{6} families of lattice equations I: First integrals

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    In this paper we prove that the trapezoidal H4H^{4} and the H6H^{6} families of quad-equations are Darboux integrable systems. This result sheds light on the fact that such equations are linearizable as it was proved using the Algebraic Entropy test [G. Gubbiotti, C. Scimiterna and D. Levi, Algebraic entropy, symmetries and linearization for quad equations consistent on the cube, \emph{J. Nonlinear Math. Phys.}, 23(4):507543, 2016]. We conclude with some suggestions on how first integrals can be used to obtain general solutions.Comment: 34 page

    Assessment of the control measures of the category A diseases of Animal Health Law: Classical Swine Fever

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    EFSA received a mandate from the European Commission to assess the effectiveness of some of the control measures against diseases included in the Category A list according to Regulation (EU) 2016/429 on transmissible animal diseases (‘Animal Health Law’). This opinion belongs to a series of opinions where these control measures will be assessed, with this opinion covering the assessment of control measures for Classical swine fever (CSF). In this opinion, EFSA and the AHAW Panel of experts review the effectiveness of: (i) clinical and laboratory sampling procedures, (ii) monitoring period and (iii) the minimum radii of the protection and surveillance zones, and the minimum length of time the measures should be applied in these zones. The general methodology used for this series of opinions has been published elsewhere; nonetheless, details of the model used for answering these questions are presented in this opinion as well as the transmission kernels used for the assessment of the minimum radius of the protection and surveillance zones. Several scenarios for which these control measures had to be assessed were designed and agreed prior to the start of the assessment. Here, several recommendations are given on how to increase the effectiveness of some of the sampling procedures. Based on the average length of the period between virus introduction and the reporting of a CSF suspicion, the monitoring period was assessed as non-effective. In a similar way, it was recommended that the length of the measures in the protection and surveillance zones were increased from 15 to 25 days in the protection zone and from 30 to 40 days in the surveillance zone. Finally, the analysis of existing Kernels for CSF suggested that the radius of the protection and the surveillance zones comprise 99% of the infections from an affected establishment if transmission occurred. Recommendations provided for each of the scenarios assessed aim to support the European Commission in the drafting of further pieces of legislation, as well as for plausible ad hoc requests in relation to CSF


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    TĂ©matem projektu je stavba novĂ©ho gymnĂĄzia v Barceloně, v mĂ­stě, kterĂ© je typickĂ© svĂœmi pravidelnĂœmi bloky navrĆŸenĂœmi architektem Cerdou. Stavbu jsem navrhla s respektem k tvaru parcely. MĂœm cĂ­lem bylo, nevytvoƙit jen vzdělĂĄvacĂ­ budovu pro studenty, ale takĂ© kulturnĂ­ a společenskĂ© centrum pro lidi z okolĂ­. Urbanisticky je parcela koncipovanĂĄ jako město samo o sobě, kterĂ© zve kolemjdoucĂ­ k nĂĄvĆĄtěvě. ZĆŻstalo pƙíjemnĂ© měƙítko pro ĆŸivot.The subjekt of the project is the building of a new secondary school in Barcelona, the place, which is typical with his regular piles designed by architekt Cerda. I projected the building with the respect of the shape of site. My tendency was to not only make a educational building for students, but also the cultural and social centre for local inhabitants. The site is conceived as a small city, which invites passers-by to a visit. The pleasant scale factor stayed on.

    Subtypes of Sleep Disturbance in Parkinson's Disease Based on the Cross-Culturally Validated Korean Version of Parkinson's Disease Sleep Scale-2

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    BACKGROUND AND PURPOSE: This study aimed to determine the clinimetric properties of the Korean version of Parkinson's Disease Sleep Scale-2 (K-PDSS-2) and whether distinct subtypes of sleep disturbance can be empirically identified in patients with Parkinson's disease (PD) using the cross-culturally validated K-PDSS-2. METHODS: The internal consistency, test-retest reliability, scale precision, and convergent validity of K-PDSS-2 were assessed in a nationwide, multicenter study of 122 patients with PD. Latent class analysis (LCA) was used to derive subgroups of patients who experienced similar patterns of sleep-related problems and nocturnal disabilities. RESULTS: The total K-PDSS-2 score was 11.67±9.87 (mean±standard deviation) at baseline and 12.61±11.17 at the retest. Cronbach's α coefficients of the total K-PDSS-2 scores at baseline and follow-up were 0.851 and 0.880, respectively. The intraclass correlation coefficients over the 2-week study period ranged from 0.672 to 0.848. The total K-PDSS-2 score was strongly correlated with health-related quality of life measures and other corresponding nonmotor scales. LCA revealed three distinct subtypes of sleep disturbance in the study patients: "less-troubled sleepers," "PD-related nocturnal difficulties," and "disturbed sleepers." CONCLUSIONS: K-PDSS-2 showed good clinimetric attributes in accordance with previous studies that employed the original version of the PDSS-2, therefore confirming the cross-cultural usefulness of the scale. This study has further documented the first application of an LCA approach for identifying subtypes of sleep disturbance in patients with PD.ope

    High-Frequency Light Rectification by Nanoscale Plasmonic Conical Antenna in Point-Contact-Insulator-Metal Architecture

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    Numerous efforts have been undertaken to develop rectifying antennas operating at high frequencies, especially dedicated to light harvesting and photodetection applications. However, the development of efficient high frequency rectifying antennas has been a major technological challenge both due to a lack of comprehension of the underlying physics and limitations in the fabrication techniques. Various rectification strategies have been implemented, including metal-insulator-metal traveling-wave diodes, plasmonic nanogap optical antennas, and whisker diodes, although all show limited high-frequency operation and modest conversion efficiencies. Here a new type of rectifying antenna based on plasmonic carrier generation is demonstrated. The proposed structure consists of a resonant metallic conical nano-antenna tip in contact with the oxide surface of an oxide/metal bilayer. The conical shape allows for an improved current generation based on plasmon-mediated electromagnetic-to-electron conversion, an effect exploiting the nanoscale-tip contact of the rectifying antenna, and proportional to the antenna resonance and to the surface-electron scattering. Importantly, this solution provides rectification operation at 280 THz (1064 nm) with a 100-fold increase in efficiency compared to previously reported results. Finally, the conical rectifying antenna is also demonstrated to operate at 384 THz (780 nm), hence paving a way toward efficient rectennas toward the visible range