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

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

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

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

In this paper we prove that the trapezoidal $H^{4}$ and the $H^{6}$ 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

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

Assessment of the control measures of the category A diseases of Animal Health Law: peste des petits ruminants

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 peste des petits ruminants (PPR). 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, the transmission kernels used for the assessment of the minimum radii of the protection and surveillance zones are shown. Several scenarios for which these control measures had to be assessed were designed and agreed prior to the start of the assessment. The monitoring period of 21 days was assessed as effective, except for the first affected establishments detected, where 33 days is recommended. It was concluded that beyond the protection (3 km) and the surveillance zones (10 km) only 9.6% (95% CI: 3.1–25.8%) and 2.3% (95% CI: 1–5.5%) of the infections from an affected establishment may occur, respectively. This may be considered sufficient to contain the disease spread (95% probability of containing transmission corresponds to 5.3 km). 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 PPR

A magnetic reconnection model for explaining the multi-wavelength emission of the microquasars Cyg X-1 and Cyg X-3

Recent studies have indicated that cosmic ray acceleration by a first-order Fermi process in magnetic reconnection current sheets can be efficient enough in the surrounds of compact sources. In this work, we discuss this acceleration mechanism operating in the core region of galactic black hole binaries (or microquasars) and show the conditions under which this can be more efficient than shock acceleration. In addition, we compare the corresponding acceleration rate with the relevant radiative loss rates obtaining the possible energy cut-off of the accelerated particles and also compute the expected spectral energy distribution (SED) for two sources of this class, namely Cygnus X-1 and Cygnus X-3, considering both leptonic and hadronic processes. The derived SEDs are comparable to the observed ones in the low and high energy ranges. Our results suggest that hadronic non-thermal emission due to photo-meson production may produce the very high energy gamma-rays in these microquasars.Comment: 17 pages and 7 figures. Accepted for publication in the Monthly Notices of the Royal Astronomical Society (MNRAS

B + B BARCELONA

Tématem projektu je stavba nového gymnázia v Barceloně, v místě, které je typické svými pravidelnými bloky navrženými architektem Cerdou. Stavbu jsem navrhla s respektem k tvaru parcely. Mým cílem bylo, nevytvořit jen vzdělávací budovu pro studenty, ale také kulturní a společenské centrum pro lidi z okolí. Urbanisticky je parcela koncipovaná jako město samo o sobě, které zve kolemjdoucí k návštěvě. Zůstalo příjemné měřítko pro život.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.