Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians

The quartic H\'enon-Heiles Hamiltonian $H = (P_1^2+P_2^2)/2+(\Omega_1 Q_1^2+\Omega_2 Q_2^2)/2 +C Q_1^4+ B Q_1^2 Q_2^2 + A Q_2^4 +(1/2)(\alpha/Q_1^2+\beta/Q_2^2) - \gamma Q_1$ passes the Painlev\'e test for only four sets of values of the constants. Only one of these, identical to the traveling wave reduction of the Manakov system, has been explicitly integrated (Wojciechowski, 1985), while the three others are not yet integrated in the generic case $(\alpha,\beta,\gamma)\not=(0,0,0)$. We integrate them by building a birational transformation to two fourth order first degree equations in the classification (Cosgrove, 2000) of such polynomial equations which possess the Painlev\'e property. This transformation involves the stationary reduction of various partial differential equations (PDEs). The result is the same as for the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases, a general solution which is meromorphic and hyperelliptic with genus two. As a consequence, no additional autonomous term can be added to either the cubic or the quartic Hamiltonians without destroying the Painlev\'e integrability (completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200

On reductions of some KdV-type systems and their link to the quartic He'non-Heiles Hamiltonian

A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.Comment: 12 pages, 3 figures, NATO ARW, 15-19 september 2002, Elb

Kappia lobulata (Apocynaceae, Periplocoideae), a new genus from South Africa

Kappia, a new genus from the Fish River Valley in the Eastern Cape Province, South Africa is presented. At first described as Raphionacme lobulata Venter and R.L.Verh. [Venter, H.J.T., Verhoeven, R.L. 1988. Raphionacme lobulata (Periplocaceae), a new species from the eastern Cape Province, South Africa. South African Journal of Botany 54, 603–606.] based on a single specimen collected in 1936, recently discovered plants of this species proved it to be a new genus. In habit Kappia resembles Baseonema Schltr. and Rendle, Batesanthus N.E.Br., Mondia Skeels and Stomatostemma N.E.Br. However, as far as floral structure is concerned, Kappia reveals more affinity with Raphionacme Harv. DNA sequence data show Kappia to be distinct from Batesanthus, Mondia and Raphionacme Harv. and weakly supported as a sister to Stomatostemma

Feasibility of a Pulsed Ponderomotive Phase Plate for Electron Beams

We propose a scheme for constructing a phase plate for use in an ultrafast Zernike-type phase contrast electron microscope, based on the interaction of the electron beam with a strongly focused, high-power femtosecond laser pulse and a pulsed electron beam. Analytical expressions for the phase shift using the time-averaged ponderomotive potential and a paraxial approximation for the focused laser beam are presented, as well as more rigorous quasiclassical simulations based on the quantum phase integral along classical, relativistic electron trajectories in an accurate, non-paraxial description of the laser beam. The results are shown to agree well unless the laser beam is focused to a waist size below a wavelength. For realistic (off-the-shelf) laser parameters the optimum phase shift of $-\pi/2$ is shown to be achievable. When combined with RF-cavity based electron chopping and compression techniques to produce electron pulses, a femtosecond regime pulsed phase contrast microscope can be constructed. The feasibility and robustness of the scheme are further investigated using the simulations, leading to motivated choices for design parameters such as wavelength, focus size and polarization.Comment: 16 pages, 6 figure

Вплив бюджетних інструментів на економічний розвиток регіонів України

В статье проанализировано влияние бюджетных инструментов на выравнивание экономического развития регионов Украины и предложены пути по снижению дифференциации экономического развития регионов.У статті проаналізовано вплив бюджетних інструментів на вирівнювання економічного розвитку регіонів України та запропоновані шляхи по зниженню диференціації економічного розвитку регіонів.There is the influence of budget instruments on the leveling economic development of Ukrainian regions and the ways to go down differentions of regional economic development

Whole breast and regional nodal irradiation in prone versus supine position in left sided breast cancer

Background: Prone whole breast irradiation (WBI) leads to reduced heart and lung doses in breast cancer patients receiving adjuvant radiotherapy. In this feasibility trial, we investigated the prone position for whole breast + lymph node irradiation (WB + LNI). Methods: A new support device was developed for optimal target coverage, on which patients are positioned in a position resembling a phase from the crawl swimming technique (prone crawl position). Five left sided breast cancer patients were included and simulated in supine and prone position. For each patient, a treatment plan was made in prone and supine position for WB + LNI to the whole axilla and the unoperated part of the axilla. Patients served as their own controls for comparing dosimetry of target volumes and organs at risk (OAR) in prone versus in supine position. Results: Target volume coverage differed only slightly between prone and supine position. Doses were significantly reduced (P < 0.05) in prone position for ipsilateral lung (Dmean, D2, V5, V10, V20, V30), contralateral lung (Dmean, D2), contralateral breast (Dmean, D2 and for total axillary WB + LNI also V5), thyroid (Dmean, D2, V5, V10, V20, V30), oesophagus (Dmean and for partial axillary WB + LNI also D2 and V5), skin (D2 and for partial axillary WB + LNI V105 and V107). There were no significant differences for heart and humeral head doses. Conclusions: Prone crawl position in WB + LNI allows for good breast and nodal target coverage with better sparing of ipsilateral lung, thyroid, contralateral breast, contralateral lung and oesophagus when compared to supine position. There is no difference in heart and humeral head doses

(In)Complete acquisition of Turkish among Turkish German bilinguals in Germany and Turkey: an analysis of complex embeddings in narratives

Although most researchers recognise that the language repertoire of bilinguals can mvary, few studies have tried to address variation in bilingual competence in any detail. This study aims to take a first step towards further understanding the way in which bilingual competencies can vary at the level of syntax by comparing the use of syntactic embeddings among three different groups of Turkish/German bilinguals. The approach of the present paper is new in that different groups of bilinguals are compared with each other, and not only with monolingual speakers, as is common in most studies in the field. The analysis focuses on differences in the use of embeddings in Turkish, which are generally considered to be one of the more complex aspects of Turkish grammar. The study shows that young Turkish/German bilingual adults who were born and raised in Germany use fewer, and less complex embeddings than Turkish/German bilingual returnees who had lived in Turkey for eight years at the time of recording. The present study provides new insights in the nature of bilingual competence, as well as a new perspective on syntactic change in immigrant Turkish as spoken in Europe