Search results for "Conformal"
showing 10 items of 234 documents
Global Lp -integrability of the derivative of a quasiconformal mapping
1988
Let f be a quasiconformal mapping of an open bounded set U in Rn into Rn . Then f′ belongs to Lp(U) for some p > n provided that f satisfies (a) U is a uniform domain and fU is a John domain or (b) f is quasisymmetric and U satisfies a metric plumpness condition.
Enhancement of the Multipactor Threshold Inside Nonrectangular Iris
2018
Multipactor breakdown is studied inside the capacitive iris of a rectangular waveguide with a skewed slot along its longitudinal cross section. Both the iris length and height are assumed to be small compared to the electromagnetic wavelength. Therefore, the quasi-static approximation is applied so as to describe the RF field distribution inside the iris gap, whereas a 2-D model is used to analyze the electron motion. The peculiarities of RF field structure are studied using the conformal mapping approach, which shows that the electric field lines can be approximated by circular arcs when the iris length is much larger than its height. The electron motion inside the iris gap is analyzed usi…
Lie Algebras Generated by Extremal Elements
1999
We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.
Sharp capacity estimates for annuli in weighted R^n and in metric spaces
2017
We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R^n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R^n, which …
Stereotactic fractionated irradiation of optic nerve sheath meningioma: a new treatment alternative
2002
Background: Primary optic nerve sheath meningioma (ONSM) is a rare but almost invariably blinding tumour when its natural history is observed in a “wait and see” strategy. Surgery has hitherto only been advocated in case of progressive disease involving intracranial structures, as it leads to iatrogenic blindness in the overwhelming majority of cases. Therefore, treatment options bearing lesser risk of functional deterioration are highly desirable, both in cases of intracranial involvement as well as during earlier phases of the disease which are currently generally left untreated. The authors report the outcome of the largest series of patients to date treated by stereotactic fractionated …
The Potential Role of Lung Ultrasound B-Lines for Detection of Lung Radio-Induced Toxicity in Breast Cancer Patients after Radiation Therapy.
2016
Breast cancer patients exposed to doses of radiation after radiotherapy could develop toxicity to lung. Lung ultrasound (LUS) is able to detect interstitial lung disease by the evaluation of B-lines. The aim of our study was to assess the number of B-lines to diagnose lung involvement after chest radiotherapy.We measured LUS B-lines in the treated and contralateral lung of 20 breast cancer patients, 1-3 months after the end of radiotherapy and 1 year after previous LUS. The sum of the B-lines number in the 72 sites on anterior and posterior chest yielded a global B-lines score.B-lines were more numerous in treated (median: 21; 1st-3rd quartiles: 11-31) versus untreated hemithorax (median: 3…
The enveloping algebra of the Lie superalgebra osp(1,2)
1990
International audience
Star-products and phase space realizations of quantum groups
1992
It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
The new results on lattice deformation of current algebra
2008
The topic “Quantum Integrable Models” was reviewed in the literature and presented to the conferences and schools many times. Only the reports of our own have been done on quite a few occasions (see, e.g., [1], [2]). So here we shall try to present a fresh approach to the description of the ingredients of construction of integrable models. It has gradually evolved in the process of our joint work. Whereas our goal was the Sugawara construction for the lattice affine algebra (known now as the St.Petersburg algebra), (see, e.g., [1]), some technical developments happen to be new and useful for the already developed subjects. Here we shall underline this development.
Integrable models and degenerate horizons in two-dimensional gravity
1999
We analyse an integrable model of two-dimensional gravity which can be reduced to a pair of Liouville fields in conformal gauge. Its general solution represents a pair of ``mirror'' black holes with the same temperature. The ground state is a degenerate constant dilaton configuration similar to the Nariai solution of the Schwarzschild-de Sitter case. The existence of $\phi=const.$ solutions and their relation with the solution given by the 2D Birkhoff's theorem is then investigated in a more general context. We also point out some interesting features of the semiclassical theory of our model and the similarity with the behaviour of AdS$_2$ black holes.