Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry that are asymptotic to Minkowski light cones at infinity. We develop the equations of these surfaces and examine their properties. In particular, we show that they are free of caustics for all positive values of the Kerr radial coordinate r. Useful applications include the propagation of high-frequency waves, the defin...

gives an equation for a curve that represents the moduli problem [Γ0(p)] for elliptic curves over a perfect field of characteristic p. This moduli problem associates to such an elliptic curve its finite flat subgroup schemes of rank p. A choice of such a subgroup scheme is equivalent to an isogeny from the elliptic curve with a prescribed kernel. The j-invariants of the source and target curves...

We introduce a notion of quantum cell which is invariant under linear canonical transformations. These cells, which we dub “quantum blobs”, have the essential and characteristic property that their intersection with any plane of conjugate coordinates passing through their center is an ellipse with area equal to one-half of the quantum of action. We show that this notion is particularly suitable...

This work is devoted to the coupling of two fluid models, such as two Euler systems in Lagrangian coordinates, at a fixed interface. We define coupling conditions which can be expressed in terms of continuity of some well chosen variables and then solve the coupled Riemann problem. In the present setting where the interface is characteristic, a particular choice of dependent variables which are...

We prove global well-posedness of the short-pulse equation with small initial data in Sobolev spaceHs for an integer s ≥ 2. Our analysis relies on local well-posedness results of Schäfer & Wayne [12], the correspondence of the short-pulse equation to the sine– Gordon equation in characteristic coordinates, and a number of conserved quantities of the short-pulse equation. We also prove local and...

Aiming at improving the radiating characteristics (pattern and polarization) and simplifying the design of feeding network, a new approach is applied and discussed. For uniformly excited planar antenna array, by rotating each element in its local coordinates and determining the rotation angles of the elements, the 3D radiating characteristic of the planar antenna array can be improved. The Diff...

People usually try to show themselves attractively, since attractive looks are generally preferred. We propose a new method for modifying facial data in order to improve facial beauty while retaining the original features as much as possible. Based on investigations into related work of facial attractiveness, the targets for modification in our method are small and/or unbalanced eyes, and a pro...

2-Mercapto-3-phenyl-4-quinazolinone complexes of copper is synthesized characterized on the basis of chemical properties, elemental data, magnetic susceptibility and characteristic absorption band in IR and ultra-violet absorption frequencies. The structure of complex underline the ability of Cu (I) centre to exist in distorted tetrahedral environment. The binding mode of the ligand is usual an...

This paper may be regarded as a new numerical method for the analysis of triangular thin plates using the natural area coordinates. Previous studies on the solution of triangular plates with different boundary conditions are mostly based on the Rayleigh-Ritz principle which is performed in the Cartesian coordinates. Consequently, manipulation of the geometry and numerical calculation of the int...

Recently, Umirbaev proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra Kx, y, z over a field K of characteristic 0. In particular, the well known Anick automorphism is wild. In this work, we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of...