Related papers: Explicit elliptic estimates for nowhere vanishing …
On Riemannian signature conformal 4-manifolds we give a conformally invariant extension of the Maxwell operator on 1-forms. We show the extension is in an appropriate sense injectively elliptic, and recovers the invariant gauge operator of…
Any three circles theorem for discrete harmonic functions must contain an inherent error term. In this paper we find the sharp error term in an $L^2$-three circles theorem for harmonic functions defined in $\Zb^2$. The proof is highly…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
For a singular and symmetric discrete memoryless channel with positive dispersion, the third-order term in the normal approximation is shown to be upper bounded by a constant. This finding completes the characterization of the third-order…
The Schrodinger equation for an electron on the surface of an elliptical torus in the presence of a constant azimuthally symmetric magnetic field is developed. The single particle spectrum and eigenfunctions as a function of magnetic flux…
By using the complete solution of the Milburn equation (beyond the Lindblad form that it is generally used) that describes intrinsic decoherence, we study the decaying dynamics of a displaced harmonic oscillator. We calculate the…
We use the sum-of-squares theorem from number theory to construct eigenfunctions of the Laplacian on the $d$-dimensional torus, $d \geq 2$, which vanish to any prescribed order at some point. These functions are then applied to provide a…
We consider the N-vortex problem on a ellipsoid of revolution. Applying standard techniques of classical perturbation theory we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these…
We derive a numerical approximation of the Laplace-Beltrami operator on compact surfaces embedded in $\mathbb{R}^3$ with an axial symmetry. To do so we use a noncommutative Laplace operator defined on the space of finite dimensional…
The paper addresses the problem of a a semi-infinite plane crack along the interface between two 3D isotropic half-spaces. Two methods of solution have been considered in the past: Lazarus and Leblond (1998) applied the "special" method by…
In this paper, we establish $L^{\infty}$ and $L^{p}$ estimates for solutions of some polyharmonic elliptic equations via the Morse index. As far as we know, it seems to be the first time that such explicit estimates are obtained for…
We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…
We calculate the index and nullity of the three orientable focal manifolds of isoparametric hypersurfaces in spheres with three distinct principal curvatures. It turns out that the index is equal to the dimension of the ambient Euclidean…
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our…
A practical high-accuracy relativistic method of atomic structure calculations for univalent atoms is presented. The method is rooted in the coupled-cluster formalism and includes non-perturbative treatment of single and double excitations…
A well-known result by Lindenstrauss is that any two-dimensional normed space can be isometrically imbedded into $L_1(0,1)$. We provide an explicit form of a such an imbedding. The proof is elementary and self-contained. Applications are…
We study the vanishing of Massey products of order at least $3$ for absolutely irreducible smooth projective curves over a perfect field with coefficients in $\mathbb{Z}/\ell$. We mainly focus on elliptic curves, for which we obtain a…
We provide a proof of effective uniformization for nearly round 2-spheres, utilizing an identity related to the third-order differential of the conformal factor. This identity is connected to the geometry of the embedded spacelike surface…
Elliptically symmetric distributions are a classic example of a semiparametric model where the location vector and the scatter matrix (or a parameterization of them) are the two finite-dimensional parameters of interest, while the density…
We construct several sequences of asymptotically optimal definite quadrature formulae of fourth order and evaluate their error constants. Besides the asymptotical optimality, an advantage of our quadrature formulae is the explicit form of…