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We present a new numerical scheme to study systems of non-convex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, not only from a nanoparticle but also both…
We estimate the density of tubes around the algebraic variety of decomposable univariate polynomials over the real and the complex numbers.
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…
We prove the double bubble conjecture in the three-sphere $S^3$ and hyperbolic three-space $H^3$ in the cases where we can apply Hutchings theory: 1) in $S^3$, each enclosed volume and the complement occupy at least 10% of the volume of…
In this work, a review is given of some recent results and problems involved in the determination of chemical abundances of galactic planetary nebulae, particularly regarding disk and bulge objects.
We formulate conjectural blowup formulas for Segre and Verlinde numbers on moduli spaces of sheaves on projective surfaces $S$ with $p_g(S)>0$ and $b_1(S)=0$. As applications we give a give a conjectural formula for the Donaldson invariants…
In this paper we show that the solution of the discrete Double Bubble problem over $\mathbb{Z}^2$ is at most the ceiling function plus two of the continuous solution to the Double Bubble problem, with respect to the $\ell^1$ norm, found in…
By using some simple tools from graph theory, we obtain a characterization of the planar convex bodies with Borsuk number equal to two. This result allows to give some examples of planar convex bodies with Borsuk number equal to three.…
In this work we report spectrophotometric observations of a planetary nebula sample towards the galactic bulge. A total of 45 PNe was observed and their physical parameters (electron density and temperature) were derived. Ionic abundances…
We prove the equality of three conjectural formulas for the Brumer--Stark units. The first formula has essentially been proven, so the present paper also verifies the validity of the other two formulas.
Five-dimensional spacetimes of two orbifold 3-branes are studied, by assuming that {\em the two 3-branes are spatially homogeneous, isotropic, and independent of time}, following the so-called "bulk-based" approach. The most general form of…
This article focuses on estimating distribution elements over a high-dimensional binary hypercube from multivariate binary data. A popular approach to this problem, optimizing Walsh basis coefficients, is made more interpretable by an…
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…
We extend a deformation prescription recently introduced and present some new soluble nonlinear problems for kinks and lumps. In particular, we show how to generate models which present the basic ingredients needed to give rise to dimension…
A thorough search of the OGLE-III microlensing project has more than doubled the total sample of PNe known to have close binary central stars. These discoveries have enabled close binary induced morphological trends to be revealed for the…
In this exposition-type note we present detailed proofs of certain assertions concerning several algebraic properties of the cone and cylinder algebras. These include a determination of the maximal ideals, the solution of the B\'ezout…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multi-dimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
Let n,d be positive integers, with d even (say d=2e). Let X_(n,d) denote the locus of degree d hypersurfaces in P^n which consist of two e-fold hyperplanes. We bound the regularity of the ideal of this variety. Moreover, we show that this…