Differential modules defined by systems of equations
Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number
The Fourier transform of a weighted Dirac comb of beta-integers is characterized within the framework of the theory of Distributions, in particular its pure point part which corresponds to the Bragg part of the diffraction spectrum. The corresponding intensity function on this Bragg part is computed. We deduce the diffraction spectrum of weighted Delone sets on beta-lattices in the split case for the weight, when beta is the golden mean.
Digit sets of integral self-affine tiles with prime determinant
Let M ∈ Mₙ(ℤ) be expanding such that |det(M)| = p is a prime and pℤⁿ ⊈ M²(ℤⁿ). Let D ⊂ ℤⁿ be a finite set with |D| = |det(M)|. Suppose the attractor T(M,D) of the iterated function system has positive Lebesgue measure. We prove that (i) if D ⊈ M(ℤⁿ), then D is a complete set of coset representatives of ℤⁿ/M(ℤⁿ); (ii) if D ⊆ M(ℤⁿ), then there exists a positive integer γ such that , where D₀ is a complete set of coset representatives of ℤⁿ/M(ℤⁿ). This improves the corresponding results of Kenyon,...
Dihedral -tilings of the sphere by equilateral and scalene triangles. II.
Dihedral -tilings of the sphere by rhombi and triangles.
Dihedral f-tilings of the sphere by equilateral and scalene triangles. III.
Dihedral f-tilings of the sphere by equilateral and scalene triangles-I
Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles.
Dilated Sets and Characterizations of Simplexes.
Dimension of convex hyperspaces
Dimension of convex hyperspaces : nonmetric case
Directionally Euclidean structures of Banach spaces
We study Banach spaces with directionally asymptotically controlled ellipsoid-approximations of the unit ball in finite-dimensional sections. Here these ellipsoids are the unique minimum volume ellipsoids, which contain the unit ball of the corresponding finite-dimensional subspace. The directional control here means that we evaluate the ellipsoids by means of a given functional of the dual space. The term 'asymptotical' refers to the fact that we take 'lim sup' over finite-dimensional subspaces. ...
Directions De Majoration D'une Fonction Quasiconvexe Et Applications
We introduce the convex cone constituted by the directions of majoration of a quasiconvex function. This cone is used to formulate a qualification condition ensuring the epiconvergence of a sequence of general quasiconvex marginal functions in finite dimensional spaces.
Discrete and dense subgroup problems. (Problemas con subgrupos discretos y subgroupos densos.)
Discrete convexity.
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
Discrete geometry and numeration
Discrete Groups and Internal Symmetries of Icosahedral Viral Capsids
A classification of all possible icosahedral viral capsids is proposed. It takes into account the diversity of hexamers’ compositions, leading to definite capsid size.We showhowthe self-organization of observed capsids during their production results from definite symmetries of constituting hexamers. The division of all icosahedral capsids into four symmetry classes is given. New subclasses implementing the action of symmetry groups Z2, Z3 and S3 are found and described. They concern special cases...
Discrete isothermic surfaces.
Discrete minimal surface algebras.