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Showing 1 to 17 of 17 for “"LATTICE POINTS"”.
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Lattice points in disks and strongly convex domains
… best bound for the error between the number of lattice points inside a disk and that disks area, otherwise known as the lattice point discrepancy. First we state some of the required definitions and properties from Fourier analysis that will be used throughout. In particular, we establish …
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Asymptotically optimal shapes for counting lattice points and eigenvalues
… we aim to maximize the number of first-quadrant lattice points under a concave (or convex) curve with respect to reciprocal stretching in the coordinate directions. The optimal domain is shown to be asymptotically balanced, meaning that the optimal stretch factor approaches 1 as the ""radius"" …
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Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions
… study questions concerning the distribution of lattice points in dimensions two and higher. We give asymptotic formulas for the number of integer lattice points of fixed index visible from certain admissible sets. We also study the shape of the body $PA_1, \dots, PA_k$ when the lattice points …
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Counting elliptic curves of bounded Faltings height
… this to recast the problem as one of counting lattice points in an unbounded region in R2 defined by transcendental equations, and understand this region well enough to give a formula for the number of these lattice points.
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Contributions to the theory of Ehrhart polynomials
… for any rational d-polytope P, the number of lattice points, i(P,m), in the mth dilated polytope mP is always a quasi-polynomial of degree d in m, whose period divides the least common multiple of the denominators of the coordinates of the vertices of P. In particular, if P is an integral …
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Minimal Volume K-Point Lattice D-Simplices
… minimal volume occurs if and only if the P is a lattice simplex (of dimension d ≠ 2) whose interior lattice points are collinear with a vertex of P. We then show that there can only be one such class of simplices with this property. Interestingly, this statement is not true for d = 2, and …
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Boundaries of K-types in discrete series
… that the collection is very close to a set of lattice points in a noncompact convex polyhedron. In this paper we shall describe a recursive algorithm for finding the boundary facets of this polyhedron.
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Structured vector quantizers in image coding
… interest in the structured VQ schemes, such as lattice-based VQ and multi-stage VQ. The objective of this thesis is to devise techniques to reduce the complexity of vector quantizers. In order to reduce the codebook search complexity and memory requirement, a universal Gaussian codebook in a …
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An Optimized Multiple Right-Hand Side Dslash Kernel for Intel Xeon Phi
<p>Lattice quantum chromodynamics (LQCD) stands unique as the only computationally tractable, non-perturbative, and model-independent quantum field theory of the strong nuclear force. The computational core of LQCD is the Wilson Dslash operator, a nearest neighbor stencil operator summing …
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Correlations of sequences modulo one and statistics of geometrical objects associated to visible points
… and Farey-Ford parabolas associated to visible lattice points. As the names suggest, these objects are constructed based on the relation between visible points/Farey fractions and their geometrical interpretation in the form of Ford circles. We study the distribution of moments of various …
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Mixed volumes of hypersimplices, root systems and shifted young tableaux
… by the diagonal entries of these tableaux and lattice points of the (standard) associahedron. Using similar techniques, we generalize this result to arbitrary shifted shapes.
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Infinitely Often Dense Bases and Geometric Structure of Sumsets
… geometrically. Assume A is a finite set of lattice points and h*D=h˙x:x∈conv A is a full dimensional polytope. Then we'll see that there is a constant rho with the following property: for any positive integer h, any integral point in the polytope h * Delta, whose distance to the boundary …
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Equivariant Index on Toric Contact Manifolds
… to an explicit formula for the index as a sum of lattice points related to the moment cone C.
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Model X-ray scattering behaviour of arrays of structured cylinders.
… function, the swelling factor (Y), and the lattice interference function. The behaviour of the scattering function is considered as the cylinder's structure (electron density distribution) is systematically varied from the case of a solid cylinder to that of a thin shell. A ten stage …
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Size-binary Zincblende: A Colloidal Approach to Omnidirectional Photonic Bandgaps
… opal (8.0%, ε = 16). Symmetry reduction at the lattice points of the diamond structure (via a basis of spheres of different size) opens a bandgap between the fifth and sixth bands in the direct structure. This gap has only previously been reported in a handful of related structures. Our …
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Laser scanner jitter characterization, page content analysis for optimal rendering, and understanding image graininess
… spatial statistics. First, the disparity between lattice points generated by the periodicity matrix, and centroids of dot clusters are considered. Next, the area of dot clusters in regular and irregular halftone textures is considered. Third, the compactness of dot clusters in the regular and …
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ΠΡΩΤΟΙ ΑΡΙΘΜΟΙ ΚΑΙ ΚΥΚΛΟΤΟΜΙΑ-ΠΡΩΤΟΙ ΑΡΙΘΜΟΙ ΤΗΣ ΜΟΡΦΗΣ Χ + (Χ+1)
THE PRESENT DOCTORAL THESIS CONSISTS OF THREE CHAPTERS, NAMELY: CHAPTER 1: CRITERIA AND FORMULAE FOR PRIME NUMBERS. CHAPTER 2: PRIMES AND CYCLOTOMY. CHAPTER3: PRIME AND COMPOSITE NUMBERS OF THE FORM X2+(X+1)2. IN CHAPTER 1 NEW PRIMALITY CRITERIA ARE OBTAINED, ALONG WITH NEW FORMULAE FOR THE …