49,551 research outputs found
On the optimality of the Arf invariant formula for graph polynomials
We prove optimality of the Arf invariant formula for the generating function
of even subgraphs, or, equivalently, the Ising partition function, of a graph.Comment: Advances in Mathematics, 201
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ALPHA_I, Remote Manufacturing, and Solid Freeform Fabrication
Alpha_l is a nonuniform rational B-spline (NURBs) based solid modeling system that
has been developed at the University of Utah over the past 10 years. In addition to being
useful in modeling objects that are described by simple rotation and extrusion operations,
the real power of Alpha_l is demonstrated in the modeling of complex parts with sculptured
surfaces. For the past several years, a major research thrust has been to use Alpha_l to
semi-automatically generate process plan information and numerical control code to manufacture
mechanical parts directly from the models. A long term goal is to support an on-line
remote manufacturing facility for producing prototype parts. Recently, a 3D Systems stereo
lithography machine has been added to the advanced manufacturing laboratory. The stereo
lithography process and other SFF techniques are of particular interest for supporting a
remote manufacturing facility in that these processes are inherently much safer than numerically
controlled machining. Special Alpha_l interfaces including a new slicing algorithm
are being developed for the SFF machine use. By generating a SFF part directly from
its NURBs description, Alpha_l should facilitate the manufacture of complex parts while
providing smoother surfaces.Mechanical Engineerin
Universal attraction force-inspired freeform surface modeling for 3D sketching
This paper presents a novel freeform surface modeling method to construct a freeform surface from 3D sketch. The approach is inspired by Newton’s universal attraction force law to construct a surface model from rough boundary curves and unorganized interior characteristic curves which may cross the boundary curves or not.
Based on these unorganized curves, an initial surface can be obtained for conceptual design and it can be improved later in a commercial package. The approach has been tested with examples and it is capable of dealing with unorganized design curves for surface modeling
Ribbon Graphs, Quadratic Differentials on Riemann Surfaces, and Algebraic Curves Defined over
It is well known that there is a bijective correspondence between metric
ribbon graphs and compact Riemann surfaces with meromorphic Strebel
differentials. In this article, it is proved that Grothendieck's correspondence
between dessins d'enfants and Belyi morphisms is a special case of this
correspondence. For a metric ribbon graph with edge length 1, an algebraic
curve over and a Strebel differential on it is constructed. It is also
shown that the critical trajectories of the measured foliation that is
determined by the Strebel differential recover the original metric ribbon
graph. Conversely, for every Belyi morphism, a unique Strebel differential is
constructed such that the critical leaves of the measured foliation it
determines form a metric ribbon graph of edge length 1, which coincides with
the corresponding dessin d'enfant.Comment: Higher resolution figures available at
http://math.ucdavis.edu/~mulase
Equivariant embeddings of rational homology balls
We generalise theorems of Khodorovskiy and Park-Park-Shin, and give new
topological proofs of those theorems, using embedded surfaces in the 4-ball and
branched double covers. These theorems exhibit smooth codimension-zero
embeddings of certain rational homology balls bounded by lens spaces.Comment: 27 pages, 25 figures. V2: Improved exposition incorporating referee's
suggestions. Accepted for publication in Q. J. Math. V3: minor correction
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