1,330 research outputs found
Organizing information on the next generation web - Design and implementation of a new bookmark structure
The next-generation Web will increase the need for a highly organized and ever evolving method to store references to Web objects. These requirements could be realized by the development of a new bookmark structure. This paper endeavors to identify the key requirements of such a bookmark, specifically in relation to Web documents, and sets out a suggested design through which these needs may be accomplished. A prototype developed offers such features as the sharing of bookmarks between users and groups of users. Bookmarks for Web documents in this prototype allow more specific information to be stored such as: URL, the document type, the document title, keywords, a summary, user annotations, date added, date last visited and date last modified. Individuals may access the service from anywhere on the Internet, as long as they have a Java-enabled Web browser
Construction and Analysis of Projected Deformed Products
We introduce a deformed product construction for simple polytopes in terms of
lower-triangular block matrix representations. We further show how Gale duality
can be employed for the construction and for the analysis of deformed products
such that specified faces (e.g. all the k-faces) are ``strictly preserved''
under projection. Thus, starting from an arbitrary neighborly simplicial
(d-2)-polytope Q on n-1 vertices we construct a deformed n-cube, whose
projection to the last dcoordinates yields a neighborly cubical d-polytope. As
an extension of thecubical case, we construct matrix representations of
deformed products of(even) polygons (DPPs), which have a projection to d-space
that retains the complete (\lfloor \tfrac{d}{2} \rfloor - 1)-skeleton. In both
cases the combinatorial structure of the images under projection is completely
determined by the neighborly polytope Q: Our analysis provides explicit
combinatorial descriptions. This yields a multitude of combinatorially
different neighborly cubical polytopes and DPPs. As a special case, we obtain
simplified descriptions of the neighborly cubical polytopes of Joswig & Ziegler
(2000) as well as of the ``projected deformed products of polygons'' that were
announced by Ziegler (2004), a family of 4-polytopes whose ``fatness'' gets
arbitrarily close to 9.Comment: 20 pages, 5 figure
Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces
Model sets (or cut and project sets) provide a familiar and commonly used
method of constructing and studying nonperiodic point sets. Here we extend this
method to situations where the internal spaces are no longer Euclidean, but
instead spaces with p-adic topologies or even with mixed Euclidean/p-adic
topologies.
We show that a number of well known tilings precisely fit this form,
including the chair tiling and the Robinson square tilings. Thus the scope of
the cut and project formalism is considerably larger than is usually supposed.
Applying the powerful consequences of model sets we derive the diffractive
nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his
65th birthda
Monodromy of Cyclic Coverings of the Projective Line
We show that the image of the pure braid group under the monodromy action on
the homology of a cyclic covering of degree d of the projective line is an
arithmetic group provided the number of branch points is sufficiently large
compared to the degree.Comment: 47 pages (to appear in Inventiones Mathematicae
Orbit equivalence rigidity for ergodic actions of the mapping class group
We establish orbit equivalence rigidity for any ergodic, essentially free and
measure-preserving action on a standard Borel space with a finite positive
measure of the mapping class group for a compact orientable surface with higher
complexity. We prove similar rigidity results for a finite direct product of
mapping class groups as well.Comment: 11 pages, title changed, a part of contents remove
Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension
We study the combinatorial complexity of D-dimensional polyhedra defined as
the intersection of n halfspaces, with the property that the highest dimension
of any bounded face is much smaller than D. We show that, if d is the maximum
dimension of a bounded face, then the number of vertices of the polyhedron is
O(n^d) and the total number of bounded faces of the polyhedron is O(n^d^2). For
inputs in general position the number of bounded faces is O(n^d). For any fixed
d, we show how to compute the set of all vertices, how to determine the maximum
dimension of a bounded face of the polyhedron, and how to compute the set of
bounded faces in polynomial time, by solving a polynomial number of linear
programs
Parental cultural models and resources for understanding mathematical achievement in culturally diverse school settings
This paper proposes that the theoretical concept of cultural models can offer useful insights into parental involvement in their child’s mathematical achievement and the resources they use to go about gaining information in culturally diverse learning settings. This examination takes place within a cultural-developmental framework and draws on the notion of cultural models to explicate parental understandings of their child’s mathematics achievement and what resources are used to make sense of this. Three parental resources are scrutinized: (a) the teacher, (b) examination test results, and (c) constructions of child development. The interviews with 22 parents revealed some ambiguity around the interpretation of these resources by the parent, which was often the result of incongruent cultural models held between the home and the school. The resources mentioned are often perceived as being unambiguous but show themselves instead to be highly interpretive because of the diversity of cultural models in existence in culturally diverse settings. Parents who are in minority or marginalized positions tend to have difficulties in interpreting cultural models held by school, thereby disempowering them to be parentally involved in the way the school would like
Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = -1
We prove that the hyperelliptic Torelli group is generated by Dehn twists about
separating curves that are preserved by the hyperelliptic involution. This verifies a
conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel
of the Burau representation evaluated at t = −1 and also the fundamental group of
the branch locus of the period mapping, and so we obtain analogous generating sets
for those. One application is that each component in Torelli space of the locus of
hyperelliptic curves becomes simply connected when curves of compact type are added
Polydispersity and ordered phases in solutions of rodlike macromolecules
We apply density functional theory to study the influence of polydispersity
on the stability of columnar, smectic and solid ordering in the solutions of
rodlike macromolecules. For sufficiently large length polydispersity (standard
deviation ) a direct first-order nematic-columnar transition is
found, while for smaller there is a continuous nematic-smectic and
first-order smectic-columnar transition. For increasing polydispersity the
columnar structure is stabilized with respect to solid perturbations. The
length distribution of macromolecules changes neither at the nematic-smectic
nor at the nematic-columnar transition, but it does change at the
smectic-columnar phase transition. We also study the phase behaviour of binary
mixtures, in which the nematic-smectic transition is again found to be
continuous. Demixing according to rod length in the smectic phase is always
preempted by transitions to solid or columnar ordering.Comment: 13 pages (TeX), 2 Postscript figures uuencode
Hamiltonian submanifolds of regular polytopes
We investigate polyhedral -manifolds as subcomplexes of the boundary
complex of a regular polytope. We call such a subcomplex {\it -Hamiltonian}
if it contains the full -skeleton of the polytope. Since the case of the
cube is well known and since the case of a simplex was also previously studied
(these are so-called {\it super-neighborly triangulations}) we focus on the
case of the cross polytope and the sporadic regular 4-polytopes. By our results
the existence of 1-Hamiltonian surfaces is now decided for all regular
polytopes.
Furthermore we investigate 2-Hamiltonian 4-manifolds in the -dimensional
cross polytope. These are the "regular cases" satisfying equality in Sparla's
inequality. In particular, we present a new example with 16 vertices which is
highly symmetric with an automorphism group of order 128. Topologically it is
homeomorphic to a connected sum of 7 copies of . By this
example all regular cases of vertices with or, equivalently, all
cases of regular -polytopes with are now decided.Comment: 26 pages, 4 figure
- …