123,223 research outputs found
New results of intersection numbers on moduli spaces of curves
We present a series of new results we obtained recently about the
intersection numbers of tautological classes on moduli spaces of curves,
including a simple formula of the n-point functions for Witten's
classes, an effective recursion formula to compute higher Weil-Petersson
volumes, several new recursion formulae of intersection numbers and our proof
of a conjecture of Itzykson and Zuber concerning denominators of intersection
numbers. We also present Virasoro and KdV properties of generating functions of
general mixed and intersections.Comment: 9 pages, a brief surve
Quarter-fraction factorial designs constructed via quaternary codes
The research of developing a general methodology for the construction of good
nonregular designs has been very active in the last decade. Recent research by
Xu and Wong [Statist. Sinica 17 (2007) 1191--1213] suggested a new class of
nonregular designs constructed from quaternary codes. This paper explores the
properties and uses of quaternary codes toward the construction of
quarter-fraction nonregular designs. Some theoretical results are obtained
regarding the aliasing structure of such designs. Optimal designs are
constructed under the maximum resolution, minimum aberration and maximum
projectivity criteria. These designs often have larger generalized resolution
and larger projectivity than regular designs of the same size. It is further
shown that some of these designs have generalized minimum aberration and
maximum projectivity among all possible designs.Comment: Published in at http://dx.doi.org/10.1214/08-AOS656 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Finding The Sign Of A Function Value By Binary Cellular Automaton
Given a continuous function , suppose that the sign of only has
finitely many discontinuous points in the interval . We show how to use
a sequence of one dimensional deterministic binary cellular automata to
determine the sign of where is the (number) density of 1s in
an arbitrarily given bit string of finite length provided that satisfies
certain technical conditions.Comment: Revtex, uses amsfonts, 10 page
Modulo Three Problem With A Cellular Automaton Solution
An important global property of a bit string is the number of ones in it. It
has been found that the parity (odd or even) of this number can be found by a
sequence of deterministic, translational invariant cellular automata with
parallel update in succession for a total of O(N^2) time. In this paper, we
discover a way to check if this number is divisible by three using the same
kind of cellular automata in O(N^3) time. We also speculate that the method
described here could be generalized to check if it is divisible by four and
other positive integers.Comment: 10 pages in revtex 4.0, using amsfont
Higher-spin Realisations of the Bosonic String
It has been shown that certain algebras can be linearised by the
inclusion of a spin--1 current. This provides a way of obtaining new
realisations of the algebras. Recently such new realisations of were
used in order to embed the bosonic string in the critical and non-critical
strings. In this paper, we consider similar embeddings in and
strings. The linearisation of is already known, and can be
achieved for all values of central charge. We use this to embed the bosonic
string in critical and non-critical strings. We then derive the
linearisation of using a spin--1 current, which turns out to be
possible only at central charge . We use this to embed the bosonic
string in a non-critical string.Comment: 8 pages. CTP TAMU-10/95
Liouville and Toda Solitons in M-theory
We study the general form of the equations for isotropic single-scalar,
multi-scalar and dyonic -branes in superstring theory and M-theory, and show
that they can be cast into the form of Liouville, Toda (or Toda-like)
equations. The general solutions describe non-extremal isotropic -branes,
reducing to the previously-known extremal solutions in limiting cases. In the
non-extremal case, the dilatonic scalar fields are finite at the outer event
horizon.Comment: Latex, 10 pages. Minor corrections to text and titl
Calculation of stress intensity factors in an isotropic multicracked plate: Part 2: Symbolic/numeric implementation
Analytical derivations of stress intensity factors (SIF's) of a multicracked plate can be complex and tedious. Recent advances, however, in intelligent application of symbolic computation can overcome these difficulties and provide the means to rigorously and efficiently analyze this class of problems. Here, the symbolic algorithm required to implement the methodology described in Part 1 is presented. The special problem-oriented symbolic functions to derive the fundamental kernels are described, and the associated automatically generated FORTRAN subroutines are given. As a result, a symbolic/FORTRAN package named SYMFRAC, capable of providing accurate SIF's at each crack tip, was developed and validated. Simple illustrative examples using SYMFRAC show the potential of the present approach for predicting the macrocrack propagation path due to existing microcracks in the vicinity of a macrocrack tip, when the influence of the microcrack's location, orientation, size, and interaction are taken into account
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