918 research outputs found
Inverse zero-sum problems II
Let be an additive finite abelian group. A sequence over is called a
minimal zero-sum sequence if the sum of its terms is zero and no proper
subsequence has this property. Davenport's constant of is the maximum of
the lengths of the minimal zero-sum sequences over . Its value is well-known
for groups of rank two. We investigate the structure of minimal zero-sum
sequences of maximal length for groups of rank two. Assuming a well-supported
conjecture on this problem for groups of the form , we
determine the structure of these sequences for groups of rank two. Combining
our result and partial results on this conjecture, yields unconditional results
for certain groups of rank two.Comment: new version contains results related to Davenport's constant only;
other results will be described separatel
The optical field angle distortion calibration feasibility study for the Hubble Space Telescope fine guidance sensors
The results of an analytical study to investigate the feasibility of calibrating the Hubble Space Telescope's (HST's) fine guidance sensors (FGSs) within HST mission accuracy limits are presented. The study has two purposes: (1) to determine the mathematical feasibility of the optical field angle distortion (OFAD) calibration algorithm and (2) to confirm that the OFAD, plate scale, and FGS-to-FGS alignment calibration algorithms produced a calibration of the FGSs that satisfied mission requirements. The study concluded that the mathematical specification of the OFAD algorithm is adequate and permits a determination of the FGS calibration parameters (accurate to better than 0.003 arc-second) sufficient to meet the mission requirements. The algorithms implemented, the characteristics of the simulated data and procedures for data analysis, and the study's results are discussed. In addition, several useful techniques for improving the stability and accuracy of the OFAD solution are outlined
THE IMPACT OF "BIG-BOX" BUILDING MATERIALS STORES ON HOST TOWNS AND SURROUNDING COUNTIES IN A MIDWESTERN STATE
This paper analyzes 11 regions in a midwestern state where big-box building materials stores have opened. The zero-sum-game theory is verified; the sales gains in the host counties equaled the losses in the surrounding counties. The results are important to existing merchants and local officials in setting strategies and policies.Community/Rural/Urban Development,
Davenport constant for finite abelian groups
AbstractFor a finite abelian group G, we investigate the length of a sequence of elements of G that is guaranteed to have a subsequence with product identity of G. In particular, we obtain a bound on the length which takes into account the repetitions of elements of the sequence, the rank and the invariant factors of G. Consequently, we see that there are plenty of such sequences whose length could be much shorter than the best known upper bound for the Davenport constant of G, which is the least integer s such that any sequence of length s in G necessarily contains a subsequence with product identity. We also show that the Davenport constant for the multiplicative group of reduced residue classes modulo n is comparatively large with respect to the order of the group, which is φ(n),when n is in certain thin subsets of positive integers. This is done by studying the Carmichael’s lambda function, defined as the maximal multiplicative order of any reduced residue modulo n, along these subsets
New quests for better attitudes
During the past few years considerable insight was gained into the QUEST algorithm both as a maximum likelihood estimator and as a Kalman filter/smoother for systems devoid of dynamical noise. The new algorithms and software are described and analytical comparisons are made with the more conventional attitude Kalman filter. It is also described how they may be accommodated to noisy dynamical systems
Davenport constant for finite abelian groups with higher rank
For a finite abelian group the Davenport Constant, denoted by , is
defined to be the least positive integer such that every sequence of length
at least has a non-trivial zero-sum subsequence. A long-standing conjecture
is that the Davenport constant of a finite abelian group of rank is
. This conjecture is false in general,
but it remains to know for which groups it is true. In this paper, we consider
groups of the form where is a prime and
and provide sufficient condition when the conjecture holds
true.Comment: 11 page
A new algorithm for attitude-independent magnetometer calibration
A new algorithm is developed for inflight magnetometer bias determination without knowledge of the attitude. This algorithm combines the fast convergence of a heuristic algorithm currently in use with the correct treatment of the statistics and without discarding data. The algorithm performance is examined using simulated data and compared with previous algorithms
The Commonality of Earthquake and Wind Analysis
Earthquakes and wind loadings constitute dynamic effects that often must be considered in the design of buildings and structures. The primary purpose of this research
study was to investigate the common features of general dynamic analysis procedures
employed for evaluating the effects of wind and earthquake excitation. Another major
goal was to investigate and develop a basis for generating response spectra for wind
loading, which in turn would permit the use of modal analysis techniques for wind
analysis in a manner similar to that employed for earthquake engineering. In order to
generate wind response spectra, the wind loading is divided into two parts, a mean
load treated as a static component and a fluctuating load treated as a dynamic component.
The spectral representation of the wind loading constitutes a simple procedure
for estimating the forces associated with the dynamic component of the gusting wind.
Several illustrative examples are presented demonstrating the commonality.National Science Foundation Grants ENV 75-08456 and ENV 77-0719
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