• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.201-210
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• 2004

We examine a k-configuration X in P$^2$ or P$^3$ whose minimal free resolution has a non-cancelable Betti number in the last free module. We also find partial answers to the question: which Artinian O-sequences are level or not?

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.545-550
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• 2005

We find a necessary and sufficient condition that the number of some Betti numbers and shifts appear in the last free module Fn of Fx based on type vectors, where X is a finite set of points in $P^n$.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.605-614
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• 2005

We show that an Artinian O-sequence $h_0,h_1,{\cdots},h_{d-1},h_d\;=\;h_{d-1},h_{d+l}\;>\;h_d$ of codimension 3 is not level when $h_{d-1}\;=\;h_d\;=\;d + i\;and\;h{d+1}\;=\;d+(i+1)\;for\;i\;=\;1,\;2,\;and\;3$, which is a partial answer to the question in [9]. We also introduce an algorithm for finding noncancelable Betti numbers of minimal free resolutions of all possible Artinian O-sequences based on the theorem of Froberg and Laksov in [2].

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2006년도 International Symposium on GPS/GNSS Vol.1
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• pp.103-107
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• 2006

At present, most efforts tend to develop a INS which is only based linear accelerometers, because of the low cost micro-machining gyroscopes lack of the accuracy needed for precise navigation application and possible achieving the required levels of precise for micro-machining accelerometer. Although it was known in theory that a minimum of six accelerometers are required for a complete description of a rigid body motion, and any configuration of six accelerometers (except for a "measure zero " set of six-accelerometer schemes) will work. Studies on the feasible configuration of GF-INS indicate that the errors of angular velocity resolved from the six accelerometers scheme are diverged with time or have multi solutions. The angular velocity errors are induced by the biases together with the position vectors of the accelerometers, therefore, in order to treat with the problem just mentioned, researchers have been doing many efforts, such as the extra three accelerometers or the magnetometers may be taken as the reference information, the extended Kalman filter (EKF) involved to make the angular velocity errors bound and be estimated, and so on. In this paper, the typical configurations of GF-INS are introduced; for each type GF-INS described, the solutions to the angular velocity and the specific force are derived and the characteristic is indicated; one of the corresponding extend Kalman filters are introduced to estimate the angular errors; parts of the simulation results are presented to verify the validity of the equations of angular velocity and specific force and the performance of extend Kalman filter.