• East Asian mathematical journal
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• 제40권1호
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• pp.25-36
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• 2024

Full univariate moment problems have been studied using continued fractions, orthogonal polynomials, spectral measures, and so on. On the other hand, the truncated moment problem has been mainly studied through confirming the existence of the extension of the moment matrix. A few articles on the multivariate moment problem implicitly presented about some results of this note, but we would like to rearrange the important results for the existence of a representing measure of a moment sequence. In addition, new techniques with orthogonal polynomials will be introduced to expand the means of studying truncated moment problems.

• 대한수학회보
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• 제54권1호
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• pp.299-318
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• 2017

Sextic moment problems with an infinite algebraic variety are still widely open. We study the problem with a single cubic column relation associated to 3 parallel lines in which the variety is infinite. It turns out that this specific column relation has a strong connection with moment problems that have a symmetric algebraic variety. We present more concrete solutions to some sextic moment problems with a symmetric variety.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.741-747
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• 2021

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

• 대한수학회논문집
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• 제21권3호
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• pp.433-449
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• 2006

In this paper, we present some recent developments on hyponormal operator theory and truncated Curto-Fialkow and Embry complex moment problems.

• 충청수학회지
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• 제31권4호
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• pp.487-509
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• 2018

The Truncated Moment Problem (TMP) entails finding a positive Borel measure to represent all moments in a finite sequence as an integral; once the sequence admits one or more such measures, it is known that at least one of the measures must be finitely atomic with positive densities (equivalently, a linear combination of Dirac point masses with positive coefficients). On the contrary, there are more general moment problems for which we aim to find a "signed" measure to represent a sequence; that is, the measure may have some negative densities. This type of problem is referred to as the General Truncated Moment Problem (GTMP). The Jordan Decomposition Theorem states that any (signed) measure can be written as a difference of two positive measures, and hence, in the view of this theorem, we are able to apply results for TMP to study GTMP. In this note we observe differences between TMP and GTMP; for example, we cannot have an analogous to the Flat Extension Theorem for GTMP. We then present concrete solutions to lower-degree problems.

• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.673-679
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• 2021

The moment calculation in a truncated multivariate normal distribution is a long-standing problem in statistical computation. Recently, Kan and Robotti (2017) developed an algorithm able to calculate all orders of moment under different types of truncation. This result was implemented in an R package MomTrunc by Galarza et al. (2021); however, it is difficult to use the package in practical statistical problems because the computational burden increases exponentially as the order of the moment or the dimension of the random vector increases. Meanwhile, Lee (2021) presented an efficient numerical method in both accuracy and computational burden using Gauss-Hermit quadrature. This article introduces trunmnt implementation of Lee's work as an R package. The Package is believed to be useful for moment calculations in most practical statistical problems.

• Bulletin of the Korean Chemical Society
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• 제17권4호
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• pp.385-390
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• 1996

It has been well known that the Grad thirteen-moment equations have solutions only when the Mach number is less than a limiting value for the stationary plane shock-waves. The limit of Mach number has been re-examined by including successive terms in the series expansion of distribution function. The method employed is the linear analysis of moment equations near up-streaming and down-streaming flows. For the thirteen moment case, it has been confirmed that equations have solutions only when the Mach number is less than 1.6503, which is consistent with the literature value. For the case of twenty moments, the limit of Mach number is decreased to 1.3416.

• East Asian mathematical journal
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• 제36권1호
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• pp.61-71
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• 2020

Up to the present day, the best solution we can get to the truncated moment problem (TMP) is probably the Flat Extension Theorem. It says that if the corresponding moment matrix of a moment sequence admits a rank-preserving positive extension, then the sequence has a representing measure. However, constructing a flat extension for most higher-order moment sequences cannot be executed easily because it requires to allow many parameters. Recently, the author has considered various decompositions of a moment matrix to find a solution to TMP instead of an extension. Using a new approach with the Hadamard product, the author would like to introduce more techniques related to moment matrix decompositions.

• 한국정밀공학회지
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• 제16권5호통권98호
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• pp.200-208
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• 1999

The statics relation of the Stewart platform has been investigated from the viewpoint of the forward and inverse force transmission analyses. Two eigenvalue problems corresponding to the forward and inverse force transmission analyses have been formulated. The forward force transmission analysis is to determine the ranges of the magnitudes of the force and moment generated at the end-effector for the given magnitude of linear actuator forces. In reverse order, the inverse force transmission analysis is to find the range of the magnitude of actuator forces for the given ranges of the magnitudes of the force and moment at the end-effector. The inverse force transmission analysis is important since it can provide a designer with a valuable information about how to choose the linear actuators. It has been proved that two eigenvalue problems have a reciprocal relation, which implies that solving either of the eigenvalue problems may complete the forward/inverse force transmission analysis. A numerical example has been also presented.

• 대한토목학회논문집
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• 제41권6호
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• pp.617-625
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• 2021

본 연구에서는 국내 개량형 PSC거더(Prestressed Concrete Girder)의 연속화 방식의 문제점과 연속텐던(Continuous Tendon)의 휨모멘트(Bending Moment) 특성을 분석하였다. 이 결과들을 바탕으로 본 연구에서는 거더 연속부의 부모멘트(Negative Moment) 제어에 효과적인 연속텐던 모델을 제안하였다. 이 모델은 연속텐던의 정착단을 거더 하부로 최대한 내리고, 거더 하부로 배치되는 텐던 구간을 늘려, 거더 중앙부의 긴장력 모멘트가 감소하더라도 연속지점부의 긴장력 모멘트를 증가시키는 방법이다. 이러한 연속텐던 모델은 거더 중앙부보다 연속지점부에서 대응해야 할 설계모멘트가 큰 합성 전 연속화 공법에 적합한 성능을 발휘할 수 있다.