• Title/Summary/Keyword: indeterminate

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Kaplansky-type Theorems, II

  • Chang, Gyu-Whan;Kim, Hwan-Koo
    • Kyungpook Mathematical Journal
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    • v.51 no.3
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    • pp.339-344
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    • 2011
  • Let D be an integral domain with quotient field K, X be an indeterminate over D, and D[X] be the polynomial ring over D. A prime ideal Q of D[X] is called an upper to zero in D[X] if Q = fK[X] ${\cap}$ D[X] for some f ${\in}$ D[X]. In this paper, we study integral domains D such that every upper to zero in D[X] contains a prime element (resp., a primary element, a t-invertible primary ideal, an invertible primary ideal).

The Factor Domains that Result from Uppers to Prime Ideals in Polynomial Rings

  • Dobbs, David Earl
    • Kyungpook Mathematical Journal
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    • v.50 no.1
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    • pp.1-5
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    • 2010
  • Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P; L the quotient field of D; F an algebraic closure of L; ${\alpha}$ ${\in}$ L[X] a monic irreducible polynomial; ${\xi}$ any root of in F; and Q = ${\alpha}$>, the upper to P with respect to ${\alpha}$. Then R[X]/Q is R-algebra isomorphic to $D[{\xi}]$; and is R-isomorphic to an overring of D if and only if deg(${\alpha}$) = 1.

Automated design of optimum longitudinal reinforcement for flexural and axial loading

  • Tomas, Antonio;Alarcon, Antonio
    • Computers and Concrete
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    • v.10 no.2
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    • pp.149-171
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    • 2012
  • The problem of a concrete cross section under flexural and axial loading is indeterminate due to the existence of more unknowns than equations. Among the infinite solutions, it is possible to find the optimum, which is that of minimum reinforcement that satisfies certain design constraints (section ductility, minimum reinforcement area, etc.). This article proposes the automation of the optimum reinforcement calculation under any combination of flexural and axial loading. The procedure has been implemented in a program code that is attached in the Appendix. Conventional-strength or high-strength concrete may be chosen, minimum reinforcement area may be considered (it being possible to choose between the standards ACI 318 or Eurocode 2), and the neutral axis depth may be constrained in order to guarantee a certain sectional ductility. Some numerical examples are presented, drawing comparisons between the results obtained by ACI 318, EC 2 and the conventional method.

The six geometries revisited

  • Kang, Austin;Musilli, Marino;Farella, Mauro
    • The korean journal of orthodontics
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    • v.50 no.5
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    • pp.356-359
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    • 2020
  • Forces and moments delivered by a straight wire connecting two orthodontic brackets are statically indeterminate and cannot be estimated using the classical equations of static equilibrium. To identify the mechanics of such two-bracket systems, Burstone and Koenig used the principles of linear beam theory to estimate the resulting force systems. In the original publication, however, it remains unclear how the force systems were calculated because no reference or computational details on the underlying principles have been provided. Using the moment carry-over principle and the relative angulation of the brackets, a formula was derived to calculate the relative moments of the two brackets. Because of the moment equilibrium, the vertical forces that exist as a force-couple on the two brackets can also be calculated. The accuracy of the proposed approach can be validated using previously published empirical data.

Clinical Application of PET in Abdominal Cancers (소화기 암에서 PET의 임상적 의의)

  • Choi, Chang-Woon
    • The Korean Journal of Nuclear Medicine
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    • v.36 no.1
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    • pp.39-45
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    • 2002
  • Clinical application of positron emission tomography (PET) is rapidly increasing for the defection and staging of cancer at whole-body studios performed with the glucose analogue tracer 2-[fluorine-18]fluoro-2-deoxy-D-glucose (FDG). Although FDG PET cannot match the anatomic resolution of conventional imaging techniques in the liver and the other abdominal organs, it is particularly useful for identification and characterization of the entire body simultaneously. FDG PET can show foci of metastatic disease that may not be apparent at conventional anatomic imaging and can aid in the characterizing of indeterminate soft-tissue masses. Most abdominal cancer requires surgical management. FDG PET can improve the selection of patients for surgical treatment and thereby reduce the morbidity and mortality associated with inappropriate surgery. FDG PET is also useful for the early detection of recurrence and the monitoring of therapeutic effect. The abdominal cancers, such as gastroesophageal cancer, colorectal cancer, liver cancer and pancreatic cancer, are common malignancies in Korea, and PET is one of the most promising and useful methodologies for the management of abdominal cancers.

Dynamic nonlinear member failure propagation in truss structures

  • Malla, Ramesh B.;Nalluri, Butchi B.
    • Structural Engineering and Mechanics
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    • v.9 no.2
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    • pp.111-126
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    • 2000
  • Truss type structures are attractive to a variety of engineering applications on earth as well as in space due to their high stiffness to mass ratios and ease of construction and fabrication. During the service life, an individual member of a truss structure may lose load carrying capacity due to many reasons, which may lead to collapse of the structure. An analytical and computational procedure has been developed to study the response of truss structures subject to member failure under static and dynamic loadings. Emphasis is given to the dynamic effects of member failure and the propagation of local damage to other parts of the structure. The methodology developed is based on nonlinear finite element analysis technique and considers elasto-plastic material nonlinearity, postbuckling of members, and large deformation geometric nonlinearity. The pseudo force approach is used to represent the member failure. Results obtained for a planar nine-bay indeterminate truss undergoing sequential member failure show that failure of one member can initiate failure of several members in the structure.

Identification of reinforced concrete beam-like structures subjected to distributed damage from experimental static measurements

  • Lakshmanan, N.;Raghuprasad, B.K.;Muthumani, K.;Gopalakrishnan, N.;Basu, D.
    • Computers and Concrete
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    • v.5 no.1
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    • pp.37-60
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    • 2008
  • Structural health monitoring of existing infrastructure is currently an important field of research, where elaborate experimental programs and advanced analytical methods are used in identifying the current state of health of critical and important structures. The paper outlines two methods of system identification of beam-like reinforced concrete structures representing bridges, through static measurements, in a distributed damage scenario. The first one is similar to the stiffness method, re-cast and the second one to flexibility method. A least square error (LSE) based solution method is used for the estimation of flexural rigidities and damages of simply supported, cantilever and propped cantilever beam from the measured deformation values. The performance of both methods in the presence of measurement errors is demonstrated. An experiment on an un-symmetrically damaged simply supported reinforced concrete beam is used to validate the developed method. A method for damage prognosis is demonstrated using a generalized, indeterminate, propped cantilever beam.

Utility of PET in Gynecological Cancer (부인암에서 양전자방출단층촬영의 이용)

  • Choi, Chang-Woon
    • 대한핵의학회:학술대회논문집
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    • 2002.05a
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    • pp.9-13
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    • 2002
  • Clinical application of positron emission tomography (PET) is rapidly increasing for the detection and staging of cancer at whole-body studios performed with 2-[fluorine-18]fluoro-2-deoxy-D-glucose (FDG). Although many cancers can be detected by FDG-PET, there has been limited clinical experience with FDG-PET for the defection of gynecological cancers including malignancies in uterus and ovary. FDG-PET can show foci of metastatic disease that may not be apparent at conventional anatomic imaging and can and in the characterization of indeterminate soft-tissue masses. Most gynecological cancers need to surgical management. FDG-PET can improve the selection of patients for surgical treatment and thereby reduce the morbidity and mortality associated with inappropriate surgery. FDG-PET is also useful for the early detection of recurrence and the monitoring of therapeutic effect. In this review, I discuss the clinical feasibility and limitations of this imaging modality in patients with gynecological cancers.

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ON ALMOST PSEUDO-VALUATION DOMAINS, II

  • Chang, Gyu Whan
    • Korean Journal of Mathematics
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    • v.19 no.4
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    • pp.343-349
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    • 2011
  • Let D be an integral domain, $D^w$ be the $w$-integral closure of D, X be an indeterminate over D, and $N_v=\{f{\in}D[X]{\mid}c(f)_v=D\}$. In this paper, we introduce the concept of $t$-locally APVD. We show that D is a $t$-locally APVD and a UMT-domain if and only if D is a $t$-locally APVD and $D^w$ is a $PvMD$, if and only if D[X] is a $t$-locally APVD, if and only if $D[X]_{N_v}$ is a locally APVD.

KRONECKER FUNCTION RINGS AND PRÜFER-LIKE DOMAINS

  • Chang, Gyu Whan
    • Korean Journal of Mathematics
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    • v.20 no.4
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    • pp.371-379
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    • 2012
  • Let D be an integral domain, $\bar{D}$ be the integral closure of D, * be a star operation of finite character on D, $*_w$ be the so-called $*_w$-operation on D induced by *, X be an indeterminate over D, $N_*=\{f{\in}D[X]{\mid}c(f)^*=D\}$, and $Kr(D,*)=\{0\}{\cup}\{\frac{f}{g}{\mid}0{\neq}f,\;g{\in}D[X]$ and there is an $0{\neq}h{\in}D[X]$ such that $(c(f)c(h))^*{\subseteq}(c(g)c(h))^*$}. In this paper, we show that D is a *-quasi-Pr$\ddot{u}$fer domain if and only if $\bar{D}[X]_{N_*}=Kr(D,*_w)$. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr$\ddot{u}$fer *-multiplication domain if and only if $D[X]_{N_*} = Kr(D,*_w)$.