• Journal of TMJ Balancing Medicine
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• v.2 no.1
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• pp.13-16
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• 2012

Objectives: The quadrant theorem is a theorem proposed by C. M. Guzay in the field of functional, holistic dentistry. There are not much of scientific literature on the quadrant theorem. This study briefly reviewed basic concepts of quadrant theorem. Methods: A publication by Guzay and research articles were searched and reviewed. The quadrant theorem is depicted as a series of illustrations and accompanied explanations. Results: The primary concept of the quadrant theorem was presented in 1952. Based on geometric biophysics of the occlusion and related anatomical functions, physiological pivotal axis of the mandible is analyzed to occurs at the dens (the sub-atlas area). Composite muscular activity links the mandibular posture with C1-C2, which is then linked with the spinal posture. Twenty illustrations are progressively presented on the physiognomy, occlusion, and analysis of anatomical functions. The balanced distribution of the forces gives the durability of the functions in life. Conclusions: The quadrant theorem provides a functional linkage between the mandibular posture and the upper cervical vertebrae.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.707-714
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• 1995

In this note, we extend the concepts of linearly positive quadrant dependence to the random vectors and prove a functional central limit theorem for positively quadrant dependent sequence of $R^d$-valued or separable Hilbert space valued random elements which satisfy a covariance summability condition. This result is an extension of a functional central limit theorem for weakly associated random vectors of Burton et al. to positive quadrant dependence case.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.411-418
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• 1997

In this note we prove a functional central limit theorem for nonstationary linearly positive quadrant dependent random fields. We extend it to the case of random measures.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.119-126
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• 2002

For a stationary multivariate linear process of the form X$_{t}$ = (equation omitted), where {Z$_{t}$ : t = 0$\pm$1$\pm$2ㆍㆍㆍ} is a sequence of stationary linearly positive quadrant dependent m-dimensional random vectors with E(Z$_{t}$) = O and E∥Z$_{t}$∥ $^2$< $\infty$, we prove a central limit theorem.theorem.

• Journal of Dental Rehabilitation and Applied Science
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• v.26 no.2
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• pp.89-95
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• 2010

This is the third series of article on dental occlusion and relationship to TMD and systemic symptoms. In this part of the series, it will overview the theory, treatment methods, criteria, their limitation of Chirodontics, Dental Distress Syndrome (DDS) and quadrant theorem(QT). Chirodontics has its root on Chiropractic and to maintain the 'healthy status' of TMJ with stable occlusion via dental treatment. Dental distress syndrome on the other hand believes that all the TMD has originated from reduced or collapse of posterior support and incorrect posterior vertical support had caused imbalance of the head and neck structure which eventually affect the whole body symptoms. The analysis and treatment is planned using quadrant theorem where the position of head, rotatory pivot point and occlusal plane is analyzed.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.350-357
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• 1995

In this note, we obtain the central limit theorem for linearly positive quadrant dependent random fields satisfying some assumptions on the covariances and the moment condition $supE\mid X_i\mid^3\;<{\infty}$ The proofs are similar to those of a central limit theorem for associated random field of Cox and Grimmett.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.615-623
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• 2013

In this paper we establish a central limit theorem for weighted sums of $Y_n={\sum_{i=1}^{n}}a_n,_iX_i$, where $\{a_{n,i},\;n{\in}N,\;1{\leq}i{\leq}n\}$ is an array of nonnegative numbers such that ${\sup}_{n{\geq}1}{\sum_{i=1}^{n}}a_{n,i}^2$ < ${\infty}$, ${\max}_{1{\leq}i{\leq}n}a_{n,i}{\rightarrow}0$ and $\{X_i,\;i{\in}N\}$ is a sequence of linear negatively quadrant dependent random variables with $EX_i=0$ and $EX_i^2$ < ${\infty}$. Using this result we will obtain a central limit theorem for partial sums of linear processes.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.153-158
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• 2001

A central limit theorem is obtained for stationary linear process of the form -Equations. See Full-text-, where {$\varepsilon$$_{t}$} is a strictly stationary sequence of linearly positive quadrant dependent random variables with E$\varepsilon$$_{t}$=0, E$\varepsilon$$^2$$_{t}$<$\infty$ and { $a_{j}$} is a sequence of real numbers with -Equations. See Full-text- we also derive a functional central limit theorem for this linear process.ocess.s.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.265-272
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• 1996

In this note we prove a functional central limit theorem for linearly positive quadrant dependent(LPQD) random fields, satisfying some assumption on covariances and the moment condition $\sup_{n \in \Zeta^d} E$\mid$S_n$\mid$^{2+\rho} < \infty$ for some $\rho > 0$. We also apply this notion to random measures.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.591-602
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• 2011

In this paper we establish the central limit theorem and the strong law of large numbers for linear random fields generated by identically distributed linear negative quadrant dependent random variables on $\mathbb{Z}^2$.