• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.107-130
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• 2004

A $JB^{*}-triple$ is a Banach space A on which the group Aut(B) of biholomorphic automorphisms acts transitively on the open unit ball B of A. In this case, a triple product {$\cdots$} from $A\;\times\;A\;\times\;A\;to\;A$ can be defined in a canonical way. If A is also the dual of some Banach space $A_{*}$, then A is said to be a JBW triple. A projection R on A is said to be structural if the identity {Ra, b, Rc} = R{a, Rb, c, }holds. On $JBW^{*}-triples$, structural projections being algebraic objects by definition have also some interesting metric properties, and it is possible to give a full characterization of structural projections in terms of the norm of the predual $A_{*}$ of A. It is shown, that the class of structural projections on A coincides with the class of the adjoints of neutral GL-projections on $A_{*}$. Furthermore, the class of GL-projections on $A_{*}$ is naturally ordered and is completely ortho-additive with respect to L-orthogonality.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.75-78
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• 1997

We show that if a simple $C^*$-algebra A satisfies certain $K_1$-group conditions, then two unitarily equivalent projections are homotopic. Also we show that the equivalence of projections determined by a dimension function is a homotopy.

• The Journal of Korean Physical Therapy
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• v.29 no.3
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• pp.109-114
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• 2017

Purpose: The ascending reticular activating system (ARAS) is responsible for regulation of consciousness. In this study, using diffusion tensor imaging (DTI), we attempted to reconstruct the thalamocortical projections between the intralaminar thalamic nuclei and the frontoparietal cortex in normal subjects. Methods: DTI data were acquired in 24 healthy subjects and eight kinds of thalamocortical projections were reconstructed: the seed region of interest (ROI) - the intralaminar thalamic nuclei and the eight target ROIs - the medial prefrontal cortex, dorsolateral prefrontal cortex, ventrolateral prefrontal cortex, orbitofrontal cortex, premotor cortex, primary motor cortex, primary somatosensory cortex, and posterior parietal cortex. Results: The eight thalamocortical projections were reconstructed in each hemisphere and the pathways were visualized: projections to the prefrontal cortex ascended through the anterior limb and genu of the internal capsule and anterior corona radiata. Projections to the premotor cortex passed through the genu and posterior limb of the internal capsule and middle corona radiata; in contrast, projections to the primary motor cortex, primary somatosensory cortex, and posterior parietal cortex ascended through the posterior limb of the internal capsule. No significant difference in fractional anisotropy, mean diffusivity, and fiber volume of all reconstructed thalamocortical projections was observed between the right and left hemispheres (p>0.05). Conclusion: We reconstructed the thalamocortical projections between the intralaminar thalamic nuclei and the frontoparietal cortex in normal subjects. We believe that our findings would be useful to clinicians involved in the care of patients with impaired consciousness and for researchers in studies of the ARAS.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.385-397
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• 2009

We study codes over the polynomial ring ${\mathbb{F}}_q[D]$ and their projections to the finite rings ${\mathbb{F}}_q[D]/(D^m)$ and the weight enumerators of self-dual codes over these rings. We also give the formula for the number of codewords of minimum weight in the projections.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.483-492
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• 2007

In this paper, we study the map projections from pseudo-sphere $S_1^2$ onto the non-lightlike surfaces in the 3-dimensional Lorentzian space, $L^3$, with curvature zero. We show geometrical means and properties of $\mathbb{R}{\times}S_1^1-cylindrical$, $S^1{\times}L-cylindrical$ and $\mathbb{R}{\times}H_0^1-cylindrical$ projections defined on $S_1^2$ to cylinders $\mathbb{R}{\times}S_1^1,\;S^1{\times}L$ and $\mathbb{R}{\times}H_0^1$, respectively, and orthographic and stereographic projections on $S_1^2$ to Lorentzian plane, $L^2$.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• Journal of radiological science and technology
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• v.45 no.2
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• pp.117-125
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• 2022

Although stationary inverse-geometry digital tomosynthesis (s-IGDT) is able to reduce motion artifacts, image acquisition time and radiation dose, the image quality of the s-IGDT is degraded due to the truncations arisen in projections. Therefore, the effects of geometric and image acquisition conditions in the s-IGDT should be analyzed for improving the image quality and clinical applicability of the s-IGDT system. In this study, the s-IGDT images were obtained with the various X-ray source arrangement types and the various number of projections. The resolution and noise characteristics of the obtained s-IGDT images were evaluated, and the characteristics were compared with those of the conventional DT images. The s-IGDT system using linear X-ray source arrangement and 40 projections maximized the image characteristics of resolution and noise, and the corresponding system was superior to the conventional DT system in terms of image resolution. In conclusion, we expect that the s-IGDT system can be used for providing medical images in diagnosis.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1341-1360
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• 2008

In this paper we investigate the projections of bouquet graph B with two cycles. A projection of B is said to be trivial if only trivial embeddings are obtained from the projection. It is shown that, to cover all nontrivial projections of B, at least three embeddings of B are needed. We also show that a nontrivial projection of B is covered by one of some two embeddings if the image of each cycle has at most one self-crossing.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.2
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• pp.1-7
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• 1984

An algorithm, which can obtain a reconstructed image from incomplete projections in computed tomography, is proposed. The algorithm is accomplished with a simple operations of iterative correction in reconstruction - reprojection process using the measured incomplete projections the object's crossection boundary, and so on, To demonstrate effectiveness of the algotithm the results of a computer simulation is presented.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.61-74
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• 2014

This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.