• International Journal of CAD/CAM
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• v.8 no.1
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• pp.29-36
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• 2009

Domain mapping is a bijective transformation of one domain to another, usually from a complicated general domain to a chosen convex domain. This is directly useful in many application problems like shape modeling, morphing, texture mapping, shape matching, remeshing, path planning etc. A new approach considering the domain as made up of structural elements, like membranes or trusses, is developed and implemented using the nonlinear finite element formulation. The mapping is performed in two stages, boundary mapping and inside mapping. The boundary of the 3-D domain is mapped to the surface of a convex domain (in this case, a sphere) in the first stage and then the displacement/distortion of this boundary is used as boundary conditions for mapping the interior of the domain in the second stage. This is a general method and it develops a bijective mapping in all cases with judicious choice of material properties and finite element analysis. The consistent global parameterization produced by this method for an arbitrary genus zero closed surface is useful in shape modeling. Results are convincing to accept this finite element structural approach for domain mapping as a good method for many purposes.

• Journal of information and communication convergence engineering
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• v.8 no.3
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• pp.312-316
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• 2010

Conformal mapping has been a familiar tool of science and engineering for generations. The methods of numerical mapping are usually classified into those which construct the map from standard domain such as the unit disk onto the 'problem domain', and those which construct the map in the reverse direction. We treat numerical conformal mapping from the unit disk onto the Jordan regions as the problem domain in this paper. The traditional standard methods of this type are based on Theodorsen integral equation. Wegmann's method is well known as a Newton-like efficient one for solving Theodorsen equation. An improved method for convergence by applying low frequency pass filter to the Wegmann's method was proposed. In this paper we propose an effective algorithm for numerical conformal mapping based on the improved method. This algorithm is able to determine the discrete numbers and initial values automatically in accordance with the given region and the required accuracy. This results come from analyzing the shape of given domain as seen in the Fourier Transform.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.458-466
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• 1998

In this work, a frequency domain method is tested numerically and experimentally to improve nonlinear model parameters using the frequency response function at the nonlinear element connected point of structure. This method extends the force-state mapping technique, which fits the nonlinear element forces with time domain response data, into frequency domain manipulations. The force-state mapping method in the time domain has limitations when applying to complex real structures because it needd a time domain lumped parameter model. On the other hand, the frequency domain method is relatively easily applicable to a complex real structure having nonlinear elements since it uses the frequency response function of each substurcture. Since this mehtod is performed in frequency domain, the number of equations required to identify the unknown parameters can be easily increased as many as it needed, just by not only varying excitation amplitude bot also selecting excitation frequency domain method has some advantages over the classical force-state mapping technique in the number of data points needed in curve fit and the sensitivity to response noise.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1419-1431
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• 2018

Let $f=h+{\bar{g}}$ be a harmonic mapping of the unit disk ${\mathbb{D}}$ with the holomorphic part h satisfying that h is injective and $h({\mathbb{D}})$ is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.1013-1018
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• 2009

Let * be an e.a.b. star operation on an integrally closed domain D, and let $K\gamma$(D, *) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping $D_{\alpha}{\mapsto}K{\gamma}(D_{\alpha},\;{\upsilon})$ is a bijection from the set {$D_{\alpha}$} of *-linked overrings of D into the set of overrings of $K{\gamma}(D,\;{\upsilon})$. This is a generalization of [5, Proposition 32.19] that if D is a Pr$\ddot{u}$fer domain, then the mapping $D_{\alpha}{\mapsto}K_{\gamma}(D_{\alpha},\;b)$ is a one-to-one mapping from the set {$D_{\alpha}$} of overrings of D onto the set of overrings of $K_{\gamma}$(D, b).

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.81-87
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• 1992

Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

• Lingua Humanitatis
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• v.1 no.1
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• pp.221-233
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• 2001

The purpose of this paper is twofold. On the one hand it takes issue with Engstrom's claim that conceptual metaphors are propositional; on the other, it aims to demonstrate that the mathematical term 'mapping' is inappropriate for the analysis of metaphors. To my mind, the propositional analysis of metaphors, a wrong analysis for that matter, originates in the notion 'mapping' I argue that partial 'mapping' between propositional meanings and metaphorical meanings is either mental or psychological, with no concomitant 'truth' value. When concept metaphors represent propositionality, they lose metaphoricity; when they obtain metaphoricity, they are free of propositionality. The mathematical terms 'mapping' and 'proposition,' it is stressed, should be avoided in the analysis of concept metaphors like 'A is B' because they are confusing when applied to linguistic expression. 1 suggest that the term 'mapping' be replaced by phrases such as 'interaction between two domains,' projection from source-domain to target domain,' or 'understanding the properties of two domains between A and B,' etc. This would amount to proposing a pragmatic or cognitive theory of metaphor.

• International Journal of CAD/CAM
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• v.11 no.1
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• pp.1-10
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• 2011

Product lifecycle management (PLM) is a new business strategy for enterprise's product R&D. A PLM system holds and maintaining the integrity of the product data produced throughout its entire lifecycle. There is, therefore, a need to build a safe and effective product data model to support PLM system. The paper proposes a domain-based product data model for PLM. The domain modeling method is introduced, including the domain concept and its defining standard along the product evolution process. The product data model in every domain is explained, and the mapping rules among these models are discussed. Mapped successively among these models, product data can be successfully realized the dynamic evolution and the historical traceability in PLM system.

• Geophysics and Geophysical Exploration
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• v.24 no.4
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• pp.149-157
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• 2021

Given that induced polarization (IP) and direct current (DC) resistivity surveys are similar in terms of data acquisition, most DC resistivity systems are equipped with a time-domain IP data acquisition function. In addition, the time-domain IP data include the DC resistivity values. As such, IP and DC resistivity data are intimately linked, and the inversion of IP data is a two-step process based on DC resistivity inversions. Nevertheless, IP surveys are rarely applied, in contrast to DC resistivity surveys, as proper inversion software is unavailable. In this study, through numerical modeling and inversion experiments, we analyze the problems with the conventional inverse mapping technique used to invert time-domain IP data. Furthermore, we propose a modified inverse mapping technique that can effectively suppress inversion artifacts. The performance of the technique is confirmed through inversions applied to synthetic IP data.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1996.06b
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• pp.72-76
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• 1996

We propose a novel algorithm for fractal video sequence coding, based on the circular prediction mapping (CPM), in which each range block is approximated by a domain block in the circularly previous frame. In our approach, the size of the domain block is set to be same as that of the range block for exploiting the high temporal correlation between the adjacent frames, while most other fractal coders use the domain block larger than the range block. Therefore the domain-range mapping in the CPM is similar to the block matching algorithm in the motion compensation techniques, and the advantages of this similarity are discussed. Also we show that the CPM can be combined with non-contractive inter-frame mapping (NCIM), improving the performance of the fractal sequence coder further. The computer simulation results on real image sequences demonstrate that the proposed algorithm provides very promising performance at low bit-rate, ranging from 40 Kbps to 250 Kbps.