• Journal of the Korea Computer Industry Society
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• v.2 no.10
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• pp.1301-1308
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• 2001

In this paper, some interesting aspects of Grzegorczyk classes $\xi\sum{n}$, n$\geq$0 & $\sum$= { 1, 2 } of word-theoretic primitive recursive functions are observed including the classes of its corresponding predicates ($\xi\sum{n}$)* In particular, the small classes $\xi\sum{n}$($n\leq2$) are very incomparable to the corresponding small classes $\xi\sum{n}$ where $\xi\sum{n}$ is the number-theoretic Grzegorczyk classes. As one of some interesting aspects of the small classes, we show that the equivalence problem in $\xi\sum{0}$is undecidable.

• Journal of Sasang Constitutional Medicine
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• v.19 no.1
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• pp.90-97
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• 2007

1. Objectives and Methods This study was done to investigate the relationships of Sound parameters between Liver Heat Symptom and Esophagus Symptom of Taeumin using PSSC(Phonetic System of Sasang Constitution) in a sentence. Experimental Participants were 20 Korean adult males including, each 10 Liver Heat Symptom and Esophagus Symptom of Taeumin. 2. Results In Pitch segment, APQ segment and Shimmer segment, there were no significant differences between Liver Heat Symptom and Esophagus Symptom of Taeumin. In Octave segment, there were significant differences in Octave 1, Octave 3, Octave 4, Octave 6 of Liver Heat Symptom of Taeumin were significantly high compared with Esophagus Symptom of Taeumin. In Energy segment, FreQ Domain Total Sum / cnt(0), 0k-2k Total Sum,0k-2k sum dev., 2k-4k Total Sum, 2k-4k sum dev., A# Tot E, B__TOT_E, C__TOT_E, C# Tot E, D__TOT_E, A sum dev., A# sum dev., B sum dev., C sum dev., C# sum dev., Dsum dev., D# sum dev., E sum dev., F sum dev., F# sum dev., G sum dev., G# sum dev. of Liver Heat Symptom of Taeumin were significantly high compared with Esophagus Symptom of Taeumin. In Voice Recording time segment, Total Voice Recording Time, Voice Recording Time, Divide By Time3, Divide By Energy10, Total Unit, Max Unit Position, U_0 TO 3 of Liver Heat Symptom of Taeumin were significantly high compared with Esophagus Symptom of Taeumin. 3. Conclusion From above result, there is the postbility of efficiency quide constitutional sx. of Taeumin by Voice characteristics. More Soeumin, Soyangin and Taeyangin Symptoms are needed to determine Sasang Constitution using PSSC and to make PSSC effective.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.395-407
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• 2010

In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.273-286
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• 2011

Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equations $${cf\left({\displaystyle\sum_{i=1}^n\;xi}\right)+{\displaystyle\sum_{i=2}^nf}{\left(\displaystyle\sum_{i=1}^n\;x_i-(n+c-1)x_j\right)}\\ {=(n+c-1)\;\left(f(x_1)+c{\displaystyle\sum_{i=2}^n\;f(x_i)}+{\displaystyle\sum_{i in fuzzy Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.571-577
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• 2009

The notion of subdirect sum and direct sum in WFI-algebras is introduced, and several properties are investigated.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.1C
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• pp.20-25
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• 2006

In this paper, the performance of Tree-LDPC code is presented based on the min-sum algorithm with scaling and the asymptotic performance in the water fall region is shown by density evolution. We presents that the Tree-LDPC code show a significant performance gain by scaling with the optimal scaling factor which is obtained by density evolution methods. We also show that the performance of min-sum with scaling is as good as the performance of sum-product while the decoding complexity of min-sum algorithm is much lower than that of sum-product algorithm. The Tree-LDPC decoder is implemented on a FPGA chip with a small interleaver size.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.10C
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• pp.936-941
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• 2003

Density evolution was developed as a method for computing the capacity of low-density parity-check(LDPC) codes under the sum-product algorithm [1]. Based on the assumption that the passed messages on the belief propagation model can be approximated well by Gaussian random variables, a modified and simplified version of density evolution technique was introduced in [2]. Recently, the min-sum algorithm was applied to the density evolution of LDPC codes as an alternative decoding algorithm in [3]. Next question is how the min-sum algorithm is combined with a Gaussian approximation. In this paper, the capacity of various rate LDPC codes is obtained using the min-sum algorithm combined with the Gaussian approximation, which gives a simplest way of LDPC code analysis. Unlike the sum-product algorithm, the symmetry condition [4] is not maintained in the min-sum algorithm. Therefore, the variance as well as the mean of Gaussian distribution are recursively computed in this analysis. It is also shown that the min-sum threshold under a gaussian approximation is well matched to the simulation results.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.315-318
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• 2006

In this paper we present the simple updating formulas for a sum of product and a sum of cross product when a new value is added on or a specific value is eliminated from the original data. The sample variance and correlation for the new data set are derived by new computing formulas. Any statistic which is a function of the sum of product and a sum of cross product also can be updated by proposed method even though the original data is not available.

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.179-188
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• 2022

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form $$f\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$ and $$f\(\sum\limits_{i=1}^{l}x_i\)+\sum\limits_{j=1}^{l}f\(-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i\)=(l+1)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

• Radiation Oncology Journal
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• v.25 no.4
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• pp.233-241
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• 2007

Purpose: We examined the effect of the dual EGFR/HER2 tyrosine kinase inhibitor, GW572016, on EGFR/HER2 receptor phosphorylation, inhibition of downstream signaling and radiosensitization in either an EGFR or HER2 overexpressing human breast cancer xenograft. Materials and Methods: We established SCID mice xenografts from 4 human breast cancer cell line that overexpressed EGFR or HER 2 (SUM 102, SUM 149, SUM 185, SUM 225). Two series of xenografts were established. One series was established for determining inhibition of the EGFR/HER2 receptor and downstream signaling activities by GW572016. The other series was established for determining the radiosensitization effect of GW572016. Inhibition of the receptor and downstream signaling proteins were measured by the use of immunoprecipitation and Western blotting. For determining the in vivo radiosensitization effect of GW572016, we compared tumor growth delay curves in the following four treatment arms: a) control; b) GW572016 alone; c) radiotherapy (RT) alone; d) GW572016 and RT. Results: GW572016 inhibited EGFR, HER2 receptor phosphorylation in SUM 149 and SUM 185 xenografts. In addition, the p44/42 MAPK (ERK 1/2) downstream signaling pathway was inactivated by GW572016 in the SUM 185 xenograft. In the SUM 225 xenograft, we could not observe inhibition of HER2 receptor phosphorylation by GW572016; both p44/42 MAPK (Erk1/2) and Akt downstream signal protein phosphorylation were inhibited by GW572016. GW572016 inhibited growth of the tumor xenograft of SUM 149 and SUM 185. The combination of GW572016 and RT enhanced growth inhibition greater than that with GW572016 alone or with RT alone in the SUM 149 xenograft. GW572016 appears to act as an in vivo radiosensitizer. Conclusion: GW572016 inhibited EGFR/HER2 receptor phosphorylation and downstream signaling pathway proteins. GW572016 modestly inhibited the growth of tumor in the SUM 185 xenograft and showed radiosensitization in the SUM 149 xenograft. Our results suggest that a better predictor of radiation response would be inhibition of a crucial signaling pathway than inhibition of a receptor.