• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.63-72
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• 2004

It is known that each natural number can be written uniquely as a sum of Fibonacci numbers with suitably increasing indices. In 1960, Daykin showed that the sequence of Fibonacci numbers is the only sequence with this property. Consider here the problem of representing each natural number uniquely as a sum of positive integers taken from certain sequence allowing a fixed number, $\cal{l}\geq2$, of repetitions. It is shown that the $(\cal{l}+1)$-adic expansion is the only such representation possible.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.569-576
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• 2007

Let $\cal{H}$ be a separable, infinite dimensional, complex Hilbert space. We call "an operator $\cal{T}$ acting on $\cal{H}$ has a star moment sequence supported on a set K" when there exist nonzero vectors u and v in $\cal{H}$ and a positive Borel measure ${\mu}$ such that <$T^{*j}T^ku$, v> = ${^\int\limits_{K}}\;{{\bar{z}}^j}\;{{\bar{z}}^k}\;d\mu$ for all j, $k\;\geq\;0$. We obtain a characterization to find a representing star moment measure and discuss some related properties.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1017-1041
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• 2011

The parabolic Bergman space is the set of $L^p(\lambda)$-solution of the parabolic operator $L^{(\alpha)}$. In this paper, we study representin sequences on parabolic Bergman spaces. We establish a discrete version of the reproducing formula on parabolic Bergman spaces by using fractional derivatives of the fundamental solution of the parabolic operator.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.296-311
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• 2021

Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales. Representations of persistent homology include persistence barcodes and persistence diagrams, both of which are not straightforward to reconcile with traditional machine learning algorithms as they are sets of intervals or multisets. The problem of faithfully representing barcodes and persistent diagrams has been pursued along two main avenues: kernel methods and vectorizations. One vectorization is the Betti sequence, or Betti curve, derived from the persistence barcode. While the Betti sequence has been used in classification problems in various applications, to our knowledge, the stability of the sequence has never before been discussed. In this paper we show that the Betti sequence is unstable under the 1-Wasserstein metric with regards to small perturbations in the barcode from which it is calculated. In addition, we propose a novel stabilized version of the Betti sequence based on the Gaussian smoothing seen in the Stable Persistence Bag of Words for persistent homology. We then introduce the normalized cumulative Betti sequence and provide numerical examples that support the main statement of the paper.

• East Asian mathematical journal
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• v.40 no.1
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• pp.25-36
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• 2024

Full univariate moment problems have been studied using continued fractions, orthogonal polynomials, spectral measures, and so on. On the other hand, the truncated moment problem has been mainly studied through confirming the existence of the extension of the moment matrix. A few articles on the multivariate moment problem implicitly presented about some results of this note, but we would like to rearrange the important results for the existence of a representing measure of a moment sequence. In addition, new techniques with orthogonal polynomials will be introduced to expand the means of studying truncated moment problems.

• Korean Journal of Ichthyology
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• v.19 no.4
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• pp.257-265
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• 2007

We constructed a cDNA library of testis from olive flounder (Paralichthys olivaceus) and a total of 248 expressed sequence tag (EST) clones were generated. In order to understand the molecular compositions of the olive flounder testis organs, the expression profiles of the identified clones in the cDNA library were analyzed. Gene annotation procedures and homology searches of the sequenced ESTs were locally done by BLASTX for amino acid similarity comparisons. Of the 248 EST clones, 156 ESTs showed significant homology to previously described genes while 92 ESTs were unidentified or novel. Comparative analysis of the 156 identified ESTs showed that 6 (3.8%) clones were representing 5 unique genes identified as homologous to the previously reported olive flounder ESTs, 100 (64.1%) clones representing 94 unique genes were identified as orthologs of known genes from other organisms, and orthologs were established for 50 (32.1%) clones representing 44 genes of known sequences with unknown functions. Furthermore, the testis library showed a more even distribution of cDNA clones with relatively fewer abundant clones that tend to contribute redundant clones in EST projects; thus, the testis library can supply more unique and novel cDNA sequences in olive flounder EST project.

• Korean Journal of Ichthyology
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• v.18 no.4
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• pp.283-292
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• 2006

Expressed sequence tag (EST) analysis was conducted using a complementary DNA (cDNA) library made from the kidney mRNA of olive flounder (Paralichthys olivaceus). In the survey of 390 ESTs chosen from the kidney cDNA library, 250 ESTs showed significant homology to previously described genes while 140 ESTs were unidentified or novel. Comparative analysis of the 250 identified ESTs showed that 14 (5.6%) clones were representing 11 unique genes identified as homologous to the previously reported olive flounder ESTs, 198 (79.2%) clones representing 160 unique genes were identified as orthologs of known genes from other organisms, and orthologs were established for 38 (15.2%) clones representing 37 genes of known sequences with unknown functions. We also identified several kinds of immune associated proteins, indicating EST as a powerful method for identifying immunerelated genes of fish as well as identifying novel genes. Further studies using cDNA microarrays are needed to identify the differentially expressed transcripts after disease infection.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2000.11a
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• pp.28-31
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• 2000

We describe a hidden Markov model, HMMTIR, for general protein sequence based on the I-sites library of sequence-structure motifs. Unlike the linear HMMs used to model individual protein families, HMMSTR has a highly branched topology and captures recurrent local features of protein sequences and structures that transcend protein family boundaries. The model extends the I-sites library by describing the adjacencies of different sequence-structure motifs as observed in the database, and achieves a great reduction in parameters by representing overlapping motifs in a much more compact form. The HMM attributes a considerably higher probability to coding sequence than does an equivalent dipeptide model, predicts secondary structure with an accuracy of 74.6% and backbone torsion angles better than any previously reported method, and predicts the structural context of beta strands and turns with an accuracy that should be useful for tertiary structure prediction. HMMSTR has been incorporated into a public, fully-automated protein structure prediction server.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.3
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• pp.237-241
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• 2002

In this paper, we describe how to represent hand witten decimal digits by a sequence of one to five fuzzy sets. Each fuzzy set represents an arc segment of the digit and is a Cartesian product of four fuzzy sets; the first is fur the arc length of the segment, the second is for the arc direction, the third is fur the arc shape, and the fourth is a crisp number indicating whether it has a junction point and if it has an end point of a stroke. We show that an arbitrary pair of these sequences representing two different digits is mutually disjoint. We also show that various forms of a digit written in different styles can be represented by the same sequence of fuzzy sets and hence the deviations due to different writers can be modeled by using these fuzzy sets.

• The Journal of Engineering Geology
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• v.1 no.1
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• pp.85-108
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• 1991

Marine seismic processing is characterized by a great amount of data, several professional processing steps, and various parameters to be decided in each step. In general, adequate processing sequence and optimum parameters are obtained through test processing with sample set of data representing the whole group. The sequence and parameters are then applied in processing the whole data. In this paper, optimum processing sequence and parameters for the data acquired in Korean continental shelf are examined through test processing with real data. Finally, a good-quality migration section is produced using those sequence and parameters decided on the basis of the test results.