• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.329-339
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• 2019

The Banach spaces $m^p(\phi)$ and $n^p(\phi)$ are very important sequence spaces related to $l_p$, which were defined to fill the gaps between $l_p(1{\leq}p{\leq}{\infty})$. In this paper, we investigated the solubility of the infinite system of differential equations in $m^p(\phi)$ and $n^p(\phi)$ by proving related theorems. Moreover, one example has been included for the justification of the claim of this paper.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.45-56
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• 1995

D. H. Gottlieb [1, 2] studied the subgroups $G_n(X)$ of homotopy groups $\pi_n(X)$. In [5, 7, 10], the authors introduced subgroups $G_n(X, A)$ and $G_n^{Rel}(X, A) of \pi_n(X)$ and $\pi_n(X, A)$ respectively and showed that they fit together into a sequence $$ \cdots \to G_n(A) \longrightarrow^{i_*} G_n(X, A) \longrightarrow^{j_*} G_n^{Rel}(X, A) \longrightarrow^\partial $$ $$ \cdots \to G_1^{Rel}(X, A) \to G_0(A) \ to G_0(X, A) $$ where $i_*, j_*$ and \partial$ are restrictions of the usual homomorphisms of the homotopy sequence $$ \cdot \to^\partial \pi_n(A) \longrightarrow^{i_*} \pi_n(X) \longrightarrow^{j_*} \pi_n(X, A) \to \cdot \to \pi_0(A) \to \pi_0(X) $$.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.149-156
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• 1999

Let $\{X_n,\;n{\geq}1\}$ be a sequence of pairwise negative quadrant dependent (NQD) random variables which are stochastically dominated by X. Let $\{a_n,\;n{\geq}1\}$ and $\{b_n,\;n{\geq}1\}$ be sequences of constants such that $a_n>0$ and $0. In this note a weak law of large number of the form $({\sum}_{j=1}^na_jX_j-{\nu}_n)/b_n\rightarrow\limits^p0$ is established, where $\{{\nu}_n,\;n{\geq}1\}$ is a suitable sequence.

• Korean Journal of Microbiology
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• v.39 no.1
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• pp.1-7
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• 2003

The aim of this work was to investigate the characterization and sequence of catechol 2,3-dioxygenase isolated from Delfia sp. JK-2, which could utilize aniline as sole carbon, nitrogen and energy source. In initial experiments, several characteristics of C2,3O separated with ammonium sulfate precipitation, DEAE-sepharose were investigated. Specific activity of C2,3O was approximately 4.72 unit/mg. C2,3O demonstrated its enzyme activity to other substrates, catechol and 4-methylcatechol. The optimum temperature of C2,3O was $$Cu^{2+}$^{\circ}C$, and the optimal pH was approximately 8. Metal ions such as $Ag^{+}$, $Hg^{+}$, and $Cu^{2+}$ showed inhibitory effect on the activity of C2,3O. Molecular weight of the enzyme was determined to approximately 35 kDa by SDS-PAGE. N-terminal amino acid sequence of C2,3O was analyzed as $^{1}MGVMRIG-HASLKVMDMDA- AVRHYENV^{26}$, and exhibited high sequence homology with that of C2,30 from Pseudomonas sp. AW-2, Comamonas sp. JS765, Comamonas testosteroni and Burkholderia sp. RPO07. PCR product was amplified with the primers derived from N-terminal amino acid sequence. In this work, we found that the amino acid sequence of Delftia sp. JK-2 showed high sequence homology of C2,3O from Pseudomonas sp. AW-2 (100%) and Comamonas sp. JS765 (97%).

• Journal of Computing Science and Engineering
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• v.9 no.1
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• pp.1-8
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• 2015

Accessing and searching in a sequence of numbers are fundamental operations in computing that are encountered in a wide range of applications. One of the applications of the problem is cryptanalytic time-memory tradeoff which is aimed at a one-way function. A rainbow table, which is a common method for the time-memory tradeoff, contains elements from an input domain of a hash function that are normally sorted integers. In this paper, we present a practical indexing method for a monotonically increasing static sequence of numbers where the access and search queries can be addressed efficiently in terms of both time and space complexity. For a sequence of n numbers from a universe $U=\{0,{\ldots},m-1\}$, our data structure requires n lg(m/n) + O(n) bits with constant average running time for both access and search queries. We also give an analysis of the time and space complexities of the data structure, supported by experiments with rainbow tables.

• Journal of Microbiology
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• v.34 no.3
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• pp.274-278
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• 1996

Two peptides, MA-inv AND MA-ME, with the sequence 10-17 of maganin 2 at their-N-termini were designed and synthesized. The peptides had higher antifungal activities against Aspergilus fumigatus without hemolytic activities. The minimal inhibition concentratory (MIC) values of both peptides against A. fumigatus were 5 .mu.g/ml, whereas those of the native peptides, magainin 2 and melittin, were 10.mu.g/ml. At 3 .mu.g/ml, MA-inv and MA-ME inhibited the mycelium growth of A. fumigatus by 94.6% and 97.3% respectively, whereas magainin 2 and melittin inhibited by 62.2% and 32.4, respectively. MA-inv showed up to 80% inhibition of (1, 3)-.betha.-D-glucan synthase activity of A. fumigatus. The peptides also showed up to 80% inhibition of (1, 3)-.betha.-D glucan synthase activity of A. fumigatus. The peptides also showed antifungal activities for other fungi of Aspergillus sp. However, the antibiotic activities of MA-ME against Escherichia coli, Bacillus subtilis and Fusarium oxysporum were more effective than those of MA-inv, suggesting that the C-terminal sequences of MA-inv and MA-ME may also influence their antibiotic activities. These results suggest that the N-terminal sequence of the designed peptides, KKFGKAFV, is important for their antifungal activities against A. fumigatus and their C- terminal sequences are related to the organism selectivity.

• The KIPS Transactions:PartB
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• v.14B no.6
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• pp.461-472
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• 2007

The emphasis in genome projects has Been moving towards the sequence analysis in order to extract biological "meaning"(e.g., evolutionary history of particular molecules or their functions) from the sequence. Especially. palindromic or direct repeats that appear in a sequence have a biophysical meaning and the problem is to recognize interesting patterns and configurations of words(strings of characters) over complementary alphabets. In this paper, we propose an algorithm to identify variable length palindromic pairs(longer than a threshold), where we can allow gaps(distance between words). The algorithm is called palindrome algorithm(PA) and has O(N) time complexity. A palindromic pair consists of a hairpin structure. By composing collected palindromic pairs we build n-pair palindromic patterns. In addition, we dot some of the longest pairs in a circle to represent the structure of a DNA sequence. We run the algorithm over several selected genomes and the results of E.coli K12 are presented. There existed very long palindromic pair patterns in the genomes, which hardly occur in a random sequence.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.859-869
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• 2006

Let {$X,\;X_n;n\;{\geq}\;1$} be a sequence of ${\imath}.{\imath}.d.$ random variables which belong to the attraction of the normal law, and $X^{(1)}_n,...,X^{(n)}_n$ be an arrangement of $X_1,...,X_n$ in decreasing order of magnitude, i.e., $\|X^{(1)}_n\|{\geq}{\cdots}{\geq}\|X^{(n)}_n\|$. Suppose that {${\gamma}_n$} is a sequence of constants satisfying some mild conditions and d'($t_{nk}$) is an appropriate truncation level, where $n_k=[{\beta}^k]\;and\;{\beta}$ is any constant larger than one. Then we show that the conditionally trimmed sums obeys the self-normalized law of the iterated logarithm (LIL). Moreover, the self-normalized LIL for conditionally censored sums is also discussed.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.121-126
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• 2000

B.Djafari Rouhani and W.A.Kirk [3] proved the following theorem: Let Xbe a reflexive Banach space and $(x_n)_{n{\geq}0}$ be a nonexpansive (resp., firmly nonexpansive )sequence in X. Then the set of weak ${\omega}$-limit points of the sequence $(\frac{x_n}{n})_{n{\geq}1}$(resp., $(x_{n+1}-x_n)_{n{\geq}0$) always lies on a convex subset of a sphere centered at the origin of radius $d={\lim}_{n{\rightarrow}{\infty}}\frac{{\parallel}x_n{\parallel}}{n}$. In this paper we show that the above theorem for nonexpansive(resp., firmly nonexpansive) sequences holds in a general Banach space(resp., a strictly convex dual $X^*$).

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.915-931
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• 2023

Let F_n be the Farey sequence of order n. For S ⊆ F_n, let 𝓠(S) be the set of rational numbers x/y with x, y ∈ S, x ≤ y and y ≠ 0. Recently, Wang found all subsets S of F_n with |S| = n + 1 for which 𝓠(S) ⊆ F_n. Motivated by this work, we try to determine the structure of S ⊆ F_n such that |S| = n and 𝓠(S) ⊆ F_n. In this paper, we determine all sets S ⊆ F_n satisfying these conditions for n ∈ {p, 2p}, where p is prime.