• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.187-199
• /
• 2016

The r-ary number sequences given by $$(b^{(r)}_n)_{n{\geq}0}=\Large{\frac{1}{(r-1)n+1}}(^{rn}_n)$$ are analogs of the sequence of the Catalan numbers ${\frac{1}{n+1}}(^{2n}_n)$. Their history goes back at least to Lambert [8] in 1758 and they are of considerable interest in sequential testing. Usually, the sequences are considered separately and the generalizations can go in several directions. Here we link the various r first by introducing a new combinatorial structure related to GR trees and then algebraically as well. This GR transition generalizes to give r-ary analogs of many sequences of combinatorial interest. It also lets us find infinite numbers of combinatorially defined sequences that lie between the Catalan numbers and the Ternary numbers, or more generally, between $b^{(r)}_n$ and $b^{(r+1)}_n$.

• Journal of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.313-326
• /
• 2018

The paper studies some new ${\mathbb{C}}^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter ${\beta}$ for which these operators are bounded on mixed norm spaces L(p, q, ${\beta}$) over the unit ball in ${\mathbb{C}}^n$. Moreover, these operators are bounded projections as well, and the images of L(p, q, ${\beta}$) under the projections are found.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.459-479
• /
• 2020

In the last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed. In 2015, generator polynomial matrices and parity-check polynomial matrices of generalized quasi-cyclic (GQC) codes were investigated by Matsui. We extended these results to the noncommutative case. Exploring the dual structures of skew constacyclic codes, we present a direct way of obtaining parity-check polynomials of skew multi-twisted codes in terms of their generators. Further, we lay out the algebraic structures of skew multipolycyclic codes and their duals and we give some examples to illustrate the theorems.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.15 no.11
• /
• pp.955-961
• /
• 1990

Test statistics are obtained for detection of weak signals in signal-dependent noise using rank statistics. A generalized model is used in this paper in order to consider non-additivenoise as well as purely-additive noise. Locally optimum rank detectors for the model are shown to have similarity to locally optimum detectors and to be generalizations of these for the purely-additive noise model. A similar result is obtained for multi-input cases.

• East Asian mathematical journal
• /
• v.24 no.4
• /
• pp.317-328
• /
• 2008

In this paper we introduce ${\pi}G{\alpha}$-LC sets, ${\pi}G{\alpha}-LC^*$ sets and ${\pi}G{\alpha}-LC^{**}$ sets and different notions of generalizations of continuous functions in topological space and discuss some of their properties. Further we prove pasting lemma for ${\pi}G{\alpha}-LC^{**}$ continuous functions and ${\pi}G{\alpha}-LC^{**}$ irresolute functions.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.13 no.3
• /
• pp.270-276
• /
• 1988

The problem of detecting weak random signals is addressed in a generalized observation model incorporating multiplicative noised which has recently been introduced. It is shown that the locally optimum random-signal detectors in the multiplicative-noise model are interseting generalizations of those which would be obtained in the purely-additive noise model. Examples of explicits results for the locally optimum detector test statistics are given for two typical cases of well-known pdfs.

• Computers and Concrete
• /
• v.7 no.5
• /
• pp.437-453
• /
• 2010

CFRP has been widely used for strengthening reinforced concrete members in last decade. The strain transfer mechanism from concrete face to CFRP is a key factor for rigidity, ductility, energy dissipation and failure modes of concrete members. For these reasons, determination of the effective CFRP bonding length is the most crucial step to achieve effective and economical strengthening. In this paper, generalizations are made on effective bonding length by increasing the amount of test data. For this purpose, ANSYS software is employed, and an experimentally verified nonlinear finite element model is prepared. Special contact elements are utilized along the concrete-CFRP strip interface for investigating stress distribution, load-displacement behavior, and effective bonding length. Then results are compared with the experimental results. The finite element model found consistent results with the experimental findings.

• Honam Mathematical Journal
• /
• v.35 no.1
• /
• pp.83-92
• /
• 2013

The aim of this research paper is to provide certain generalizations of two well-known summations due to Ramanujan. The results are derived with the help of the generalized Dixon's theorem on the sum of $_3F_2$ and the generalized Kummer's theorem for $_2F_1$ obtained earlier by Lavoie et al. [3, 5]. As their special cases, we have obtained fifteen interesting summations which are closely related to Ramanujan's summation.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.177-186
• /
• 2016

For a map $f:A{\rightarrow}X$, there are concepts of $H^f$-spaces, $T^f$-spaces, which are generalized ones of H-spaces [17,18]. In general, Any H-space is an $H^f$-space, any $H^f$-space is a $T^f$-space. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain some sufficient conditions to having liftings $H^{\bar{f}}$-structures and $T^{\bar{f}}$-structures on $E_k$ of $H^f$-structures and $T^f$-structures on X respectively. We can also obtain some results about $H^f$-spaces and $T^f$-spaces in Postnikov systems for spaces, which are generalizations of Kahn's result about H-spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.1
• /
• pp.129-139
• /
• 2017

For a map $p:X{\rightarrow}A$, there are concepts of co-$H^p$-spaces, co-$T^p$-spaces, which are generalized ones of co-H-spaces [17,18]. For a principal cofibration $i_r:X{\rightarrow}C_r$ induced by $r:X^{\prime}{\rightarrow}X$ from $\imath:X^{\prime}{\rightarrow}cX^{\prime}$, we obtain some sufficient conditions to having extensions co-$H^{\bar{p}}$-structures and co-$T^{\bar{p}}$-structures on $C_r$ of co-$H^p$-spaces and co-$T^p$-structures on X respectively. We can also obtain some results about co-$H^p$-spaces and co-$T^p$-spaces in homology decompositions for spaces, which are generalizations of Golasinski and Klein's result about co-H-spaces.