• 제목/요약/키워드: generalizations

검색결과 285건 처리시간 0.024초

A LINK BETWEEN ORDERED TREES AND GREEN-RED TREES

  • CHEON, GI-SANG;KIM, HANA;SHAPIR, LOUIS W.
    • 대한수학회지
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    • 제53권1호
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    • pp.187-199
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    • 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 $b^{(r+1)}_n$.

NORMAL WEIGHTED BERGMAN TYPE OPERATORS ON MIXED NORM SPACES OVER THE BALL IN ℂn

  • Avetisyan, Karen L.;Petrosyan, Albert I.
    • 대한수학회지
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    • 제55권2호
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    • pp.313-326
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    • 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.

ON GENERALIZATIONS OF SKEW QUASI-CYCLIC CODES

  • Bedir, Sumeyra;Gursoy, Fatmanur;Siap, Irfan
    • 대한수학회보
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    • 제57권2호
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    • pp.459-479
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    • 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.

비가산성 잡음에서 순위 통계량을 이용한 신호 검파 : 신호의존성 잡음과 확률 신호 검파 (Signal Detection in Non-Additive Noise Using Rank Statistics: Signal-Dependent Noise and Random Signal Detection)

  • 송익호;김상엽;김선용;손재철
    • 한국통신학회논문지
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    • 제15권11호
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    • pp.955-961
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    • 1990
  • 신호 의존성 잡음(signal-dependent noise)이 섞인 관측 모형에서 순위 통계량(rank statistic)을 써서 약한 신호를 검파하는 검파기의 검정 통계량을 얻었다. 이 논문에서는 비가선성 잡음(non-additive noise)환경을 생각하려고 순가산성 잡음 뿐만 아니라 신호 의존성 잡음도 함께 나타내는 일반화된 관측모델을 썼다. 이 모형에서 얻은 국소 최적순위(locally optimum rank) 검파기는 국소 최적(locally optimum) 검파기와 비슷한 몰을 가지고, 순가산성 잡음 모형에서의 국소 최적 순위 검파기를 일반화한 것임을 보였다. 또한 다중 입력인 때에도 비슷한 결과를 얻을 수 있음을 알 수 있었다.

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${\pi}G{\alpha}$-LOCALLY CLOSED SETS AND ${\pi}G{\alpha}$-LOCALLY CONTINUOUS FUNCTIONS

  • Rani, I. Arockia;Balachandran, K.;Janaki, C.
    • East Asian mathematical journal
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    • 제24권4호
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    • pp.317-328
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    • 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.

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적산성 잡음에서의 약한 확률적 신호 검파기의 검정통계량 (Test Statistics of a Detection Scheme for Weak Random Signals in Multiplicative Noise)

  • 송익호
    • 한국통신학회논문지
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    • 제13권3호
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    • pp.270-276
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    • 1988
  • 최근에 제안된 적산성 잡음을 포함하는 일반화된 관측 모델에서의 약한 확률적 신호검파를 다루었다. 적산성 잡음이 있을 경우, 확률적 신호를 검파하기 위한 국소최적 검파기의 검정통계량은 순수 가산성 잡음만 있을 경우의 국소최적검파기의 검정통계량이 확장된 것임을 보였다. 이는 이미 발표된 약한 알려진 신호 검파의 경우와 비슷한 결과이다. 널리 쓰이는 두 확률밀도 함수에 대해, 검정통계량을 구성하는 국소최적 비선형성들의 형태를 예시해 보였다.

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Nonlinear finite element analysis of effective CFRP bonding length and strain distribution along concrete-CFRP interface

  • Dogan, Ali Baran;Anil, Ozgur
    • Computers and Concrete
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    • 제7권5호
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    • pp.437-453
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    • 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.

ANOTHER GENERALIZATION OF A RAMANUJAN SUMMATION

  • Lee, Seung Woo;Lee, Chang Hyun;Kim, Yong Sup
    • 호남수학학술지
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    • 제35권1호
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    • pp.83-92
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    • 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.

PRINCIPAL FIBRATIONS AND GENERALIZED H-SPACES

  • Yoon, Yeon Soo
    • 충청수학회지
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    • 제29권1호
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    • pp.177-186
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    • 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.

PRINCIPAL COFIBRATIONS AND GENERALIZED CO-H-SPACES

  • Yoon, Yeon Soo
    • 충청수학회지
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    • 제30권1호
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    • pp.129-139
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    • 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.