• 제목/요약/키워드: Double Summation

검색결과 21건 처리시간 0.023초

GENERALIZATION OF WHIPPLE'S THEOREM FOR DOUBLE SERIES

  • RATHIE, ARJUN K.;GAUR, VIMAL K.;KIM, YONG SUP;PARK, CHAN BONG
    • 호남수학학술지
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    • 제26권1호
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    • pp.119-132
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    • 2004
  • In 1965, Bhatt and Pandey have obtained an analogue of the Whipple's theorem for double series by using Watson's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty five results for double series closely related to the analogue of the Whipple's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty five summation formulas closely related to the Watson's theorem on the sum of a $_3F_2$ obtained recently by Lavoie, Grondin, and Rathie.

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GENERALIZATION OF WATSON'S THEOREM FOR DOUBLE SERIES

  • Kim, Yong-Sup;Rathie, Arjun-K.;Park, Chan-Bong;Lee, Chang-Hyun
    • 대한수학회논문집
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    • 제19권3호
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    • pp.569-576
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    • 2004
  • In 1965, Bhatt and Pandey obtained the Watson's theorem for double series by using Dioxon's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty three results for double series closely related to the Watson's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty three summation formulas closely related to the Dison's theorem on the sum of a $_3F_2$ obtained in earlier work by Lavoie, Grondin, Rathie and Arora.

The Fourth and Eighth Order Mock Theta Functions

  • Srivastava, Bhaskar
    • Kyungpook Mathematical Journal
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    • 제50권1호
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    • pp.165-175
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    • 2010
  • In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to $a^2$. I presume they will be helpful in getting fundamental transformations.

CERTAIN NEW GENERATING RELATIONS FOR PRODUCTS OF TWO LAGUERRE POLYNOMIALS

  • CHOI, JUNESANG;RATHIE, ARJUN KUMAR
    • 대한수학회논문집
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    • 제30권3호
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    • pp.191-200
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    • 2015
  • Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton [13] presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation [13], the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.

삼중이온 주입기술에 의한 GaAs Varactor diode의 설계

  • 류시찬;조광래;이진구;윤현보
    • 한국통신학회:학술대회논문집
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    • 한국통신학회 1986년도 춘계학술발표회 논문집
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    • pp.206-210
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    • 1986
  • Double Ion Implantation methods are used to improve the stiffness os carrier profiles, and then the analytical solutions to Poisson`s equation are derived with summation of each carrier profile. Numerical analyses are done using profer boudary conditions and the results show that the improvement of voltage-dependent-capacitance ratio (C(!)/C(25)) is obtained up to B.6. The third ion implantation is for the enhancement of the Schottky barrier height.

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적응 반향제거기에서 퍼지규칙에 기초한 동시통화 검출 (Double Talk Detection Based on the Fuzzy Rules in Adaptive Echo Canceller)

  • 류근택;김대성;배현덕
    • 한국음향학회지
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    • 제19권7호
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    • pp.34-41
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    • 2000
  • 본 논문에서는 장거리 통신시스템의 적응 반향제거 기에서 퍼지제어 시스템에 기초한 새로운 동시통화 검출방법을 제안하였다. 이 방법에서, 동시통화 검출을 위한 퍼지추론의 두 입력 변수는 근단 신호와 실제 반향 신호가 더해진 소요 신호와 에러 신호 사이의 상호상관계수와 소요 신호와 추정된 신호 사이의 상호상관계수를 사용하였다. 퍼지 제어기에서 사다리꼴 소속함수로 퍼지화하고 if-then 추론규칙을 이용하여 max-min 합성하였으며, 합성된 결과를 무게중심법에 의하여 디퍼지화한 값으로 동시통화와 반향경로 변화 그리고 동시통화시 반향경로 변화를 검출하도록 하였다. 퍼지 동시통화 검출기는 기존의 알고리듬보다 동시통화와 반향경로 변화를 추정할 수 있었으며 동시통화시에 반향경로 변화에도 좋은 성능을 보였다.

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A NEW EXTENSION ON THE HARDY-HILBERT INEQUALITY

  • Zhou, Yu;Gao, Mingzhe
    • 대한수학회논문집
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    • 제27권3호
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    • pp.547-556
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    • 2012
  • A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter ${\lambda}$ (with ${\lambda}>1-\frac{2}{pq}$) and a weight function of the form $x^{1-\frac{2}{r}}$ (with $r$ > 1). And the constant factors of new inequalities established are proved to be the best possible. In particular, for case $r$ = 2, a new Hilbert type inequality is obtained. As applications, an equivalent form is considered.

파랑집중에 의한 다방향 극한파 생성의 효율성에 관한 실험적 연구 (An Experimental Study on Wave Focusing Efficiency in the Generation of Directional Extreme Waves)

  • 홍기용;류슈쉐;양찬규
    • 한국해양공학회지
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    • 제16권5호
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    • pp.1-6
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    • 2002
  • Extreme waves are generated in a model basin based on directional wave focusing. The targeted wave field is described by double summation method and it is applied to serpent-type wavemaker system. The extreme crest amplitude at a designed location is obtained by syncronizing the phases and focusing the directions of wave components. Two distinguished spectrums of constant wave amplitude and constant wave steepness are adapted to describe the frequency distribution of component waves. The surface profile of generated wave packets is measured by wave guage array and the effects of dominant spectral parameters governing extreme wave characteristics are investigated. It is found that frequency bandwidth, center frequency, shape of frequency spectrum and directional range play a significant role in the wave focusing. In particular, the directional effect significantly enhances the wave focusing efficiency.

상호 정보 포텐셜과 델타함수를 이용한 블라인드 알고리듬의 복잡도 개선 (Complexity Reduction of Blind Algorithms based on Cross-Information Potential and Delta Functions)

  • 김남용
    • 인터넷정보학회논문지
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    • 제15권3호
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    • pp.71-77
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    • 2014
  • 상호정보 포텐셜과 델타 함수열 (cross-information potential and Dirac-delta functions, CIPD) 을 이용한 Equalizer 알고리듬이 충격성 잡음 하에서도 채널의 ISI 제거 성능이 우수한 반면, 블록 처리 방식으로 가중치 갱신을 행하고 있어서 계산량이 많다는 단점을 갖고 있다. 이 논문에서는 CIPD 알고리듬의 계산량을 크게 줄일 수 있는 방법으로서 매 샘플 시간마다 수행하는 CIPD 알고리듬의 이중 합산을 단일 합산으로 바꿀 수 있는 방법을 제시하였다. 실험 결과에서 제안된 방식은 기존 CIPD 알고리듬과 동일한 기울기 학습 곡선을 나타냈다. 또한 충격성 잡음 상황에서도 기존 방식이 블록처리 데이터 수에 비례하는 계산량을 나타낸 반면 제안된 방식은 이와 관계없이 더 작은 계산량을 유지하면서 CIPD 알고리듬과 동일한 기울기 값을 산출해낸다.

nif-Gene Organization and Nucleotide Sequence of nifV, nifH, D, K and nifE from Frankia Strain FaCl

  • An, Chung-Sun
    • 한국동물학회:학술대회논문집
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    • 한국동물학회 1995년도 한국생물과학협회 학술발표대회
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    • pp.120-120
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    • 1995
  • The total size of the pF AR1, a genomic clone of Frankia FaCI, was estimated to be about 44Kb by summation of the individual fragment length generated by single or double restriction enzymes. Southern hybridization analyses with Azotobacter vinelandii nif-genes as probes and partial sequencing analyses of the subclones revealed that organization of the nif-gene in the FaCI strain was nifV, H, D, K, E, N, X, W, B. The organization of the structural genes for nitrogenase is the same in this Frankia strain as it is in most other nitrogen-fixing prokaryotes but the positioning of the nifV-like gene relative to the nifHDK cluster differs. A consensus nif-promoter-like sequence, found at 5' of nifH, was not detected upstream of the niJV-like gene. nifV-like gene contained a ORF of 1206 NT encoding 401 amino acids. The nucleotide sequence and deduced amino acid sequence of the gene exhibit homology value of 65% and 41% with that from A vinelandii, respectively. The putative Shine-Dargamo sequences were present preceding nitK, nifH, D, K, and nifE, and in nitK gene putative start codon GTG was detected instead of A TG. The nucleotide and amino acid sequence of niIK of FaCI showed 82% and 76% homolgy with those of Frankia HFPCc 13, respectively. Amino acid sequence of niIK showed 69% and 61% homology with those of A vinelandii, Klebsiella pnewnoniae, respectively, while that of nifE 73% and 71%, respecti vely.i vely.

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