• Kyungpook Mathematical Journal
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• 제51권4호
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• pp.419-427
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• 2011

In this paper, making use of transformation due to S. N. Singh [21], an at-tempt has been made to establish certain results involving basic bilateral hypergeometric series and continued fractions.

• 대한수학회보
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• 제57권2호
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• pp.345-354
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• 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of ₂𝜓₂ series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.

• 대한수의학회지
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• 제29권2호
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• pp.11-18
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• 1989

This study was undertaken to obtain basic data of the sternal development in Korean native cattle from the earliest sternal formation to the ossification using histological and histochemical methods. Thrity three sterna were collected from a series of embryos and fetuses ranging from 11 to 225mm (estimated age 37~120days) in crown rump length. The bilateral sternal bars were observed in the 2nd group(CRL 21~3mm) of Korean cattle embryos. Those bars initiated to be fused in the 3rd group (CRL 31~4mm) and completed in the 7th group(CRL 71~80mm). The ossification centers were detected in the 8th group(CRL 81~90mm) also bilateral ossification centers were found in the same group. The typical epiphyseal plates, endochondral bone and calcium deposit were found in the 9th group(CRL 91~100mm). Osteocytes, osteoblasts, osteoclasts and myeloid cells appeared in ossification centers in the 10th group(more than CRL 101mm). The alcianophility responded markedly in the 9th group that was decreased and showed slightly positive reaction in territorial matrix of the 10th group. Marked positive reaction to PAS was observed in bony trabeculae in the 10th group. The positive reaction to calcium deposit by trichrome stain was observed initially in the hypertrophied zone of epiphyseal plate in the 9th group and was conspicuous in the calcified zone of epiphyseal plate in the 10th group. The 1st positive reaction to the von Kossa stain was observed in the 9th group.