• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.733-747
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• 2021

Recently, Kim-Kim introduced Lah-Bell polynomials and numbers, and investigated some properties and identities of these polynomials and numbers. Kim studied Lah-Bell polynomials and numbers of degenerate version. In this paper, we study degenerate Lah-Bell polynomials arising from differential equations. Moreover, we investigate the phenomenon of scattering of the zeros of these polynomials.

• Clinical and Experimental Reproductive Medicine
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• v.28 no.2
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• pp.147-153
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• 2001

Objective: The present study was performed to investigate the efficiency of partial laser assisted hatching (p-LAH; lased 1/2 ZP width from ZP edge) on hatching of mouse blastocysts. Methods: We used non-contact $1.48{\mu}m$ diode laser (MTM, Switzland) to create a precise hole on zona pellucida. 2-cell embryos were collected from the mouse (ICR) oviduct at 48 hours after hCG administration. Collected 2-cell embryos were cultured in the P-1 medium supplemented with 0.4% BSA. For experiments, embryos at 8-cell stage were used after $20{\sim}22$ hours in culture. After conventional (c-LAH) or partial laser assisted hatching, the embryos were further cultured in P-1 medium supplemented with 0.4% BSA for 3 days. To compare efficiency of complete and partial laser assisted hatching, hatching rate, hatching time and blastocyst diameter and zona pellucida thickness at hatching time were investigated. Embryos were examined every 12 hours. Blastocyst diameter and zona pellucida thickness at hatching time were measured with an ocular micrometer. Results: Hatching rates of p-LAH group (84.2%) was significantly higher than that of control group (39.3%), but there was no difference between the p-LAH (84.2%) and c-LAH (91.2%). p-LAH group was hatched 12 hours earlier than control group, but hatched 12 hours later than c-LAH group. The diameter of blastocyst at hatching time of p-LAH group ($113.1{\pm}6.4{\mu}m$) was smaller than that of control group ($122.2{\pm}5.0{\mu}m$), but larger than that of c-LAH group ($102.2{\pm}2.7{\mu}m$). Zona pellucida thickness at hatching time of p-LAH group ($6.4{\pm}0.9{\mu}m$) was thicker than that of control group ($4.5{\pm}1.5{\mu}m$), but thinner than that of c-LAH group ($10.0{\pm}0.8{\mu}m$). Conclusion: These results suggest that p-LAH may maintains the cell arrangement of early embryos to ensure successful development and prevent precocious hatching of blastocyst when compare to c-LAH and conventional (acidic tyrode) AH. Thus, p-LAH may provide a valuable and effective AH technique for human ART program.

• Clinical and Experimental Reproductive Medicine
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• v.44 no.4
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• pp.193-200
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• 2017

Objective: This study was conducted to investigate the efficacy of laser-assisted hatching (LAH) and various vitrification times for embryonic development and blastocyst cell numbers. Methods: First, 2-cell and 8-cell embryos were collected by flushing out the oviducts. In the control groups, they were vitrified for 8 or 10 minutes without LAH. The LAH groups underwent quarter laser zona thinning-assisted hatching before vitrification (4, 6, and 8 minutes or 4, 7, and 10 minutes, respectively). After incubation, double-immunofluorescence staining was performed. Results: The hatched blastocyst rate 72 hours after the 2-cell embryos were thawed was significantly higher in the 2LAH-ES8 group (33.3%) than in the other groups (p< 0.05). In the control-8 group ($22.1{\pm}4.6$), the cell number of the inner cell mass was higher than in the LAH groups (p< 0.05). The number of trophectoderm cells was higher in the 2LAH-ES6 group ($92.8{\pm}8.9$) than in the others (p< 0.05). The hatched blastocyst rate 48 hours after the 8-cell embryos were thawed was higher in the 8LAH-ES4 group (45.5%) than in the other groups, but not significantly. The inner cell mass cell number was highest in the 8LAH-ES7 group ($19.5{\pm}5.1$, p< 0.05). The number of trophectoderm cells was higher in the 8LAH-ES10 group ($73.2{\pm}12.1$) than in the other groups, but without statistical significance. Conclusion: When LAH was performed, 2-cell embryos with large blastomeres had a lower hatched blastocyst rate when the exposure to vitrification solution was shorter. Conversely, 8-cell embryos with small blastomere had a higher hatched blastocyst rate when the exposure to vitrification solution was shorter.

• Journal of the Korean Ceramic Society
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• v.39 no.1
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• pp.68-73
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• 2002

The dielectric properties and synthesis of $LaAlO_3$ ceramics from mixtures of $La_2O_3-Al_2O_3$ (LAO) and $La_2O_3-Al(OH)_3$(LAH) via grinding process were investigated. The single phase $LaA1O_3$of LAO and LAH powders were formed at $1300^{\circ}C$ and $1000^{\circ}C$, respectively. A non-reacted $La_2O_3$ existing in calcined powder was changed to La(OH)$_3$by moisture in the air, and their samples were worse than those of the samples made from a $LaA1O_3$single phase powder. The densities of LAO samples sintered at 150$0^{\circ}C$ for 4 h and LAH samples sintered at $1400^{\circ}C$ for 4 h were 97.3% and 98.3% of theory density, respectively. Grains of LAH sample showed uniformity and their sizes were 0.75 ${\mu}{\textrm}{m}$, and LAO samples showed non-uniformity and their sizes were 4-5 ${\mu}{\textrm}{m}$. Dielectric constant of LAO and LAH samples were the same value (≒22), however dielectric loss of LAH sample (0.0003) were lower than that of LAO sample(0.001)due to grain size.

• Clinical and Experimental Reproductive Medicine
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• v.41 no.2
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• pp.68-74
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• 2014

Objective: In search of an ideal method of assisted hatching (AH), we compared the effects of conventional micropipette-AH and laser-AH on the blastocyst formation rate (BFR) and blastocyst cell numbers. Methods: Four-to five-week-old ICR female mice were paired with male mice after superovulation using Pregnant mare's serum gonadotropin (PMSG) and hCG. The two-cell embryos were flushed from the oviducts of female mice. The retrieved two-cell embryos underwent one of five AH procedures: single mechanical assisted hatching (sMAH); cross mechanical assisted hatching (cMAH); single laser assisted hatching (sLAH); quarter laser assisted hatching (qLAH); and quarter laser zona thinning assisted hatching (qLZT-AH). After 72 hours incubation, double immunofluorescence staining was performed. Results: Following a 72 hours incubation, a higher hatching BFR was observed in the control, sMAH, cMAH, and sLAH groups, compared to those in the qLAH and qLZT-AH groups (p<0.05). The hatched BFR was significantly higher in the qLAH and qLZT-AH groups than in the others (p<0.05 for each group). The inner cell mass (ICM) was higher in the control and sMAH group (p<0.05). The trophectoderm cell number was higher in the cMAH and qLAH groups (p<0.05). Conclusion: Our results showed that the hatched BFR was higher in groups exposed the the qLAH and qLZT-AH methods compared to groups exposed to other AH methods. In the qLAH group, although the total cell number was significantly higher than in controls, the ICM ratio was significantly lower in than controls.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.21-41
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• 2020

In this paper, we establish an explicit formula for r-Dowling numbers in terms of r-Whitney Lah and r-Whitney numbers of the second kind. This is a generalization of the Qi formula for Bell numbers in terms of Lah and Stirling numbers of the second kind. Moreover, we define the q, r-Dowling numbers, q, r-Whitney Lah numbers and q, r-Whitney numbers of the first kind and obtain several fundamental properties of these numbers such as orthogonality and inverse relations, recurrence relations, and generating functions. Hence, we derive an analogous Qi formula for q, r-Dowling numbers expressed in terms of q, r-Whitney Lah numbers and q, r-Whitney numbers of the second kind.

• Reproductive and Developmental Biology
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• v.28 no.1
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• pp.29-36
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• 2004

The objective of this study was to investigate the effects of amino acid supplementation of oocyte maturation medium on 1st polar body(PB) extrusion, embryo development and blastocsyt cell number. In experiment 1, Cumulus oocyte complexes(COCs) were matured in in vitro maturation(IVM) medium supplemented with 1, 2, or 4-fold of 10 $\mu$l/ml MEM non-essential amino acid(NEAA) and 20 Park, $\mu$ l/ml BME essential amino acid(EAA). The PB extrusion rate of oocytes matured in 1-fold amino acid group was significantly higher than that matured in medium without amino acid (p＜0.05), but it was decreased by the increase of the dosage of amino acid. There were no difference in the percentage of embryos reaching 2-cell, 8-cell and blastocyst in all treatments. The number of trophectoderm(TE) cells and total cell number of blastocysts were highest in 2-fold amino acid group, and the number of inner cell mass(ICM) cells was increased by the increase of the dosage of amino acid. In experiment 2, COCs were matured in IVM medium with 1, 5, or 10 mg/ml lactalbumin hydrolysate(LAH). The PB extrusion rate of oocytes matured in medium with 5 mg LAH was significantly higher than that matured in medium with 1 mg LAH (p＜0.05). The development rate to the blastocyst stage was significantly higher in non-supplement and 1 mg LAH group than in 5 mg and 10 mg LAH group (p＜0.05). The number of TE cells and total cell number did not differ among treatment groups, but the number of ICM cells was increased by the increase of LAH supplement. These results suggested that the supplement of certain group of amino acid in IVM medium effective on the quality of blastocyst, and further studies will be accompany with the search of new sources of amino acid used for the use of in vitro embryo production.

• Proceedings of the Korean Society of Developmental Biology Conference
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• 2003.10a
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• pp.115-115
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• 2003

아미노산은 수정란의 체외생산에 있어서 배발달에 유효하게 작용한다. 이러한 이유로 체외배양 단계에 아미노산 첨가에 관한 보고는 많지만, 체외성숙 단계에서의 아미노산 효과와 관련된 보고는 소수이다. 본 실험에서는 먼저 체외성숙 배지에 NEAA와 EAA군들의 첨가 농도가 PB 출현율, 배발달율 그리고 생산된 배반포의 세포수에 미치는 영향과 더불어 새로운 아미노산원으로 LAH의 효과를 검토하였다. 체외성숙을 위한 난포란은 도축 한우 난소에서 2-8mm의 가시난포로부터 회수하였다. 체외성숙용 배지는 10% FBS가 첨가된 CRlaa 용액을 사용하였고, 실험1에서는 NEAA와 EAA(20$\mu l$/ml)군을 각각 $\times$l (NEAA:10$\mu l$/ml, EAA:20$\mu l$/ml), $\times$2 및 $\times$4를, 실험2에서는 LAH를 각각 1, 5 및 10 mg/ml를 첨가하였다. 체외수정은 fer-TALP 용액을, 체외배양은 CRlaa 용액을 배양 2일째까지는 0.3% BSA를, 그 이후에는 10% FBS와 난관상피세포를 첨가하여 사용하였다. 그리고 배양 8일째 확장배반포의 세포수를 조사하기 위하여 이중형광염색을 실시하였다. 통계분석은 $X^2$-test를 이용하였다. 실험 1에서 NEAA와 EAA 첨가 농도에 따른 PB 출현율은 $\times$l 첨가군(46.6%)이 대조군(29.9%)에 비하여 유의적으로 높았다. 수정을, 8세포기 및 배반포까지 발달율은 비슷한 경향이었으나, $\times$l 첨가군이 가장 높았다. 한편 ICM 세포수가 아미노산 첨가 농도의 높을수록 증가하는 경향이었고, 특히 $\times$4 첨가군($23.9 \mu 3.9$)이 대조군($14.8 \mu 2.5$)에 비하여 유의적(P<0.05)으로 높았다. 실험 2에서 LAH 첨가에 따른 핵성숙율은 5mg 첨가군, 배반포까지 발달율은 1mg 첨가군(25.9%)이 각각 가장 높았다. 배양 8일째 배반포의 세포수에 있어서 총세포수와 TE 세포수는 차이가 없었으나, ICM 세포수가 l0mg 첨가군에서 가장 높았다. 본 실험 결과에서 체외성숙 배지에 NEAA와 EAA 첨가가 배발달율에는 효과가 없었지만, 첨가농도의 증가에 따라 ICM 세포수가 증가하였다. 한편 체외성숙 배지에 LAH 첨가는 첨가 농도가 높을수록 배발달율은 낮았지만 ICM 세포수는 증가하였다.

• Clinical and Experimental Reproductive Medicine
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• v.45 no.3
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• pp.129-134
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• 2018

Objective: In frozen and thawed embryos, the zona pellucida (ZP) can be damaged due to hardening. Laser-assisted hatching (LAH) of embryos can increase the pregnancy rate. This study compared thinning and drilling of the ZP before frozen embryo transfer (FET). Methods: Patients were randomly allocated into two groups for LAH using thinning or drilling on day 2 after thawing. Twenty-five percent of the ZP circumference and 50% of the ZP thickness was removed in the thinning group, and a hole $40{\mu}m$ in diameter was made in the drilling group. Results: A total of 171 in vitro fertilization/intracytoplasmic sperm injection FET cycles, including 85 cycles with drilling LAH and 86 cycles with thinning LAH, were carried out. The thinning group had a similar ${\beta}$-human chorionic gonadotropin-positive rate (38.4% vs. 29.4%), implantation rate (16.5% vs. 14.4%), clinical pregnancy rate (36.0% vs. 25.9%), miscarriage rate (5.8% vs. 2.4%), ongoing pregnancy rate (30.2% vs. 23.5%), and multiple pregnancy rate (7.0% vs. 10.6%) to the drilling LAH group. There were no significant differences in pregnancy outcomes between subgroups defined based on age (older or younger than 35 years) or ZP thickness (greater or less than $17{\mu}m$) according to the LAH method. Conclusion: The present study demonstrated that partial ZP thinning or drilling resulted in similar outcomes in implantation and pregnancy rates using thawed embryos, irrespective of women's age or ZP thickness.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.417-423
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• 2019

In the paper, by virtue of the $Fa{\grave{a}}$ di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag-Leffler polynomials.