• Honam Mathematical Journal
• /
• v.46 no.3
• /
• pp.365-377
• /
• 2024

In this paper, we give some sums involving the generalized harmonic numbers H^r_n (σ) and the (q, r)-binomial coefficient $\left({L \atop k}\right)_{q,r}$ by using Euler's transform. For example, for (c, r) ∈ ℤ⁺ × ℝ⁺, $${\sum_{n=0}^{\infty}}{\sum_{k=0}^{n}}\,(-1)^k\,\left({n+r \atop n-k}\right)\frac{c^{n+1}H^{r-1}_k({\sigma})}{(n+1)(1+c)^{n+1}}=-(c+{\frac{1}{{\sigma}}})\,{\ln}\,(1+c{\sigma})+c,$$ and $${\sum_{k=0}^{n}}\left({n \atop k}\right)\left({L \atop k}\right)_{2,r}={\sum_{j=0}^{n}}{\sum_{k=0}^{j}}(-1)^k\left({j-k+2L+r \atop j-k}\right)\left({r \atop n-j}\right)\left({L \atop k}\right)_2,$$ where σ is appropriate parameter, H^r_n (σ) is the generalized hyperharmonic number of order r and $\left({L \atop k}\right)_q$ is the q-binomial coefficient.

• Kyungpook Mathematical Journal
• /
• v.52 no.4
• /
• pp.413-431
• /
• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

• Journal of Power System Engineering
• /
• v.12 no.4
• /
• pp.26-31
• /
• 2008

The evaporation heat transfer coefficient and pressure drop of R-22 and R-407C in a small diameter copper tube were investigated experimentally. The main components of the refrigerant loop are a receiver, a compressor, a mass flow mete, a condense and a double pipe type evaporate (test section). The test section consists of a smooth copper tube of 4.3 mm inner diameter. The refrigerant mass fluxes were varied from 100 to $300[kg/m^{2}s]$ and the saturation temperature of evaporator were $5[^{\circ}C]$. The evaporation heat transfer coefficients of R-22 and R-407C increase with the Increase in mass flux and vapor quality. The evaporation heat transfer coefficient of R-22 is about $7.3\sim47.1%$ higher than that of R-407C. The evaporation pressure drop of R-22 and R-407C increase with the increase of mass flux. The pressure drop of R-22 is about $8\sim20%$ higher than that of R-407C.

• Journal of the Korean Institute of Gas
• /
• v.12 no.3
• /
• pp.43-49
• /
• 2008

The evaporation heat transfer coefficient and pressure drop of R-22 and R-407C in horizontal copper tubes were investigated experimentally. The main components of therefrigerant loop are a receiver, a compressor, a mass flow meter, a condenser and a double pipe type evaporator (test section). The test section consists of a smooth copper tube of 4.3 mm and 6.4 mm inner diameter. The refrigerant mass fluxes were varied from 100 to $300[kg/m^2s]$ and the saturation temperature of evaporator were 5 [$^{\circ}C$]. The evaporation heat transfer coefficients of R-22 and R-407C rise with the increase in mass flux and vapor quality. The evaporation heat transfer coefficient of R-22 for inner diameter tube of 4.3 mm and 6.4 mm is about $7.3{\sim}47.1%$ and $5.68{\sim}46.6%$ higher than that of R-407C, respectively.

• Microbiology and Biotechnology Letters
• /
• v.39 no.1
• /
• pp.93-96
• /
• 2011

It has been shown that a nucleotide substitution at position 770 in Escherichia coli 16S rRNA, which is implicated in forming the evolutionary conserved B2c intersubunit bridge, has a detrimental effect on ribosome function. In order to isolate second-site revertants that complement ribosomes containing C770G, we performed a random mutagenesis of the 16S rRNA gene and selected clones that could produce more CAT protein translated by specialized ribosome. One of the clones contained two nucleotide substitutions at positions 569 and 904 (C569G and U904C) and these mutations partially complemented the loss of protein-synthesis ability caused by C770G. Further studies using the isolated revertant will provide information about which part of 16S rRNA is interacting with C770 and the consequence of the structure formed by these interactions in the process of protein synthesis.

• 한국정보디스플레이학회:학술대회논문집
• /
• 2008.10a
• /
• pp.113-116
• /
• 2008

The active layer thickness and curing condition dependent performance of an organic thin film transistor (OTFT) with inkjetted organic semiconductor (OSC) layer is studied The best performance of the OTFT was found when the thickness of ose was ~120 nm cured at $60^{\circ}C$. The performance enhancement of the OTFT with inkjetted OSC layer was discussed by comparing the OTFT with spin-coated ose layer.

• Journal of Energy Engineering
• /
• v.15 no.3 s.47
• /
• pp.166-173
• /
• 2006

R134a is considered as an alternative refrigerant to R22 for air conditioners. An experimental investigation was made to study the characteristics of the heat transfer and pressure drop for R134a flowing in a fin-and-tube heat exchanger used for commercial air-conditioning units. Experiments were carried out under the conditions of inlet refrigerant temperature of $60^{\circ}C$ and refrigerant mass fluxes of $150,\;200,\;and\;250\;kg/m^{2}s$. The inlet air has dry bulb temperature or $35^{\circ}C$, relative humidity of 40% and air velocity varying from 0.68 to 1.6 m/s. Experiments show that air velocity decreased by 5.9% is needed for R134a than that of R22 while pressure drop for R134a was $18.1{\sim}20.4%$ higher than that of R22 for the degree of subcooling $5^{\circ}C$. The results are useful in designing more compact and effective condensers for various refrigeration and air conditioning systems using refrigerant R134a.

• The Korean Journal of Mycology
• /
• v.21 no.1
• /
• pp.16-22
• /
• 1993

Morphological and cultural characteristics of fungi causing rice sclerotial diseases were examined. Hyphal widths of R. solani and R. oryzae were same and ranged $6.0-12.0\;{\mu}m$ with average $9.0\;{\mu}m$, the widest among those of the sclerotial fungi examined. Hyphal width of R. oryzae sativae ranged $6.0-9.0{\mu}m$ with average $7.4{\mu}m$. Hyphal width of R. cerealis was the narrowest among those of Rhizoctonia species examined, and the same was hyphal width of S. oryzae among those of Sclerotium species. Nuclear staining by HCL-Giemsa method showed that R. solani and R. oryzae had many nuclei within one hyphal cell, S. oryzae one nucleus, and the other sclerotial fungi mostly two nuclei. The nuclear number of R. solani was the largest, which ranged 2-17 with average 6.3. Average size of sclerotia of the sclerotial fungi except S. hydrophilum and S. oryzae produced in lesions ranged 1.0-2.0mm. Average size of sclerotia of S. hydrophilum and S. oryzae was 0.5mm and 0.24mm, respectively. Sclerotia of R. solani and R. oryzae produced in culture were more variable in size and larger than those produced in lesions. However, the sclerotial sizes of the other sclerotial fungi produced in culture were almost the same as those produced in lesions. Sclerotial colors of sclerotial fungi produced in lesions were similar to those produced in culture, but sclerotial shapes of some sclerotial fungi exhibited somewhat difference between the sclerotia produced in lesions and in culture. Optimum temperature for mycelial growth of R. cerealis was $23^{\circ}C$, and that of the other sclerotial fungi ranged from $27\;to\;33^{\circ}C$. Maximum temperature for mycelial growth of some sclerotial fungi was as high as $41^{\circ}C$, while that of R. cerealis was as low as $31^{\circ}C$. Minimum temperature for mycelial growth of R. cerealis was $2^{\circ}C$, and that of the other sclerotial fungi ranged from $6\;to\;10^{\circ}C$.

• Bulletin of the Korean Chemical Society
• /
• v.5 no.6
• /
• pp.237-240
• /
• 1984

2,2'-Diaminobiphenyl platinum (II) complexes of optically active trans-1,2-diaminocyclohexane and 1,2-diaminopropane, [Pt(S,S-chxn)(dabp)]Cl2, [Pt(R,R-chxn)(dabp)]$C_{12}$, [Pt(S-pn)(dabp)]$C_{l2}$, and [Pt(R-pn)(dabp)]Cl2, where S,S-chxn and R,R-chxn are, respectively, S and R isomers of trans-1,2-diaminocyclohexane, and S-pn and R-pn are, respectively, S and R isomers of 1,2-diaminopropane, and dabp the 2,2'-diaminobipheny, have been prepared. The dabp ligand has been found to take the $=delta$ conformation in the S,S-chxn and S-pn platinum (II) complexes, while it takes the $\lambda$ conformation in the R,R-chxn and R-pn platinum (II) complexes.

• Korean Journal of Poultry Science
• /
• v.33 no.1
• /
• pp.33-39
• /
• 2006

This study was conducted to investigate the feeding effect of $bio-silverlite^{(R)}$ on growth performance, organ phenomenon and cecum microflora in broiler chicks. The $bio-silverlite^{(R)}$ was made by an ion exchange between illite and $silver(Ag^+)$. There were four treatment groups: negative control group(non-treatment), antibiotic supplement group (positive control), 0.5% $bio-silverlite^{(R)}$ supplment group and 1.5% $bio-silverlite^{(R)}$ supplement group. Total 200 birds was assigned for this five replication tests, allocating 10 birds into each treatment. Experimental diets were formulated on isocalories and isonitrogen for the whole experimental period. Body weight gain was higher in antibiotic supplementation (+C) and $bio-silverlite^{(R)}$ supplement groups(S 0.5% and 51.5%) than the negative control group(-C), and feed efficiency was significantly enhanced with increase of the level of $bio-silverlite^{(R)}$ supplement. The length of small intestine was longer in +C than in -C and $bio-silverlite^{(R)}$ supplement groups (P<0.05), and the weight of small intestine was proportional to the level of $bio-silverlite^{(R)}$ supplement. Crop weight was lower in $bio-silverlite^{(R)}$ supplement group than in -C and +C groups (P<0.05), and the cecum weight was heavier in $bio-silverlite^{(R)}$ supplementation group. Intestinal villi height was longer in 51.5% group at 3 weeks and 6 weeks of age than in -C and +C groups. With the respect of the formation of intestinal microflora, TBC and CBC was not affected by age and feed additive. However, the number of LAB was slightly higher in $bio-silverlite^{(R)}$ supplement group than in -C and +C groups.