• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1007-1025
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• 2015

Let $\mathbb{N}_0$ be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., $P(n,l)=\{(x_1,x_2,{\cdots},x_l){\in}\mathbb{N}^l_0\;:\;x_1+x_2+{\cdots}+x_l=n\}$. For any element $u=(u_1,u_2,{\cdots},u_l){\in}P(n,l)$, denote its ith-coordinate by u(i), i.e., $u(i)=u_i$. A family $A{\subseteq}P(n,l)$ is said to be t-intersecting if ${\mid}\{i:u(i)=v(i)\}{\mid}{\geq}t$ for all $u,v{\epsilon}A$. A family $A{\subseteq}P(n,l)$ is said to be trivially t-intersecting if there is a t-set T of $[l]=\{1,2,{\cdots},l\}$ and elements $y_s{\in}\mathbb{N}_0(s{\in}T)$ such that $A=\{u{\in}P(n,l):u(j)=yj\;for\;all\;j{\in}T\}$. We prove that given any positive integers l, t with $l{\geq}2t+3$, there exists a constant $n_0(l,t)$ depending only on l and t, such that for all $n{\geq}n_0(l,t)$, if $A{\subseteq}P(n,l)$ is non-trivially t-intersecting, then $${\mid}A{\mid}{\leq}(^{n+l-t-l}_{l-t-1})-(^{n-1}_{l-t-1})+t$$. Moreover, equality holds if and only if there is a t-set T of [l] such that $$A=\bigcup_{s{\in}[l]{\backslash}T}\;A_s{\cup}\{q_i:i{\in}T\}$$, where $$A_s=\{u{\in}P(n,l):u(j)=0\;for\;all\;j{\in}T\;and\;u(s)=0\}$$ and $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• Nuclear Engineering and Technology
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• v.14 no.1
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• pp.22-40
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• 1982

The nuclear LS-energy matrix elements have been calculated with the harmonic oscillator shell model wave functions for the configurations ( $l_{i}$ $l_{i+1}$｜ $l_{i}$ $l_{i+1}$) where 1$_1$= $l_{s}$ , $l_2$=lp, $l_3$=ld, 2s, $l_4$=1f, 2p, $l_{5}$ =1g, 2d, 3s. The resulting matrix elements are expressed in terms of both Talmi integrals $I_1$ and Slater integrals $F^{k}$ . In addition to this various sum rules are derived and applied to check the results of the calculations.ons.

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.179-188
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• 2022

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form $$f\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$ and $$f\(\sum\limits_{i=1}^{l}x_i\)+\sum\limits_{j=1}^{l}f\(-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i\)=(l+1)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

• Journal of the Korean Institute of Rural Architecture
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• v.3 no.2
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• pp.13-24
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• 2001

Some companies of domestic construction indicate recently that modern life for the aged prefer an advanced technical alliance between O.D.L and I.D.L systems. It means the quality of housing life of the aged has been raised and changed quickly as well as the O.D.L and I.D.L systems since the last year. These preliminary studies suggest that the aged people in the country suffer from insufficient O.D.L and I.D.L systems caused by nation-wide economic poverty compared with the aged people in Seoul. The information from the country has been restricted for several decades therefore some details of the results of the studies are at times difficult to believe and differ depending on the research methods. The purpose of this study is to clarify the quality housing life of the aged, based on the comparative analysis between the O.D.L and I.D.L systems. The quality of housing life of the aged in countryside has been revealed by the clarification of the conditions housing supply, facilities, and therefore housing the cost amount. The conclusions are as follows ; The quickly changing architectural O.D.L elements are presented below in 17 items, while the I.D.L elements are presented in 18 items.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.113-118
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• 1998

In this paper we study central limit theorem(C.L.T.) and law of iterated logarithm (L.I.L.) for fuzzy random variables with respect to Hausdorff distance.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.221-231
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• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• Animal Bioscience
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• v.34 no.2
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• pp.295-305
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• 2021

Objective: The objectives of this study were to compare the effects of normal and low protein content (PC) of starter diet supplemented or not with blends of branched-chain amino acids (BCAAs) on growth performance of broilers under summer conditions and to investigate whether these effects altered some quality traits and the characteristics of gastrointestinal tract. Methods: A total of 768 mixed-sex broiler chicks (Ross 308, one-d-old) with an average initial body weight (BW) of 47.6±1.03 g were allocated into six treatments with four replications in 2×3 factorial arrangement. Factors were: PC, normal (N, 22% to d 15); and low (L, 20% to d 15); and added BCAA blends, L-leucine, L-isoleucine, and L-valine at zero (0L:0I:0V); 1.0, 0.25, and 0.25 (4L:1I:1V); or 1.0, 0.25, 0.75 (4L:1I:3V) g/kg of diet. Hence, six dietary treatments were named as N0L:0I:0V, N4L:1I:1V, N4L:1I:3V, L0L:0I:0V, L4L:1I:1V, and L4L:1I:3V. Average indoor temperature and humidity were 32.8℃±1.7℃ and 61.1%±4.12%, respectively. Results: BW, feed conversion ratio (FCR) and carcass weight were not affected by PC, BCCA and their interaction (p>0.05). The L diets decreased the water holding capacity of the breast (p = 0.002) and thigh (p = 0.050) meats and dressing percentage (p = 0.005) compared to the N diets. The 4L:1I:1V diet decreased breast yield compared to the 0L:0I:0V diets (p = 0.041). The effect of PC on feed intake, mortality and gastrointestinal trait weight were depended on the L:I:V ratios under summer conditions due to interactions between factors (p<0.05). The FI and mortality of L4L:1I:1V broilers were lower than those of N4L:1I:1V birds (p<0.05). Conclusion: It was concluded that the blends of BCAAs used failed to improve performance and to promote breast yields, because diets with normal or with reduced protein supplemented or not with BCAAs up to d 15 produced a similar BW and FCR in broilers raised in hot-climate conditions.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.293-299
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• 2005

Let ${\cal{L}}$ be a commutative subspace lattice on a Hilbert space ${\cal{H}}$ and X and Y be operators on ${\cal{H}}$. Let $${\cal{M}}_X=\{{\sum}{\limits_{i=1}^n}E_{i}Xf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}$$ and $${\cal{M}}_Y=\{{\sum}{\limits_{i=1}^n}E_{i}Yf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}.$$ Then the following are equivalent. (i) There is an operator A in $Alg{\cal{L}}$ such that AX = Y, Ag = 0 for all g in ${\overline{{\cal{M}}_X}}^{\bot},A^*A=AA^*$ and every E in ${\cal{L}}$ reduces A. (ii) ${\sup}\;\{K(E, f)\;:\;n\;{\in}\;{\mathbb{N}},f_i\;{\in}\;{\cal{H}}\;and\;E_i\;{\in}\;{\cal{L}}\}\;<\;\infty,\;{\overline{{\cal{M}}_Y}}\;{\subset}\;{\overline{{\cal{M}}_X}}$and there is an operator T acting on ${\cal{H}}$ such that ${\langle}EX\;f,Tg{\rangle}={\langle}EY\;f,Xg{\rangle}$ and ${\langle}ET\;f,Tg{\rangle}={\langle}EY\;f,Yg{\rangle}$ for all f, g in ${\cal{H}}$ and E in ${\cal{L}}$, where $K(E,\;f)\;=\;{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Y\;f_{i}{\parallel}/{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Xf_{i}{\parallel}$.

• Parasites, Hosts and Diseases
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• v.22 no.1
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• pp.11-20
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• 1984

A number of studies on the papillae of cercariae of trematodes reported that the papillar patterns (or chaetotaxy) of cercariae might be an excellent method to attain better understanding of the digenetic trematodes (Richard, 1971 ; Short and Cartrett, 1973; Bayssade-Dufour, 1979) . The present study was aimed to determine the number, distribution pattern and structure of the sensory papillae of Metagonimus yokogawai cercariae, and to elucidate the chaetotaxy of this digenetic trematode. M. yokogawai cercariae were pipetted from a vial in which infected snails (Semisulcospira libertina) had been kept for 3 hours. The snails were collected from an endemic area of M. yokogawai, Boseong river in west-southern part of Korea. Observations of papillae were based on light microscopy of those stained with silver nitrate, and on scanning electron microscopy The results are summarized as follows: 1, All papillae observed were uniciliated. 2. Cilia in anterior tip were shorter than the others in other portions. 3. The body papillae were arranged in essentially symmetrical patterns, Total number of the papillae was 126(63 pairs) in average; anterior tip 40(20 pairs), ventral 20(10 pairs), lateral 42(21 pairs), and caudal 8(4 pairs). 4. The chaetotany of M. yokogawai cercaria was: Ci cycle ($3+3C_{I}V,{\;}2+2C_{I}L,{\;}2+3C_{I}D),{\;}C_{II}{\;}cycle(2C_{II}V,{\;}1C_{II}L,{\;}2C_{II}D),{\;}C_{lll}{\;}cycle{\;}(1+lC_{III}V,{\;}1C_{IlI}L),{\;}C_{IV}{\;}cycle{\;}(1C_{IV}V,{\;}IC_{lV}L){\;}in{\;}cephalic{\;}region:{\;}A_I(1A_{IV}V,{\;}1+2A_{I}L,{\;}1A_{I}D),{\;}A_{II}(1A_{II}V,{\;}1+3A_{II}L,{\;}1A_{II}D),{\;}A_{III}(1A_{III}V,{\;}1+1A_{III}L,{\;}1A_{III}D){\;}and{\;}A_{IV}(1A_{IV}V,{\;}2A_{IV}L)$ in antacetabular region: $1M_{I}V{\;}and{\;}2M_{I}L$ in median: $1+1P_{I}L,{\;}1P_{II}L,{\;}1P_{II}D,{\;}1P_{III}L,{\;}1P_{IV}L{\;}and{\;}1P_{IV}D$ in postacetabular region: 2-2-2-2 in caudal region.

• Korean Journal of Materials Research
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• v.11 no.3
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• pp.184-184
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• 2001

The effect of neutral ligand(L) on the precursor characteristics of (hfac)Cu(I)-L and on Cu MOCVD Process was studied. The neutral ligands of (hac)Cu(I)-L$_{x}$, such as ATMS(allytrimethylsilane), VTMS(vinyltrimethylsilane), VCH(vinylcyclohexane), MP(4-methyl-1-pentene), ACP(allylcyclopentane), and DMB(3,3-dimethyl-1-butene) were investigated. When the dissociation temperature of Cu(I)-L bond is low, low temperature deposition below $100^{\circ}C$ is possible and the resistivity of the film is low. But thermal stability of the precursor is low in this case. The resistivity is almost the same regardless of L at the deposition temperature range of $125~175^{\circ}C$. The resistivity is increased as the molecular weight of L becomes higher above $225^{\circ}C$ The vapor pressure of the precursor was closely related to the boiling point of L, the lower the boiling point of L, the higher the vapor pressurere.