• 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 $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• The Korean Nurse
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• v.36 no.5
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• pp.63-73
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• 1998

The home visiting health nurses are important man-power who can serve various and persistent rehabilitation care to disabled person in community. The Community Based Rehabilition project(CBR) of national rehabilition center have been carried out from 1995. As a part of that project national health center performed rehabilition education program for home visiting health nurses. The purpose of this study is to analysis the effect of this education. In the first stage all of those groups were educated for two weeks in national rehabilitation center. But only two group nurses, one is in a urban and the other in a rural community, have been educated continually in the field through discussing rehabilitation care case study. The data in this study were gathered from three group healh nurses and analysed by SAS computer program. The results about knowledge, attitude and practice changes of the three group nurses were as follows. 1. In the pre education state the mean point of all nurses' attitude for rehabilition was 59, but in the post education state that was 90. The difference between pre and post attitude is very significant(t=-14.1. p<0.0001l). 2. In the pre education state the mean point of all nurses' knowledge for rehabilition was 45, but in the post education state that was 78. The difference between pre and post knowledge is very significant(t=-12.7, p<0.000l). 3. In the pre education state the mean point of all nurses' practice for rehabilition care was 37, but in the post education state that was 62. The difference between pre and post practice is very significant(t=-7.3, p<0.000l). 4. In practice point, the two group nurses who have been educated continuously were superior to the other(t=-3.9. p<0.00l). 5. All points between the urban and rural nurses were no significant differences(p>0.l). 6. All changes of the attitude, knowledge and practice did not affected by age(F=0.58, p>0.l). professional career(F=O.61, p>0.l), educational background(F=0.97, p>0.l).

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.237-244
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• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.542-554
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• 2023

Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α - p/q| < (Lq²)^-1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {l_p/q : p/q ∈ ℚ ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) - C(0) is equal to the sum of all numbers 3 - l_p/q where the Farey index p/q is less than α.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.93-100
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• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• Korean Journal of Veterinary Service
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• v.34 no.1
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• pp.69-73
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• 2011

This was conducted to determine the effects of body weight, organ weight, hematological values and biochemical parameters by L-carnitine (Carn) on the orchidectomized (Orch) rats. The animals were divided into 4 groups. Intact group (n=10) received no treatment and operation. Sham group (n=10) received only sham operation and no treatment. Orch group received operation and no treatment. Orch+Carn received operation and L-carnitine. The body weights of each group increased, but that of the Orch+Carn group were significantly lower than those in all the other groups. There were significant differences (P<0.05, P<0.001) of body weights between Orch+Carn group and all the other groups. Also, organ weights such as heart, liver, spleen and kidney were measured. The heart weights were significantly lower (P<0.001) in the Orch+Carn group than those in Intact and Sham groups, respectively. The weights of liver and kidney in the Orch+Carn group were significantly differences (P<0.001) in comparison with those in all the other groups. Also, the spleen weights were significantly lower (P<0.05) in the Orch+Carn group than those in Intact and Sham groups, respectively. The hematological values of mean corpuscular volume (MCV) and mean corpuscular hemoglobin (MCH) were significantly differences (P<0.05, P<0.01, P<0.001) in comparison with those in all the other groups. On the other hand, the hematological values of white blood cell (WBC), red blood cell (RBC) and mean corpuscular hemoglobin concentration (MCHC) were not significantly different in any other groups. The concentrations of total cholesterol (T-chol), triglyceride (TG) and high density lipoprotein (HDL) decreased significantly (P<0.05) in the Orch+Carn group as compared to those in the Orch group. We conclude that L-carnitine was significantly decreased the body weight in the orchidectomized rats. Our findings suggest that L-carnitine may influence the process of lipid packaging and absorption in the orchidectomized rats.

• Asian-Australasian Journal of Animal Sciences
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• v.15 no.8
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• pp.1128-1133
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• 2002

The whole plant of crop maize was chopped and ensiled in airtight 1-L capacity glass jars to determine the influence of residual sugar on anaerobic yeast growth and on the fermentation of lactic acid by L. buchneri in whole crop maize silage. There were a total of six treatments used in this experiment as follow: added 25 g de-mineralised water per kg chopped maize serving as control (con), 37.5 g glucose solution containing 12.5 g glucose ($g_1$), 75 g glucose solution containing 25 g glucose ($g_2$), 25 g L. buchneri suspension intended for $10^6$ cfu $g^{-1}$ (L.b.), $g_1+L.b.$ and $g_2+L.b.$ All silos were stored in the dark at $20^{\circ}C$ until end of experiment. Jars were opened on duplicates at day 2, 7, 14, 28, 56 or triplicates at day 91 after ensiling for measuring the pH, microbiological enumeration and fermentative products. Results indicated that acidification rates for all silages were very fast, no difference occurred among treatments before day 28. After day 28 the pH values for silages inoculated by L. buchneri. with or without sugar tended to increase especially for treated only with L. buchneri, resulting in higher (p<0.01) finial pH than uninoculated silages. Compared with control silage, the added sugar significantly (p<0.01) increased dry matter (DM) loss, L. buchneri enhanced (p<0.01) DM loss further at different sugar existence. Silages inoculated by L. buchneri only or in combination with sugar addition contained less (p<0.01) lactic acid than the correspondent silages without inoculation with L. buchneri. In comparison with control, ethanol production is about 3 or 6 fold higher due to addition 12.5 or 25 g glucose per kg chopped maize at ensiling. The added sugar resulted in less acetic acid concentration (p<0.01) than control, but inoculation with L. buchneri increased (p<0.01) acetic acid than correspondent uninoculated silages at different sugar levels. No butyric acid and propionic acid were found in uninoculted silages, silages inoculated with L. buchneri. produced more propionic acid, 1-propanol and butyric acid. Lactobacilli counts were not influenced by added sugar, but increased (p<0.01) with inoculation of L. buchneri. The added sugar increased significantly (p<0.01) the yeast count, whereas L. buchneri showed the contrary effect. No differences were found in the aerobic stability among all treatments. In conclusions, 1) the added sugars encourage the growth of yeast and yeasts convert extra sugar into ethanol in maize silages. 2) The added sugars and L. buchneri do not influence the aerobic stability of silages stored in anaerobic silos.

• Korean Journal of Food Science and Technology
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• v.29 no.6
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• pp.1241-1247
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• 1997

Gel-type fermented milk was prepared from milk or mixture of milk and apple juice/grape juice. Acid production (pH change) and growth of Lactobacillus acidophilus (KCTC 2182) were studied. The effects of juice addition on sensory property of fermented milk were also studied. The pH value of samples containing mixture of milk and apple juice/grape juice (25 mL : 25 mL to 5 mL : 45 mL) was lower than that of milk sample. However, number of viable cells of L. acidophilus at 21 hr in milk and samples containing juices was similar. During lactic fermentation for 24 hr, pH of all samples dropped significantly between 6 hr and 21 hr. pH values of mixture of milk and juices were lower than that of milk sample. Growth curve showed that lag phase continued to approximately 3 hr and log phase continued to approximately 15 hr in all samples. Number of viable cells in all samples was similar Sensory evaluation showed that overall acceptability of fermented milk prepared from apple juice/grape juice and milk (15 mL : 35 mL or 5 mL : 45 mL) was better than that of reference sample. The optimum ratio of mixture of juice and milk was 15 mL : 35 mL. The score values of sensory test of fermented milk prepared from mixture of grape juice and milk were slightly higher than those of mixture of apple juice and milk.

• The Mathematical Education
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• v.21 no.3
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• pp.7-11
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• 1983

A measurable function f defined on a measurable subset A of the real line R is called pth power summable on A if │f│$^{p}$ is integrable on A and the set of all pth power summable functions on A is denoted by L$^{p}$ (A). For each member f in L$^{p}$ (A), we define ∥f∥$_{p}$ =(equation omitted) For real numbers p and q where (equation omitted) and (equation omitted), we discuss the Holder's inequality ∥fg∥$_1$<∥f∥$_{p}$ ∥g∥$_{q}$ , f$\in$L$^{p}$ (A), g$\in$L$^{q}$ (A) and the Minkowski inequality ∥＋g∥$_{p}$ <∥f∥$_{p}$ ＋∥g∥$_{p}$ , f,g$\in$L$^{p}$ (A). In this paper also discuss that L$_{p}$ (A) becomes a metric space with the metric $\rho$ : L$^{p}$ (A) $\times$L$^{p}$ (A) longrightarrow R where $\rho$(f,g)=∥f-g∥$_{p}$ , f,g$\in$L$^{p}$ (A). Then, in this paper prove the Riesz-Fischer theorem, i.e., the space L$^{p}$ (A) is complete and that the space L$^{p}$ (A) is separable.

• Preventive Nutrition and Food Science
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• v.22 no.3
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• pp.231-236
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• 2017

Fermented kale juices using four types of lactobacilli were produced in the present study. After 48 h of fermentation time, viable cell counts of all ferments reached an above $10^9CFU/mL$. The viability of the ferments after cold storage in the refrigerator for 4 weeks showed $10^8CFU/mL$ in all ferments. Among four types of fermented kale juices, the ferment of Lactobacillus acidophilus IFO 3025 indicated a good nutritional composition, including neutral sugar ($1,909.76{\mu}g/mL$), reducing sugar ($564.00{\mu}g/mL$, P<0.05), and protein contents ($160.06{\mu}g/mL$, P<0.05). The results of mineral composition analysis had the highest potassium value in all ferments ($854.16{\sim}895.07{\mu}g/mL$), particularly in the ferment of Lactobacillus brevis FSB-1 (P<0.001), which is necessary to sustain osmotic pressure, prevention of high blood pressure, and protein synthesis. Moreover, calcium, phosphorus, and magnesium contents related to bone health were generally sufficient in all ferments. Consequently, in this study, fermented kale juices may be suggested as a healthy fermented beverage with essential nutrients. However, the acceptability of the fermented kale juice to the Korean taste should be further investigated with a trained taste panel to determine whether inoculated fermentation could be an option for the consumers.