• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.247-262
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• 2006

The main objective of this paper is to study the boundedness character, the periodic character and the global stability of the positive solutions of the following difference equation $x_{n+1}=\frac{{\alpha}x_n+{\beta}x_{n-1}+{\gamma}x_{n-2}+{\delta}x_{n-3}}{Ax_n+Bx_{n-1}+Cx_{n-2}+Dx{n-3}}$, n=0, 1, 1, ... where the coefficients A, B, C, D, ${\alpha},\;{\beta},\;{\gamma},\;{\delta}$ and the initial conditions x-3, x-2, x-1, x0 are arbitrary positive real numbers.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.349-358
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• 2017

The cyclic group $C_n={\langle}(12{\cdots}n){\rangle}$ acts on the set $(^{[n]}_k)$ of all k-subsets of [n]. In this action of $C_n$ the number of orbits of size d, for d | n, is $$O^{n,k}_d={\frac{1}{d}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})(^{n/s}_{k/s})$$. Stanton and White [6] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)={\frac{1}{[d]_{q^{n/d}}}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})[^{n/s}_{k/s}]_{q^s}$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a constructive proof for the positivity of coefficients of the orbit polynomial $O^{n,2}_d(q)$.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.5
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• pp.87-93
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• 2014

For n/m=qm+r, there is no simple divisibility rule for simple m=7 such that is the n multiply by m? This problem can be more complex for two or more digits of m. The Dunkels method has been known for generalized divisibility test method, but this method can not compute very large digits number that can not processed by computer. This paper suggests simple and exact divisibility method for m completely irrelevant n and m of digits. The proposed method sets $r_1=n_1n_2{\cdots}n_l(mod m)$ for $n=n_1n_2n_3{\cdots}n_k$, $m=m_1m_2{\cdots}m_l$. Then this method computes $r_i=r_{i-1}{\times}10+n_i(mod m)$, $i=2,3,{\cdots}k-l+1$ and reduces the digits of n one-by-one. The proposed method can be get the quotient and remainder with easy, fast and correct for various n,m experimental data.

• Asian-Australasian Journal of Animal Sciences
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• v.27 no.11
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• pp.1608-1614
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• 2014

The objective of this study was to investigate the different dietary ratios of n-6 to n-3 (n-6/n-3) fatty acid (FA) on performance and n-6/n-3 FA in muscles of broiler chickens. A total of 300 one-day-old Cobb chicks were randomly assigned to 3 treatments of 10 replicates in each (10 birds/replicate). Birds were fed on a corn-soybean meal-based diet containing 1% oil during starter (day 1 to 21) and 2% oil during finisher (day 22 to 39) phases, respectively. Treatments of high, medium and low dietary n-6/n-3 FA were formulated by replacing rice bran oil with linseed oil to achieve n-6/n-3 FA close to >20:1, 10:1 and 5:1, respectively. Average daily gain, average daily feed intake, and feed conversion ratio were similar (p>0.05) among the treatments. Serum glucose, cholesterol and triglycerides concentrations were not affected (p>0.05) by dietary treatments. In breast, concentration of C18:3n-3 was significantly greater (p = 0.001) for medium and low vs high n-6/n-3 FA, while concentrations of C20:5n-3, C22:6n-3, total n-3 FA, and n-6/n-3 FA were significantly higher for low vs medium, and medium vs high dietary n-6/n-3 FA. In contrast, concentrations of C18:2 and mono-unsaturated FA (MUFA) were lower for low vs high dietary n-6/n-3 FA. In thigh muscles, concentrations of C20:5n-3 were higher (p<0.05) for medium and low vs high dietary n-6/n-3 FA, and concentrations of C18:3n-3, C22:6, and n-3 FA were greater (p<0.05) for medium vs high, low vs medium dietary n-6/n-3 FA. However, concentrations of C18:1, MUFA, n-6/n-3 were lower (p<0.05) for low and medium vs high dietary n-6/n-3 FA. In conclusion, lowering the dietary n-6/n-3 FA did not affect the performance of chickens, but enhanced beneficial long-chain n-3 FA and decreased n-6/n-3 FA in chicken breast and thigh, which could be advantageous for obtaining healthy chicken products.

• Applied Biological Chemistry
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• v.26 no.4
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• pp.231-238
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• 1983

N-Benzoylglycylanilide and N-benzoylalanylanilide derivatives were synthesized from N-benzoylglycine and N-benzoylalane with anilines. respectively. The products were identified by elemental analysis, IR, UV and NMR spectra with N-benzoylglycylanilide (I), N-benzoylglycyl-o-toluidide(II), N-benzoylglycyl-m-toluidide(III), N-benzoylglycyl-p-toluidide(IV), N-benzoyl-L-alanylanilide(V), N-bnzoyl-L-alanyl-o-toluidide(VI), N-benzoyl-L-alnnyl-m-toluidise(VII), N-benzoyl-L-alanyl-p-toluidide(VIII). These compounds were tested for their phytotoxicity to the germination and seedling growth of rice, radish, green pea plants and turf grass. Among them, N-benzoyl-Lalanyl-m-toluidide had strongly inhibitory effect on the seedling growth of radish seeds, and N-benzoyl-L-alanylanilide showed an inhibitory activity especially upon the seedling growth of turf seeds. In addition, the inhibitory rate of plant seed growth differed with the isomeric position(ortho, meta and para) of methyl group; N-benzoylglycyl-m-toluidide was more effective than both N-benzoylglycyl-o-toluidide and N-benzoylglycyl-p-toluidide derivatives, and also N-benzoyl-L-alanyl-m-toluidide was more effective than both N-benzoyl-L-alanyl-o-toluidide and N-benzoyl-L-alanyl-p-toluidide.

• The Journal of Korean Society for Radiation Therapy
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• v.31 no.1
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• pp.57-65
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• 2019

Purpose: The purpose is to clarify the effect of additional scattering ratio on the edge of the block according to the increasing block thickness with low melting point lead alloy and pure lead in electron beam therapy. Methods and materials: $10{\times}10cm^2$ Shielding blocks made of low melting point lead alloy and pure lead were fabricated to shield mold frame half of applicator. Block thickness was 3, 5, 10, 15, 20 (mm) for each material. The common irradiation conditions were set at 6 MeV energy, 300 MU / Min dose rate, gantry angle of $0^{\circ}$, and dose of 100 MU. The relative scattering ratio with increasing block thickness was measured with a parallel plate type ion chamber(Exradin P11) and phantom(RW3) by varying the position of the shielding block(cone and on the phantom), the position of the measuring point(surface ans depth of $D_{max}$), and the block material(lead alloy and pure lead). Results : When (depth of measurement / block position / block material) was (surface / applicator / pure lead), the relative value(scattering ratio) was 15.33 nC(+0.33 %), 15.28 nC(0 %), 15.08 nC(-1.31 %), 15.05 nC(-1.51 %), 15.07 nC(-1.37 %) as the block thickness increased in order of 3, 5, 10, 15, 20 (mm) respectively. When it was (surface / applicator / alloy lead), the relative value(scattering ratio) was 15.19 nC(-0.59 %), 15.25 nC(-0.20 %), 15.15 nC(-0.85 %), 14.96 nC(-2.09 %), 15.15 nC(-0.85 %) respectively. When it was (surface / phantom / pure lead), the relative value(scattering ratio) was 15.62 nC(+2.23 %), 15.59 nC(+2.03 %), 15.53 nC(+1.67 %), 15.48 nC(+1.31 %), 15.34 nC(+0.39 %) respectively. When it was (surface / phantom / alloy lead), the relative value(scattering ratio) was 15.56 nC(+1.83 %), 15.55 nC(+1.77 %), 15.51 nC(+1.51 %), 15.42 nC(+0.92 %), 15.39 nC(+0.72 %) respectively. When it was (depth of $D_{max}$ / applicator / pure lead), the relative value(scattering ratio) was 16.70 nC(-10.87 %), 16.84 nC(-10.12 %), 16.72 nC(-10.78 %), 16.88 nC(-9.93 %), 16.90 nC(-9.82 %) respectively. When it was (depth of $D_{max}$ / applicator / alloy lead), the relative value(scattering ratio) was 16.83 nC(-10.19 %), 17.12 nC(-8.64 %), 16.89 nC(-9.87 %), 16.77 nC(-10.51 %), 16.52 nC(-11.85 %) respectively. When it was (depth of $D_{max}$ / phantom / pure lead), the relative value(scattering ratio) was 17.41 nC(-7.10 %), 17.45 nC(-6.88 %), 17.34 nC(-7.47 %), 17.42 nC(-7.04 %), 17.25 nC(-7.95 %) respectively. When it was (depth of $D_{max}$ / phantom / alloy lead), the relative value(scattering ratio) was 17.45 nC(-6.88 %), 17.44 nC(-6.94 %), 17.47 nC(-6.78 %), 17.43 nC(-6.99 %), 17.35 nC(-7.42 %) respectively. Conclusions: When performing electron therapy using a shielding block, the block position should be inserted applicator rather than the patient's body surface. The block thickness should be made to the minimum appropriate shielding thickness of each corresponding using energy. Also it is useful that the treatment should be performed considering the influence of scattering dose varying with distance from the edge of block.

• East Asian mathematical journal
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• v.24 no.1
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.497-510
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• 2010

Let R be a ring and n a fixed non-negative integer. $\cal{TI}_n$ (resp. $\cal{TF}_n$) denotes the class of all right R-modules of FGT-injective dimensions at most n (resp. all left R-modules of FGT-flat dimensions at most n). We prove that, if R is a right $\prod$-coherent ring, then every right R-module has a $\cal{TI}_n$-cover and every left R-module has a $\cal{TF}_n$-preenvelope. A right R-module M is called n-TI-injective in case $Ext^1$(N,M) = 0 for any $N\;{\in}\;\cal{TI}_n$. A left R-module F is said to be n-TI-flat if $Tor_1$(N, F) = 0 for any $N\;{\in}\;\cal{TI}_n$. Some properties of n-TI-injective and n-TI-flat modules and their relations with $\cal{TI}_n$-(pre)covers and $\cal{TF}_n$-preenvelopes are also studied.

• Journal of the Korean Chemical Society
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• v.23 no.6
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• pp.368-373
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• 1979

Kinetic studies have been carried out on solvolyses and halide exchanges $(Cl^-,\;Br^-,\;I^-)$ of N,N-dimethyl-, N,N-diethylcarbamoyl chlorides, and solvolyses of N,N-diphenylcarbamoyl chloride. Kinetic results together with simple MO analysis indicated that: (a) N,N-dialkylcarbamoyl chlorides reacted via the $S_N2$ mechanism, while N,N-diphenylcarbamoylchloride reacted via the $S_N1$ mechanism; (b) in chloride exchanges, the bond-breaking appeared to be important, whereas in bromide and iodide exchanges, the bond-formation was shown to be important.

• Journal of the Korean Society of Propulsion Engineers
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• v.2 no.3
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• pp.47-53
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• 1998

Using Michael Reaction, commercially available 3-aminopropyltrimethoxysilane and N-[3-(trimethoxysilyl)propuyl]ethylenediamine were reacted with various Michael acceptors, ethyl acrylate, acrylonitrile, acrylamide, 2-cyanoethyl acrylate, 2-hydroxyethyl acrylate and 3-(trimethoxysilyl)propylmethacrylate, to the new aminosilanes. All compounds which are [3-(N-2-carboethoxyethyl)aminopropyl]triethoxysilane, [3-(N-2-cyanoethyl)aminopropyl]triethoxysilane, [3-(N-di-2-car-boethoxyethyl)aminopropyl]triethoxysilane, [3-N-di-cyanoethyl) aminopropyl]triethoxysilane, [3-(N-2-cyanoethoxypropionyl)aminopropyl]triethoxysilane, [3-(N-di-2-cyanoethoxypropionyl)aminopropyl]triethoxysilane, [3-(N-di-2-hydroxyethoxy propionyl)aminopropyl]triethoxysilane, [3-(N-2-amidoethyl)aminopropyl]triethoxysil-ane,｛3-[N-(N-di-2-cyanoethyl)ethyl]aminopropyl｝triethoxysilane and ｛3-[N-(3-trimethoxysilylpropyl)-2-methylpropionyl]aminopropyl｝triethoxysilane were succes-sfully prepared in 35-70% yields and which were identified with $^1{H}$-NMR and FT-IR spectroscopy.