• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제10권4호
• /
• pp.199-206
• /
• 2003

Let N be a right near-ring. N is said to be strongly reduced if, for $a\inN$, $a^2 \in N_{c}$ implies $a\;\in\;N_{c}$, or equivalently, for $a\inN$ and any positive integer n, $a^{n} \in N_{c}$ implies $a\;\in\;N_{c}$, where $N_{c}$ denotes the constant part of N. We will show that strong reducedness is equivalent to condition (ⅱ) of Reddy and Murty's property $(^{\ast})$ (cf. [Reddy & Murty: On strongly regular near-rings. Proc. Edinburgh Math. Soc. (2) 27 (1984), no. 1, 61-64]), and that condition (ⅰ) of Reddy and Murty's property $(^{\ast})$ follows from strong reducedness. Also, we will investigate some characterizations of strongly reduced near-rings and their properties. Using strong reducedness, we characterize left strongly regular near-rings and ($P_{0}$)-near-rings.

• 대한수학회보
• /
• 제59권4호
• /
• pp.917-928
• /
• 2022

Let R be a commutative Noetherian ring and I an ideal of R. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the finiteness of generalized local cohomology modules. Let M be a finitely generated R-module and N a representable R-module. We introduce the notions of the representation dimension r^I(M, N) and artinianness dimension a^I(M, N) of M, N with respect to I by r^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not representable} and a^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not artinian} and we show that a^I(M, N) = r^I(M, N) = inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)} ≥ inf{a^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)}. Also, in the case where R is semi-local and N a semi discrete linearly compact R-module such that N/∩_t>0I^tN is artinian we prove that inf{i : H^I_i(M, N) is not minimax}=inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)＼Max(R)}.

• 한국분말재료학회지
• /
• 제27권5호
• /
• pp.406-413
• /
• 2020

Ti_0.5Al_0.5N/CrN nano-multilayers, which are known to exhibit excellent wear resistances, were prepared using the unbalanced magnetron sputter for various periods of 2-7 nm. Ti_0.5Al_0.5N and CrN comprised a cubic structure in a single layer with different lattice parameters; however, Ti_0.5Al_0.5N/CrN exhibited a cubic structure with the same lattice parameters that formed the superlattice in the nano-multilayers. The Ti_0.5Al_0.5/CrN multilayer with a period of 5.0 nm exceeded the hardness of the Ti_0.5Al_0.5N/CrN single layer, attaining a value of 36 GPa. According to the low-angle X-ray diffraction, the Ti_0.5Al_0.5N/CrN multilayer maintained its as-coated structure up to 700℃ and exhibited a hardness of 32 GPa. The thickness of the oxidation layer of the Ti_0.5Al_0.5N/CrN multilayered coating was less than 25% of that of the single layers. Thus, the Ti_0.5Al_0.5N/CrN multilayered coating was superior in terms of hardness and oxidation resistance as compared to its constituent single layers.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2002년도 춘계 학술발표회 논문집
• /
• pp.49-54
• /
• 2002

For arbitrary random variables {$X_{n},n{\geq}1$}, the order of growth of the series. $S_{n}\;=\;{\sum}_{j=1}^n\;X_{j}$ is studied in this paper. More specifically, when the series S_{n}$ diverges almost surely, the strong law of large numbers $S_{n}/g_{n}^{-1}$($A_{n}{\psi}(A_{n}))\;{\rightarrow}\;0$ a.s. is constructed by extending the results of Petrov (1973). On the other hand, if the series $S_{n}$ converges almost surely to a random variable S, then the tail series $T_{n}\;=\;S\;-\;S_{n-1}\;=\;{\sum}_{j=n}^{\infty}\;X_{j}$ is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series $S_{n}$, a tail series strong law of large numbers $T_{n}/g_{n}^{-1}(B_{n}{\psi}^{\ast}(B_{n}^{-1}))\;{\rightarrow}\;0$ a.s., which generalizes the result of Klesov (1984), is also established by investigating the duality between the limiting behavior of partial sums and that of tail series. In particular, an example is provided showing that the current work can prevail despite the fact that previous tail series strong law of large numbers does not work.

• Bulletin of the Korean Chemical Society
• /
• 제19권10호
• /
• pp.1105-1109
• /
• 1998

A chiral stationary phase derived from (S)-N-(3,5-dinitrobenzoyl)leucine N-phenyl N-alkyl amide (CSP 2) was applied in separating the two enantiomers of various π-basic aromatic derivatives of leucine N-propyl amide in order to evaluate π-basic aromatic groups as an effective derivatizing group for the resolution of a-amino acids. Subsequently N-(3,5-dimethoxybenzoyl) group was found to be very effective as a π-basic aromatic derivatizing group. Based on these results, N-(3,5-dimethoxybenzoyl) derivatives of various a-amino N-propyl amides, N,N-diethyl amides and esters were resolved on the CSP derived from (S)-N-(3,5-dinitrobenzoyl) leucine N-phenyl N-alkyl amide (CSP 2) and the resolution results were compared with those on the CSP derived from (S)-N-(3,5-dinitrobenzoyl)leucine N-alkyl amide (CSP 1). The enantioselectivities exerted by CSP 2 were much greater than those exerted by CSP 1. In addition, racemic N-(3,5-dimethoxybenzoyl)-a-mino N,Ndiethyl amides were resolved much better than the corresponding N-(3,5-dimethoxybenzoyl)-a-mino N-propyl amides and esters on both CSPs. Based on these results, a chiral recognition mechanism utilizing the π-π donor-acceptor interaction and the two hydrogen bondings between the CSP and the analyte was proposed.

• Korean Journal of Mathematics
• /
• 제31권1호
• /
• pp.35-48
• /
• 2023

Let 𝔼 be a CAT(0) space and K be a nonempty closed convex subset of 𝔼. Let T : K → 𝓟(K) be a multimap such that F(T) ≠ ∅ and ℙ_T(x) = {y ∈ Tx : d(x, y) = d(x, Tx)}. Define sequence {x_n} by x_n+1 = (1 - α)𝜈_n⊕αw_n, y_n = (1 - β)u_n⊕βw_n, z_n = (1-γ)x_n⊕γu_n where α, β, γ ∈ [0; 1]; u_n ∈ ℙ_T (x_n); 𝜈_n ∈ ℙ_T (y_n) and w_n ∈ ℙ_T (z_n). (1) If ℙ_T is quasi-nonexpansive, then it is proved that {x_n} converges strongly to a fixed point of T. (2) If a multimap T satisfies Condition(I) and ℙ_T is quasi-nonexpansive, then {x_n} converges strongly to a fixed point of T. (3) Finally, we establish a weak convergence result. Our results extend and unify some of the related results in the literature.

• 대한수학회지
• /
• 제47권1호
• /
• pp.135-163
• /
• 2010

Motivated by [Science in China (Ser. A Mathematics) 36 (2006), no. 7, 721?732], this article deals with the following discrete type BVP $\LARGE\left\{{{\;{\Delta}[{\phi}({\Delta}x(n))]\;+\;f(n,\;x(n\;+\;1),{\Delta}x(n),{\Delta}x(n + 1))\;=\;0,\;n\;{\in}\;[0,N],}}\\{\;{x(0)-{\sum}^m_{i=1}{\alpha}_ix(n_i) = A,}}\\{\;{x(N+2)-\;{\sum}^m_{i=1}{\beta}_ix(n_i)\;=\;B.}}\right.$ The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operator ${\Delta}$x(n).

• Journal of applied mathematics & informatics
• /
• 제9권1호
• /
• pp.239-252
• /
• 2002

A sort sequence $S_n$ is sequence of all unordered pairs of indices in $I_n$={1,2,…n}. With a sort sequence $S_n$ = ($s_1,S_2,...,S_{\frac{n}{2}}$),one can associate a predictive sorting algorithm A($S_n$). An execution of the a1gorithm performs pairwise comparisons of elements in the input set X in the order defined by the sort sequence $S_n$ except that the comparisons whose outcomes can be inferred from the results of the preceding comparisons are not performed. A sort sequence is said to be extremal if it maximizes a given objective function. First we consider the extremal sort sequences with respect to the objective function $\omega$($S_n$) - the expected number of tractive predictions in $S_n$. We study $\omega$-extremal sort sequences in terms of their prediction vectors. Then we consider the objective function $\Omega$($S_n$) - the minimum number of active predictions in $S_n$ over all input orderings.

• Corrosion Science and Technology
• /
• 제22권4호
• /
• pp.232-241
• /
• 2023

The mechanical properties of the hydrogen valve responsible for supplying and blocking hydrogen gas in a hydrogen fuel cell electric vehicle (FCEV) were researched. Mechanical properties by hydrogen embrittlement were investigated by coating chromium nitride (CrN) and titanium nitride (TiN) on aluminum alloy by arc ion plating method. The coating layer was deposited to a thickness of about 2 ㎛, and a slow strain rate test (SSRT) was conducted after hydrogen embrittlement to determine the hydrogen embrittlement resistance of the CrN and TiN coating layers. The CrN-coated specimen presented little decrease in mechanical properties until 12 hours of hydrogen charging due to its excellent resistance to hydrogen permeation. However, both the CrN and TiN-coated specimens exhibited deterioration in mechanical properties due to the peeling of the coating layer after 24 hours of hydrogen charging. The specimens coated at 350 ℃ presented a significant decrease in ultimate tensile strength due to abnormal grain growth.

• 한국초지조사료학회지
• /
• 제11권3호
• /
• pp.175-181
• /
• 1991

The purpose of this experiment was to evaluate the effects of shade and levels of N fertilization on the dry matter yield and chemical compositions of orchardgrass grown under floor of chestnut tree. Shading conditions consist of $S_0$, (full light), $S_1$, (about 6OC4 shade) and $S_2$, (about 70% shade). And, nitrogen fertilizer was applied at 3 levels, O($N_0$), 12($N_1$), and 30($N_2$) kg per 10a, respectively. The results are may be summarized as follows: 1. Maximum total dry matter yield of $S_0$, was obtained about 1.28 ton/lOa at $N_2$, level. But, total dry matter yields of N levels in $S_1$, and $S_2$, were decreased about 42-45% compared with $S_0$. 2. The response of the dry matter yield to N fertilization were differences between shading and levels of N. Thus, the dry matter yield of $S_1$, increased almost linear up to about 30 kg/l0a level, while the dry matter yield of S, was increased slightly up to 30 kgIl0a. But. $S_2$, was increased up to 12 kg/lOa and then decreased slightly with N fertilization over the 12 kg/l0a. 3. Average increase in total dry matter yield to N fertilization were 23.85 kg, 7.97 kg and 5.08 kg DM for $S_0$, $S_1$, and $S_2$, respectively. 4. The level of 12 kg N/lOa is the limiting N level to obtain dry matter production under 60-709 shading conditions. 5. The contents of crude protein arid nitrate nitrogen were increased with shading and incremental N fertilization up to 30 kg/l0a. But, water soluble carbohydrate content was decreased greatly with high shading and high levels of N. 6. Nitrate nitrogen content indicated highly significant positive correlation with crude protein, but significant negative correlation with water soluble carbohydrate content. 7. At 30 kg N level with $S_1$, was necessary to exceed the potentially toxic nitrate nitrogen level of 0.20%.