• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.387-399
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• 2008

We investigate approximately higher ternary derivations in Banach ternary algebras via the Cauchy functional equation $$f({\lambda}_{1x}+{\lambda}_{2y}+{\lambda}_{3z}={\lambda}_1f(x)+{\lambda}_2f(y)+{\lambda}_3f(z)$$.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.683-710
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• 2020

Let ℕ be the set of nonnegative integers and 𝕬 be a 2-torsion free triangular algebra over a commutative ring ℛ. In the present paper, under some lenient assumptions on 𝕬, it is proved that if Δ = {𝛿_n}_n∈ℕ is a sequence of ℛ-linear mappings 𝛿_n : 𝕬 → 𝕬 satisfying ${\delta}_n([[x,\;y],\;z])\;=\;\displaystyle\sum_{i+j+k=n}\;[[{\delta}_i(x),\;{\delta}_j(y)],\;{\delta}_k(z)]$ for all x, y, z ∈ 𝕬 with xy = 0 (resp. xy = p, where p is a nontrivial idempotent of 𝕬), then for each n ∈ ℕ, 𝛿_n = d_n + 𝜏_n; where d_n : 𝕬 → 𝕬 is ℛ-linear mapping satisfying $d_n(xy)\;=\;\displaystyle\sum_{i+j=n}\;d_i(x)d_j(y)$ for all x, y ∈ 𝕬, i.e. 𝒟 = {d_n}_n∈ℕ is a higher derivation on 𝕬 and 𝜏_n : 𝕬 → Z(𝕬) (where Z(𝕬) is the center of 𝕬) is an ℛ-linear map vanishing at every second commutator [[x, y], z] with xy = 0 (resp. xy = p).

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.741-748
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• 2010

Let R be a 2-torsionfree prime ring. Our goal in this note is to show that the existence of a nonzero Jordan higher left derivation on R implies R is commutative. This result is used to prove a noncommutative extension of the classical Singer-Wermer theorem in the sense of higher derivations.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.117-122
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• 1994

In this paper we show that if {$H_n$} is a continuous strong higher derivation of order n on an ultraprime Banach algebra with a constant c, then $c||H_1||^2{\leq}4||H_2||$ and for each $1{\leq}l$ < n $$c^2||H_1||\;||H_{n-l}{\leq}6||H_n||+\frac{3}{2}\sum_{\array{i+j+k=n\\i,j,k{\geq}1}}||H_i||\;||H_j||\;||H_k||+\frac{3}{2}\sum_{\array{i+k=n\\i{\neq}l,\;n-1}}||H_i||\;||H_k|| $$ and for a strong higher derivation {$H_n$} of order n on a prime ring A we also show that if [$H_n$(x),x]=0 for all $x{\in}A$ and for every $n{\geq}1$, then A is commutative or $H_n=0$ for every $n{\geq}1$.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.251-256
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• 1997

We show that a strong system of derivations ${D_0, D_1,\cdots,D_m}$ on a commutative Banach algebra A is contained in the radical of A if it satisfies one of the following conditions for separating spaces; (1) $\partial(D_i) \subseteq rad(A) and \partial(D_i) \subseteq K D_i(rad(A))$ for all i, where $K D_i(rad(A)) = {x \in rad(A))$ : for each $m \geq 1, D^m_i(x) \in rad(A)}$. (2) $(D^m_i) \subseteq rad(A)$ for all i and m. (3) $\bar{x\partial(D_i)} = \partial(D_i)$ for all i and all nonzero x in rad(A).

• Journal of the Chungcheong Mathematical Society
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• v.2 no.1
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• pp.37-44
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• 1989

In this paper, it is shown that automatic continuity of derivations on some semi prime Banach algebras can be extended to higher derivations. In particular, we show that if every prime ideal is closed in a commutative semi prime Banach algebra then every higher derivation on it is continuous.

• Journal of Biosystems Engineering
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• v.23 no.6
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• pp.571-582
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• 1998

The PLS(Partial Least Square) and ANN(Artificial Neural Network) were introduced to develop the soluble solids content prediction model of apples which is followed by making a subsequent selection of photosensor. For the optimal PLS model, number of factors needed for spectrum analysis were increased until the convergence of prediction residual error sum of squares. Analysis has shown that even part of the overall wavelength with no pretreatment may turn out better performing. The best PLS model was found in the 800 to 1,100nm wavelength region without pretreatment of second derivation, having $R^2$=0.9236, bias= -0.0198bx, SEP=0.2527bx for unknown samples. On the other hand, for the ANN model the second derivation led to higher performance. On partial range of 800 to 1,100nm wavelengh region, prediction model with second derivation for unknown samples reached $R^2$=0.9177, SEP=0.2903bx in contrast to $R^2$=0.7507, SEP =0.4622bx without pretreatment.

• Korean Journal of Plant Resources
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• v.20 no.6
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• pp.548-552
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• 2007

This research is the basic research to develop new anti-inflammatory medicine by feeding Scutellariae Radix extract to lipopolysaccharide(LPS) exposed rats, and analyzed it's effect on inflammatory response by LPS derivation. As a result, Plasma interleukin-$1\beta(IL-1\beta)$ and Plasma interleukin-6(IL-6) concentration showed the highest point at 5h after LPS injection, and in this time, the concentration of $IL-1\beta$ and IL-6 in the Scutellariae Radix extract groups at 200mg/kg and 300mg/kg showed lower values than that of control group. Plasma tumor necrosis $factor-\alpha(TNF-\alpha)$ concentration after LPS injection showed the highest point at 2h and showed similar level till at 5h. $TNF-\alpha$ concentration at 2h after LPS injection showed the low value only in the Scutellariae Radix extract 300mg/kg group compared to others, and in 5h, the all Scutellariae Radix extract groups showed lower value than that of the control group. Plasma interleukin-10(IL-10) concentration increased at 2h after LPS injection and reached the highest at 5h. After LPS injection the IL-10 concentration at 2h, the Scutellariae Radix extract injection group at 300mg/kg showed higher value than that of the others, and in 5h after LPS injection, Scutellariae Radix extract 200mg and 300mg groups showed higher value than the control group. Concluding from the above results, in inflammatory response by LPS derivation, the Scutellariae Radix gives positive effect.

• Korean Journal of English Language and Linguistics
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• v.2 no.2
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• pp.207-226
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• 2002

In this paper we provide an alternative explanation for there construction, by assuming that the expletive there (EXPL) has independently uninterpretable Case feature as well as u[person], not as being pied-pipied with $\varphi$-feature. If EXPL has only u[person], we could analyse incorrectly some there constructions, including an embedded infinitive clause: by Chomsky (1998, 1999) in the construction, EXPL is ‘frozen’ and cannot participate in the computation of higher. As a result, we could predict incorrectly that the derivation is crashed. But if EXPL has two uninterpretable features, u[person] and u[Case], we could predict correctly that the derivation is converged: the u[person] of EXPL is deleted under Matching/Agree with $T_{def}$; still, the undeleted u[Case] of EXPL is activating; so EXPL can be raised to [SPEC, T] to satisfy the EPP-feature of matrix T.

• Journal of Welding and Joining
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• v.32 no.2
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• pp.43-47
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• 2014

Famous artificial neural network (ANN) is applied to predict proper process window of arc welding. Target weldment is variously combined lap joint fillet welding of automotive steel plates. ANN's system variable such as number of hidden layers, perceptrons and transfer function are carefully selected through case by case test. Input variables are welding condition and steel plate combination, for example, welding machine type, shield gas composition, current, speed and strength, thickness of base material. The number of each input variable referred in welding experiment is counted and provided to make it possible to presume the qualitative precision and limit of prediction. One of experimental process windows is excluded for predictability estimation and the rest are applied for neural network training. As expected from basic ANN theory, experimental condition composed of frequently referred input variables showed relatively more precise prediction while rarely referred set showed poorer result. As conclusion, application of ANN to arc welding process window derivation showed comparatively practical feasibility while it still needs more training for higher precision.