• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4A
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• pp.325-328
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• 2011

In this paper, we present a new and simple derivation of the Craig representation for the two-dimensional (2-D) Gaussian Q-function in the viewpoint of geometry. The geometric derivation also leads to an alternative Craig form for the 2-D Gaussian Q-function. The derived Craig form is newly obtained from the geometry of two wedge-shaped regions generated by the rotation of Cartesian coordinates over two correlated Gaussian noises. The presented Craig form can play a important role in computing the probability represented by the 2-D Gaussian Q-function.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.83-93
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• 2019

Let R be a noncommutative prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R and f($x_1,{\ldots},x_n$) a noncentral multilinear polynomial over C in n noncommuting variables. Denote by f(R) the set of all the evaluations of f($x_1,{\ldots},x_n$) on R. If d is a nonzero derivation of R and G a nonzero generalized derivation of R such that $$d(G(u)u){\in}Z(R)$$ for all $u{\in}f(R)$, then $f(x_1,{\ldots},x_n)^2$ is central-valued on R and there exists $b{\in}U$ such that G(x) = bx for all $x{\in}R$ with $d(b){\in}C$. As an application of this result, we investigate the commutator $[F(u)u,G(v)v]{\in}Z(R)$ for all $u,v{\in}f(R)$, where F and G are two nonzero generalized derivations of R.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.1-11
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• 2019

Let R be a prime ring with involution of the second kind and centre Z(R). Suppose R admits a generalized derivation $F:R{\rightarrow}R$ associated with a derivation $d:R{\rightarrow}R$. The purpose of this paper is to study the commutativity of a prime ring R satisfying any one of the following identities: (i) $F(x){\circ}x^*{\in}Z(R)$ (ii) $F([x,x^*]){\pm}x{\circ}x^*{\in}Z(R)$ (iii) $F(x{\circ}x^*){\pm}[x,x^*]{\in}Z(R)$ (iv) $F(x){\circ}d(x^*){\pm}x{\circ}x^*{\in}Z(R)$ (v) $[F(x),d(x^*)]{\pm}x{\circ}x^*{\in}Z(R)$ (vi) $F(x){\pm}x{\circ}x^*{\in}Z(R)$ (vii) $F(x){\pm}[x,x^*]{\in}Z(R)$ (viii) $[F(x),x^*]{\mp}F(x){\circ}x^*{\in}Z(R)$ (ix) $F(x{\circ}x^*){\in}Z(R)$ for all $x{\in}R$.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.44 no.1
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• pp.12-17
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• 2018

Objectives: Airway management in patients with panfacial trauma is complicated. In addition to involving facial lesions, such trauma compromises the airway, and the use of intermaxillary fixation makes it difficult to secure ventilation by usual approaches (nasotracheal or endotracheal intubation). Submental airway derivation is an alternative to tracheostomy and nasotracheal intubation, allowing a permeable airway with minimal complications in complex patients. Materials and Methods: This is a descriptive, retrospective study based on a review of medical records of all patients with facial trauma from January 2003 to May 2015. In total, 31 patients with complex factures requiring submental airway derivation were included. No complications such as bleeding, infection, vascular, glandular, or nervous lesions were presented in any of the patients. Results: The use of submental airway derivation is a simple, safe, and easy method to ensure airway management. Moreover, it allows an easier reconstruction. Conclusion: Based on these results, we concluded that, if the relevant steps are followed, the use of submental intubation in the treatment of patients with complex facial trauma is a safe and effective option.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.384-392
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• 1998

Dr. Taguchi proposed three models of ideal functions for dynamic systems with double signal factors. He also gave examples for each model yet without derivation. It will be difficult for other engineers to follow because Dr. Taguchi didn't show us how he obtained those models. Actually we can analyze each example from engineering aspect based on basic mechanism. In this paper we use brake systems to illustrate our approach of derivation and obtain a different form of ideal function from what Taguchi proposed. Our purpose is to provide an example that engineers can imitate and solve his problem at hand.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.523-530
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• 2016

Let R be a 3!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. In this case, we show that [D(x), x]D(x) = 0 if and only if D(x)[D(x), x] = 0 for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A). If D is a continuous linear Jordan derivation on A, then we see that $[D(x),x]D(x){\in}rad(A)$ if and only if $[D(x),x]D(x){\in}rad(A)$ for all $x{\in}A$.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.531-542
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• 2016

Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that [[D(x),x], x]D(x) = 0 or D(x)[[D(x), x], x] = 0 for all $x{\in}R$. In this case we have $[D(x),x]^3=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $[[D(x),x],x]D(x){\in}rad(A)$ or $D(x)[[D(x),x],x]{\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.

• IEMEK Journal of Embedded Systems and Applications
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• v.15 no.1
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• pp.1-8
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• 2020

A derivation method for a quantized gradient for machine learning on an embedded system is proposed, in this paper. The proposed differentiation method induces the quantized gradient vector to an objective function and provides that the validation of the directional derivation. Moreover, mathematical analysis shows that the sequence yielded by the learning equation based on the proposed quantization converges to the optimal point of the quantized objective function when the quantized parameter is sufficiently large. The simulation result shows that the optimization solver based on the proposed quantized method represents sufficient performance in comparison to the conventional method based on the floating-point system.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.203-218
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• 2018

An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.97-103
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• 2004

In this paper, we will prove that a free join algebra and a universal derivation module of its subalgebras have a universal derivation module induced by its subalgebras.