• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.71-102
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• 2003

The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold $M_q$ of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in $M_q$, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in $M_q$.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.231-253
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• 2007

The purpose of this paper is to study the geometry of null curves in a semi-Riemannian manifold (M, g) of index 2. We show that it is possible to construct new Frenet equations of two types of null curves in M.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.211-221
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• 2005

The purpose of this paper is to study the geometry of null curves in a Lorentzian manifold (M, g). We show that it is possible to construct new type of Frenet equations of null curves in M, supported by two examples.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.805-812
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• 2021

In this study, we obtain various conditions for the non-null curve flows to be inextensible in the 6-dimensional Lorentzian space 𝕃⁶. Then, we find partial differential equations which characterize the family of inextensible non-null curves.

• Language and Information
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• v.9 no.2
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• pp.69-83
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• 2005

This paper discusses the distribution of a null complementizer C, as opposed to an overt counterpart 'that', presenting empirical support both for and against the PF-merge analysis of C proposed by Boscovic and Lasnik (2003, henceafter B&L) who in turn attribute to the proposal in Pesetsky (1992) and Halle & Marantz (1993). In Section I, as a background, I discuss B&L's proposal that a null complementizer C is a PF-affix which undergoes a PF-merger operation at the PF component. In Section 2, after a brief sketch of the distribution of a null C mostly in bare-relatives, I explore the possibility of extending B&L's analysis to accomodate the null C's in the bare-relative constructions. In Section 3, I argue that despite some empirical difficulties, B&L's analysis of a null C as a PF-affix can still be maintained, if Adverb Fronting is an operation to Spec-C position. Furthermore, I propose a rule - PF Spell-Out Constraint - to account for the C-trace (i.e. that-trace) effect in relative constructions. With the PF Spell-Out Constraint and B&L's PF-merge account, the distribution of a null C can better be analyzed.

• Journal of Electrical Engineering and Technology
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• v.2 no.4
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• pp.532-536
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• 2007

Carbon nanotube (CNT) properties, produced using a magnetic null discharge (MND) plasma production technology, were investigated. We firstly deposited the Fe layer 200 nm in thickness on Si substrate by the magnetic null discharge sputter method at the substrate temperature of $300도C$, and then prepared CNTs on the catalyst layer by using the magnetic null discharge (MND) based CVD method. CNTs were deposited in a gas mixture of CH4 and N2 at a total pressure of 1 Torr by the MND-CVD method. The substrate temperature and the RF power were $650^{\circ}C$ and 600W, respectively. The characterization data indicated that the proposed source could synthesize CNTs even under relatively severe conditions for the magnetic null discharge formation.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.1003-1016
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• 2016

In this paper, we introduce a new kind of slant helix for null curves called null $W_n$-slant helix and we give a definition of new harmonic curvature functions of a null curve in terms of $W_n$ in (n + 2)-dimensional Lorentzian space $M^{n+2}_1$ (for n > 3). Also, we obtain a characterization such as: "The curve ${\alpha}$ s a null $W_n$-slant helix ${\Leftrightarrow}H^{\prime}_n-k_1H_{n-1}-k_2H_{n-3}=0$" where $H_n,H_{n-1}$ and $H_{n-3}$ are harmonic curvature functions and $k_1,k_2$ are the Cartan curvature functions of the null curve ${\alpha}$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.2
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• pp.114-120
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• 1992

In this paper we derived the asymptotic distribution of the MUSIC null-spectrum, form which an exact expression of the asymptotic variance of the MUSIC null-spectrum can be obtained. From this result in addition an explicit expression of the normalized standard deviation has been derived and it is shown that the normalized standard deviation depends only on the number of sensors and the number of signals.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.209-215
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• 2008

The purpose of this paper is to study the geometry of null Bertrand curves in a Lorentz manifold.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.141-148
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• 2020

We consider estimating the proportion of true null hypotheses in multiple testing problems. A traditional multiple testing rate, family-wise error rate is too conservative and old to control type I error in multiple testing setups; however, false discovery rate (FDR) has received significant attention in many research areas such as GWAS data, FMRI data, and signal processing. Identify differentially expressed genes in microarray studies involves estimating the proportion of true null hypotheses in FDR procedures. However, we need to account for unknown dependence structures among genes in microarray data in order to estimate the proportion of true null hypothesis since the genuine dependence structure of microarray data is unknown. We compare various procedures in simulation data and real microarray data. We consider a hidden Markov model for simulated data with dependency. Cai procedure (2007) and a sliding linear model procedure (2011) have a relatively smaller bias and standard errors, being more proper for estimating the proportion of true null hypotheses in simulated data under various setups. Real data analysis shows that 5 estimation procedures among 9 procedures have almost similar values of the estimated proportion of true null hypotheses in microarray data.