• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.207-213
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. An interpolating operator for n-vectors satisfies the equation Ax$_{i}$=y$_{i}$. for i=1,2, …, n. In this article, we investigate unitary interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H. Let x and y be vectors in H. When does there exist a unitary operator A in AlgL such that Ax=y?

• Applied Microscopy
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• v.30 no.4
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• pp.337-345
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• 2000

Introduction of the buffer layer and the nitridation of a sapphire substrate were one of the most general methods employed for the reduction of lattice defects in GaN thin films Brown on sapphire by MOCVD. In an effort to improve the initial nucleation and growth condition of the GaN, reactive ion beam (RIB) of nitrogen treatment of the sapphire surface has been attempted. The 10 nm thick, amorphous $AlO_xN_y$ layer was formed by RIB and was partially crystallized alter the main growth of GaN at high temperature, leaving isolated amorphous regions at the interface. The beneficial effect of amorphous layer at interface in relieving the thermal stress between substrate and GaN film was examined by measuring the lattice strain value of the GaN film grown with and without the RIB treatment. Higher order Laue zone pattern (HOLZ) of $[\bar{2}201]$ zone axis was compared with simulated patterns and lattice strain was estimated It was confirmed that the great reduction of thermal strain was achieved by RIB process and the amount of thermal stress was 6 times higher in the GaN film grown by conventional method without the RIB treatment.

• Journal of Magnetics
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• v.10 no.2
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• pp.63-65
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• 2005

The $^1H$ NMR spin-lattice relaxation in a series of the organic-inorganic hybrid systems $(C_nH_{2n+1}NH_3)_2SnCl_6$ (n = 8, 10, 12, 14) undergoing two successive phase transitions was studied. A discontinuity characteristic of a first order phase transition was observed at the high-temperature conformational transition. Besides, the spin-lattice relaxation rate below the conformational transition temperature was well fitted by four types of molecular motions, from which the chain-length dependence of the activation energies of the molecular groups was obtained.

• Journal of the Korean Magnetic Resonance Society
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• v.15 no.2
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• pp.146-156
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• 2011

The line widths and spin-lattice relaxation times of protons in $[N(C_2H_5)_4]_2CoCl_4$ and $[N(CH_3)_4]_2CoCl_4$ single crystals were investigated in the temperature range 160-400 K. The temperature dependences of the spin-lattice relaxation times are attributed to the molecular motions of the ethyl and methyl groups in the $[N(C_2H_5)_4]^+$ and $[N(CH_3)_4]^+$ ions respectively. The NMR line widths indicate that the ethyl groups in $[N(C_2H_5)_4]_2CoCl_4$ have one more degree of freedom than the methyl groups in $[N(CH_3)_4]_2CoCl_4$. The experimental results are interpreted in terms of the reorientations of the methyl and ethyl groups.

• Electrical & Electronic Materials
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• v.7 no.5
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• pp.403-408
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• 1994

Dielectric and structural properties of $Ba_{1-x}$(Z $n_{1}$3/T $a_{2}$3/) $O_{3}$+1 mol% Mn $O_{2}$ (x=0, 0.01, 0.02, 0.03, 0.04) ceramics was investigated at microwave frequencies. With $Ba_{+2}$ shortage, the sinterability and the unloaded Q( $Q_{u}$) were much improved, and the ordering in B site and the lattice distortion was greatly enhanced and the structure approached the completely ordered structure. $Q_{u}$ was strongly correlated with these factors such as ordering ratio, lattice distortion and sinterability, and had the maximum value of 7500 at x=0.01. The dielectric constant was near 30 and the temperature coefficient of the resonant frequency was 2 ppm/.deg. C at x=0.01.1.1.1.

• Journal of the Korean Magnetic Resonance Society
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• v.6 no.2
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• pp.132-141
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• 2002

$^1H$ nuclear magnetic resonance (NMR) relaxations have been investigated in ammonium sulfate $((NH_4)_2SO_4)$ power at temperatures ranging form 102 K to 440 K. There is a bottleneck in the spin-lattice relaxation between the nuclear spin system and the hindered rotation of ammonium ions, which is certified by measuring the relaxation according to the initial condition of the spin system. For temperatures below 318 K the $^1H$ spin-lattice relaxations have double-exponential behaviors with the exponent, n, having a value 2>n>1 initially and n=l after a long time. Above 318 K not only is the relaxation exponential initially with exponent n=1, but it is a single-exponential over the entire time, resulting in one $T_1$ value. The two types of $NH_4^+$ ions have different activation energies for hindered rotation, $E_a^1=0.27{\pm}0.02eV$ and $E_a^11=0.12{\pm}0.0eV$, in the ferroelectric phase.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2006.06a
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• pp.116-117
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• 2006

I-D ZnO nanostructures were fabricated by thermal evaporation method on Si(100), GaN and $Al_2O_3$ substrates without a catalyst at the reaction temperature of $700^{\circ}C$. Only pure Zn powder was used as a source material and Ar was used as a carrier gas. The shape and growth direction of synthesized ZnO nanostructures is determined by the crystal structure and the lattice mismatch between ZnO and substrates. The ZnO nanostructure on Si substrate were inclined regardless of their substrate orientation. The origin of ZnO/Si interface is highly lattice-mismatched and the surface of the Si substrate inevitably has the $SiO_2$ layer. The ZnO nanostructure on the $Al_2O_3$ substrate was synthesized into the rod shape and grown into particular direction. For the GaN substrate, however, ZnO nanostructure with the honeycomb-like shape was vertically grown, owing to the similar lattice parameter with GaN substrate.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.1
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• pp.414-430
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• 2016

Verifier-local revocation (VLR) seems to be the most flexible revocation approaches for any group signature scheme, because it just only requires the verifiers to possess some up-to-date revocation information, but not the signers. Langlois et al. (PKC 2014) proposed the first VLR group signature based on lattice assumptions in the random oracle model. Their scheme has at least Õ(n²) ⋅ log N bit group public key and Õ(n) ⋅ log N bit signature, respectively. Here, n is the security parameter and N is the maximum number of group members. In this paper, we present a simpler lattice-based VLR group signature, which is more efficient by a O(log N) factor in both the group public key and the signature size. The security of our VLR group signature can be reduced to the hardness of learning with errors (LWE) and small integer solution (SIS) in the random oracle model.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.409-420
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• 2006

In this paper we consider the set of all n + 1-tuples of real numbers, not necessarily all distinct, in the decreasing order from the unit interval under the usual ordering of real numbers, always including 1. Such n + 1-tuples inherently arise as the membership values of fuzzy subsets and are called keychains. An natural equivalence relation is introduced on this set and the equivalence classes of keychains are studied here. The number of such keychains is finite and the set of all keychains is a lattice under the coordinate-wise ordering. Thus keychains are subchains of a finite chain of real numbers in the unit interval. We study some of their properties and give some applications to counting fuzzy subsets of finite sets.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.463-469
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• 2004

This paper discusses 2D lattice models of beams for simulating the fracture of brittle materials. A simulation of an experiment on a connote beam subjected to bending, in which two overlapping cracks occur, is used to study the effect of individual beam characteristics and different arrangements of the beams in the overall lattice. It was found that my regular orientation of the beams influences the resulting crack patterns. Methods to implement a wide range of poisson's ratios are also developed, the use of the lattice to study arbitrary micro-structures is outlined The crack pattern that n obtained with lattice m in good agreement with the experimental results. Also, numerical simulations of the tests were performed by means of a lattice model, and non-integer dimensions were measured on the predicted lattice damage patterns.