• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1211-1226
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• 2021

The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some ℚ-polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.9
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• pp.3087-3103
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• 2022

Nearest neighbor query in location-based services has become a popular application. Aiming at the shortcomings of the privacy protection algorithms of traditional ciphertext nearest neighbor query having the high system overhead because of the usage of the double Hilbert curves and having the inaccurate query results in some special circumstances, a privacy protection algorithm of ciphertext nearest neighbor query which is based on the single Hilbert curve has been proposed. This algorithm uses a single Hilbert curve to transform the two-dimensional coordinates of the points of interest into Hilbert values, and then encrypts them by the order preserving encryption scheme to obtain the one-dimensional ciphertext data which can be compared in numerical size. Then stores the points of interest as elements composed of index value and the ciphertext of the other information about the points of interest on the server-side database. When the user needs to use the nearest neighbor query, firstly calls the approximate nearest neighbor query algorithm proposed in this paper to query on the server-side database, and then obtains the approximate nearest neighbor query results. After that, the accurate nearest neighbor query result can be obtained by calling the precision processing algorithm proposed in this paper. The experimental results show that this privacy protection algorithm of ciphertext nearest neighbor query which is based on the single Hilbert curve is not only feasible, but also optimizes the system overhead and the accuracy of ciphertext nearest neighbor query result.

• Journal of Biomedical Engineering Research
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• v.14 no.1
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• pp.9-16
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• 1993

For efficient storage and transmission of medical images, the requirement of image com pression is increasing. Because differences between reconstructed images and original images are related with errors In the diagnosis, lossless compression is generally preferred in mod- ical images. in Run Length Coding which is one of the lossless compression method, we have applied modified scanning direction based on the Hilbert curve, which is a kind of space fill ins curve. We have substituted the traditional raster scanning by Hilbert curve direction scanning. Using this method, we have studied enhancement of compression efficiency for medical images.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.1
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• pp.125-129
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• 2014

In this paper, design and fabrication of the GPS receiving antenna using Hilbert curve fractal structure was proposed. The size of the antenna was miniaturized by transforming dipole structure into monopole structure because its size increases if Hilbert curve fractal dipole structure is used. To use a Hilbert curve structure, the current directions of the radiator were made oppositely each other. The size of the antenna is $10{\times}10{\times}0.8[mm]$, the line width is 0.25[mm]. The resonant frequency is 1.58[GHz] and its range is 1.52[GHz] ~ 1.65[GHz]. Frequency bandwidth is 130[MHz]. Antenna maximum gain is 3.09[dBi].

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.38-41
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• 2002

Many scientifc applications include manipulation of data points tying in a space. We describe a method, based on sector labeling to generate a space-filling curve for partitioning such given data points. Our method is straightforward and flexible, equipping a one-one correspondence between point-values on the curve and data points in space in more efficient than designated methods found in the literature. It is widely believed that the Hilbert curve achieves the desired properties on linear mappings due to the locality between data points. Therefore we focus on the Hilbert curve since, later on, we identify it as the most suitable for our application. We demonstrate on using our method for the data particles of an n-body simulation that based on Barnes-Hut algorithm.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.12
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• pp.1184-1187
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• 2011

In this letter, a planar monopole UWB antenna with dual band-notched characteristics is proposed. The band-stop characteristics is realized by embedding the 1st/3rd order Hilbert-curve slots on the patch. With the dimension adjustment of each Hilbert-curve slots, the band rejection from 3.3 to 3.7 GHz and from 5.3 to 6 GHz can be accomplished easily. The VSWR and radiation pattern of the fabricated antenna are measured, and the proposed antenna would be adequate to a UWB applications.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.11
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• pp.1071-1075
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• 2010

Because a sensor node in wireless sensor networks(WSNs) has limited resources, such as battery capacity and memory, data aggregation techniques have been studied to manage the limited resources efficiently. Because sensor network uses wireless communication, a data can be disclosed by attacker. Thus, the study on data protection schemes for data aggregation is essential in WSNs. But the existing data aggregation methods require both a large number of computation and communication, in case of network construction and data aggregation processing. To solve the problem, we propose a data protection scheme based on Hilbert-curve for data aggregation. Our scheme can minimizes communications among neighboring sensor nodes by using tree-based routing. Moreover, it can protect the data from attacker by doing encryption through a Hilbert-curve technique based on a private seed, Finally, we show that our scheme outperforms the existing methods in terms of message transmission and average sensor node lifetime.

• Transactions on Electrical and Electronic Materials
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• v.17 no.5
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• pp.257-260
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• 2016

In this paper, two configurations (T-type and Y-type) of dual band Wilkinson Power Divider based upon Hilbert curves are presented. Formerly, the concept of Hilbert Curves was implemented in only designing microstrip antennas. In power dividers, this is the very first attempt of incorporating them for size reduction. In addition to this, an effect of inculcation of high-dielectric constant layer (Hafnium-oxide, HfO₂, ε_r= 25) between a substrate and top metallization in both configurations was investigated. The proposed configurations are designed on a high resistive silicon substrate (HRS) for L and S bands with resonating frequencies of 1.575 and 3.4 GHz. Both configurations have return loss that is better than 20 dB and an insertion loss of around 6 dB; isolation better than 30 dB was achieved for both models.

• The Journal of the Korea Contents Association
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• v.7 no.4
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• pp.30-38
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• 2007

In this paper, UHF band RFID reader antenna using filbert curve fractal structure and adding the partially grounded plane at the bottom of antenna, which has a resonant frequency at 910MHz, is proposed. Input impedance of antenna is matched with the feed line of 50ohm by varying the length and width of line segment making up the antenna, and by moving the position of via hole. The gain and directivity of antenna is enhanced as varying the dimension of the partially grounded plane and adding the line segment. The size of fabricated antenna is $68mm\times68mm$. The impedance band width(VSWR<2) is $882\sim942MHz$. The return loss and the gain of fabricated antenna are -18.2dB, 5.3dBi at 910MHz.

• The Journal of the Korea Contents Association
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• v.7 no.7
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• pp.11-23
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• 2007

Applications involving moving objects require index structures to handle frequent updates of objects' locations efficiently. Several methods to index the current, the past and the future positions of moving objects have been proposed for the applications. Most of them are based on R-tree like index structures. Some researches have made efforts to improve update performance of R-trees that are actually focused on query performance. Even though the update performance is improved by researchers' efforts, the overhead and immaturity of concurrency control algorithms of R-trees makes us hesitate to choose them for moving objects. In this paper, we propose an update efficient indexing method that can be applicable for indexing the past, the current and the future locations. The proposed index is based on B+-Trees and Hilbert curve. We present an advanced Hilbert curve that adjusts automatically the order of Hilbert curve in subregions according to the data distribution and the number of data objects. Through empirical studies, we show that our strategy achieves higher response time and throughput.