• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.101-129
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• 2018

From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.265-272
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• 2009

Fuzzy number intuitionistic fuzzy sets (FNIFSs), each of which is characterized by a membership function and a non-membership function whose values are trigonometric fuzzy number rather than exact numbers, are a very useful means to describe the decision information in the process of decision making. Wang [10] developed some arithmetic aggregation operators, such as the fuzzy number intuitionistic fuzzy weighted averaging (FIFWA) operator, the fuzzy number intuitionistic fuzzy ordered weighted averaging (FIFOWA) operator and the fuzzy number intuitionistic fuzzy hybrid aggregation (FIFHA) operator. In this paper, based on the FIFHA operator and the FIFWA operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as fuzzy number intuitionistic fuzzy decision matrices where each of the elements is characterized by fuzzy number intuitionistic fuzzy numbers, and the information about attribute weights is partially known. An example is used to illustrate the applicability of the proposed approach.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2011.10a
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• pp.415-418
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• 2011

This paper describes a circuit-level optimization of DFU(decoding function unit) for LDPC decoder which is used in wireless communication systems such as WiMAX and WLAN. The conventional DFU which is based on min-sum decoding algorithm needs conversions between two's complement values and sign-magnitude values, resulting in complex hardware. In this paper, a new design of DFU that is based on sign-magnitude arithmetic is proposed to achieve a simplified circuit and high-speed operation.

• The Journal of the Acoustical Society of Korea
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• v.23 no.8
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• pp.554-561
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• 2004

As the technologies of semiconductor and multimedia communication have been improved. the high-quality video and the multi-channel audio have been highlighted. MPEG Audio Layer 3 decoder has been implemented as a Processor using a standard. Since the synthesis filter of MPEG-1 Audio Layer 3 decoder requires the most outstanding operation in the entire decoder. the synthesis filter that can reduce the amount of operation is needed for the design of the high-speed processor. Therefore, in this paper, the synthesis filter. the most important part of MPEG Audio, is materialized in FPGA using the method of DAULT (distributed arithemetic look-up table). For the design of high-speed synthesis filter, the DAULT method is used instead of a multiplier and a Pipeline structure is used. The Performance improvement by 30% is obtained by additionally making the result of multiplication of data with cosine function into the table. All hardware design of this Paper are described using VHDL (VHIC Hardware Description Language) Active-HDL 6.1 of ALDEC is used for VHDL simulation and Synplify Pro 7.2V is used for Model-sim and synthesis. The corresponding library is materialized by XC4013E and XC4020EX. XC4052XL of XILINX and XACT M1.4 is used for P&R tool. The materialized processor operates from 20MHz to 70MHz.

• The KIPS Transactions:PartC
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• v.14C no.5
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• pp.431-438
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• 2007

RFID system is core technology that construct ubiquitous environment for replacement of barcode technology. Use ratio of RFID system rapidly increase because the technology has many good points such as identification speed, storage space, convenience etc. But low-cost tag operates easily by query of reader, so the system happened user privacy violent problem by tag information exposure. The system studied many ways for security application, but operation capability of low-cost tag is about $5K{\sim}10K$ gates, but only $250{\sim}3K$ gates allocated security part. So it is difficult to apply security to the system. Therefore, this scheme uses dividing 64 bits and reduces arithmetic, so proposed scheme provide mutual authentication that can apply to low-cost RFID system. Existing methods divide by 4 and used 96 bits. However, that reduces 32 bits length for lightweight and reduced from communication number of times of 7 times to 5 times. Also, because offer security by random number than existing scheme that generate two random numbers, that is more efficient. However, uses hash function for integrity that was not offered by XOR arithmetic and added extension of proposed scheme. Extended scheme is not offered efficiency than methods that use XOR arithmetic, but identification distance is mode that is proposed secure so that can use in for RFID system.

• JSTS:Journal of Semiconductor Technology and Science
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• v.4 no.4
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• pp.307-311
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• 2004

This paper presents an efficient architecture that optimizes the design of SEED S-box using composite field arithmetic. SEED is the Korean standard 128-bit block cipher algorithm developed by Korea Information Security Agency. The nonlinear function S-box is the most costly operation in terms. of size and power consumption, taking up more than 30% of the entire SEED circuit. Therefore the S-box design can become a crucial factor when implemented in systems where resources are limited such as smart cards. In this paper, we transform elements in $GF(2^8)$ to composite field $GF(((2^2)^2)^2)$ where more efficient computations can be implemented and transform the computed result back to $GF(2^8)$. This technique reduces the S-box portion to 15% and the entire SEED algorithm can be implemented at 8,700 gates using Samsung smart card CMOS technology.

• Proceedings of the KIEE Conference
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• 2008.04a
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• pp.155-156
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• 2008

In this paper, an interval type-2 fuzzy logic system is designed and compared with a type-1 fuzzy logic system. To compare performance of a type-1 fuzzy logic system with the type-2 fuzzy logic system, we apply type-1 fuzzy logic system and type-2 system to modeling the noised data. Membership function of interval type-2 fuzzy logic system is designed consequents of rules including uncertainty. For general type-2 fuzzy logic system computational complexity is severe. On the other hand, theoretic and arithmetic computations for interval type-2 fuzzy logic systems are very simple.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.351-372
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• 2013

In this paper, we study a distinction the two generating functions : ${\varphi}^k(q)=\sum_{n=0}^{\infty}r_k(n)q^n$ and ${\varphi}^{*,k}(q)={\varphi}^k(q)-{\varphi}^k(q^2)$ ($k$ = 2, 4, 6, 8, 10, 12, 16), where $r_k(n)$ is the number of representations of $n$ as the sum of $k$ squares. We also obtain some congruences of representation numbers and divisor function.

• Proceedings of the IEEK Conference
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• 2004.06b
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• pp.589-592
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• 2004

The CORDIC algorithm can be implemented very simple H/W, but needs a lot of latency to compute trigonometric function. The RA(Redundant Arithmetic) resolves this problem, but also has difficulty to determine the directions of micro-rotations. The pre-computed direction of micro-rotation algorithm relieves the RA of this matter. In this paper, we proposed the modified the pre-computed algorithm adopted with a table-lookup. Instead of reducing H/W complexity, its performance and calculation errors are improved.

• Journal of Industrial Technology
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• v.20 no.A
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• pp.203-209
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• 2000

The fluctuation integrals which give useful information in the structure of solution are associated with the mixed direct correlation integral ($C_{12}$) known. Using its weighted arithmetic mean of $C_{11}$ and $C_{22}$ and the activity coefficient model, the fluctuation integrals on solute-solute, solvent-solute, and solvent-solvent can be calculated in the function of mole fraction. In this work, several binary mixtures containing c-hexane were tested and the results on the fluctuation integrals were rather good.