• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1015-1021
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• 2011

A point of a Riemann surface X is said to be its fixed point if it is a fixed point of one of its nontrivial holomorphic automorphisms. We start this note by proving that the set Fix(X) of fixed points of Riemann surface X of genus g${\geq}$2 has at most 82(g-1) elements and this bound is attained just for X having a Hurwitz group of automorphisms, i.e., a group of order 84(g-1). The set of such points is invariant under the group of holomorphic automorphisms of X and we study the corresponding symmetric representation. We show that its algebraic type is an essential invariant of the topological type of the holomorphic action and we study its kernel, to find in particular some sufficient condition for its faithfulness.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.29A no.3
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• pp.96-105
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• 1992

The use of fixed-point digital signal processors, such as the TMS 320C25, requires scaling of data at each arithmetic step to prevent overflows while keeping the accuracy. A software which automatizes this process is developed for TMS 320C25. The programmers use a model of a hypothetical floating-point digital signal processor and a floating-point format for data representation. However, the program and data are automatically translated to a fixed-point version by this software. Thus, the execution speed is not sacrificed. A fixed-point variable has a unique binary-point location, which is dependent on the range of the variable. The range is estimated from the floating-point simulation. The number of shifts needed for arithmetic or data transfer step is determined by the binary-points of the variables associated with the operation. A fixed-point code generator is also developed by using the proposed automatic scaling software. This code generator produces floating-point assembly programs from the specifiations of FIR, IIR, and adaptive transversal filters, then floating-point programs are transformed to fixed-point versions by the automatic scaling software.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.40 no.4
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• pp.331-341
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• 1991

The discrete cosine transform (DCT) is widely used in many signal processing areas, including image and speech data compression. In this paper, we investigate a fixed-point error analysis for fast DCT algorithms, namely, Lee [6], Hou [7] and Vetterli [8]. A statistical model for fixed-point error is analyzed to predict the output noise due to the fixed-point implementation. This paper deals with two's complement fixed-point data representation with truncation and rounding. For a comparison purpose, we also investigate the direct form DCT algorithm. We also propose a suitable scaling model for the fixed-point implementation to avoid an overflow occurring in the addition operation. Computer simulation results reveal that there is a close agreement between the theoretical and the experimental results. The result shows that Vetterli's algorithm is better than the other algorithms in terms of SNR.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.22 no.1
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• pp.1-8
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• 2018

Recently, the convolutional neural network shows high performance in many computer vision tasks. However, convolutional neural networks require enormous amount of operation, so it is difficult to adopt them in the embedded environments. To solve this problem, many studies are performed on the ASIC or FPGA implementation, where an efficient representation method is required. The fixed-point representation is adequate for the ASIC or FPGA implementation but causes a performance degradation. This paper proposes a separate optimization of representations for the convolutional layers and the batch normalization layers. With the proposed method, the required bit width for the convolutional layers is reduced from 16 bits to 10 bits for the ResNet-50 neural network. Since the computation amount of the convolutional layers occupies the most of the entire computation, the bit width reduction in the convolutional layers enables the efficient implementation of the convolutional neural networks.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.33-37
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• 2008

Let G be a compact abelian Lie group, and M an odd-dimensional closed smooth G-manifold. If the fixed point set $M^G\neq\emptyset$ and dim $M^G=0$, then G has a subgroup H with $G/H{\cong}\mathbb{Z}_2$, the cyclic group of order 2. The tangential representation $\tau_x$(M) of G at $x{\in}M^G$ is also regarded as a representation of H by restricted action. We show that the number of fixed points is even, and that the tangential representations at fixed points are pairwise isomorphic as representations of H.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.3
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• pp.454-468
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• 1997

This paper presents a bitwidth optimization algorithm for efficient hardware sharing in digital signal processing system. The proposed algorithm determines the fixed-point representation for each signal through bitwidth optimization to generate the hardware requiring less area. To reduce the operator area, the algorithm partitions the abstract operations in the design description into several groups, such that the operations in the same group can share an operator. The partitioning result are fed to a high-level synthesis system to generate the pipelined fixed-point datapaths. The proposed algorithm has been implemented in SODAS-DSP an automatic synthesis system for fixed-point DSP hardware. Accepting the models of DSP algorithms in schematics, the system automatically generates the fixed-point datapath and controller satisfying the design constraints in area, speed, and SNR(Signal-to-Noise Ratio). Experimental results show that the efficiency of the proposed algorithm by generates the area-efficient DSP hardwares satisfying performance constraints.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.557-570
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• 2015

Let $\mathbb{G}$ be a von Neumann algebraic locally compact quantum group, in the sense of Kustermans and Vaes. In this paper, as a consequence of a notion of amenability for actions of Lau algebras, we show that $\hat{\mathbb{G}}$, the dual of $\mathbb{G}$, is co-amenable if and only if there is a state $m{\in}L^{\infty}(\hat{\mathbb{G}})^*$ which is invariant under a left module action of $L^1(\mathbb{G})$ on $L^{\infty}(\hat{\mathbb{G}})^*$. This is the quantum group version of a result by Stokke [17]. We also characterize amenable action of Lau algebras by several properties such as fixed point property. This yields in particular, a fixed point characterization of amenable groups and H-amenable representation of groups.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.433-444
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• 2024

Our study explores the connection between the Pythagorean theorem and the Fixed-point theorem in metric spaces. Both of which center around the concepts of distance transformations and point relationships. The Pythagorean theorem deals with right triangles in Euclidean space, emphasizing distances between points. In contrast, fixed-point theorems pertain to the points that remain unchanged under specific transformations thereby preserving distances. The article delves into the intrinsic correlation between these concepts and presents a novel study in Euclidean metric spaces, examining the relationship between contraction mapping and Pythagorean Right Triangles. Practical applications are also discussed particularly in the context of image compression. Here, the integration of the Pythagorean right triangle paradigm with contraction mappings results in efficient data representation and the preservation of visual data relation-ships. This illustrates the practical utility of seemingly abstract theories in addressing real-world challenges.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.647-649
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• 2004

When a controller is implemented by a one-chip processor with fixed-point operations, the finite alphabet problem usually occurs since parameters and signals should be taken in a finite set of values. This paper formulates PID finite alphabet PID control problem which combines the PID controller with the finite alphabet problem. We will propose a PID parameter tuning method based on an optimization algorithm under the finite alphabet condition. The PID parameters can be represented by a fixed-point representation, and then the problem is formulated as an optimization with constraints that parameters are taken in the finite set. Some simulation are to be performed to exemplify the performance of the PID parameter tuning method proposed in this paper.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.5 no.7
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• pp.1301-1307
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• 2001

Video retrieval system must offer representation frame list to do to do play from point that user wants. Representation frame list can get though cut detection point exactly. This paper dismembers frame to fixed block to cut detection point, and compare same block histogram cost of next time frame. If result that compare does not exceed thresold, detect next frame to cutting.