• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.265-279
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• 2023

In this paper, we firstly presented the definitions of arithmetic ${\mathcal{I}}$-statistically convergence, ${\mathcal{I}}$-lacunary arithmetic statistically convergence, strongly ${\mathcal{I}}$-lacunary arithmetic convergence, ${\mathcal{I}}$-Cesàro arithmetic summable and strongly ${\mathcal{I}}$-Cesàro arithmetic summable using weighted density via Orlicz function ${\tilde{\phi}}$. Then, we proved some theorems associated with these concepts, and we examined the relationship between them. Finally, we establish some sequential properties of ${\mathcal{I}}$-lacunary arithmetic statistical continuity.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.327-339
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• 2022

In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.715-718
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• 2005

Mobile devices is getting to include more functions according to the demand of digital convergence. Applications based on 3D graphic calculation such as 3D games and navigation are one of the functions. 3D graphic calculation requires heavy calculation. Therefore, we need dedicated 3D graphic hardware unit with high performance. 3D graphic calculation needs a lot of complicated floating-point arithmetic operation. However, most of current mobile 3D graphics processors do not have efficient architecture for mobile devices because they are based on those for conventional computer systems. In this paper, we propose arithmetic units for special functions of lighting operation of 3D graphics. Transcendental arithmetic units are designed using approximation of logarithm function. Special function units for lighting operation such as reciprocal, square root, reciprocal of square root, and power can be obtained. The proposed arithmetic unit has lower error rate and smaller silicon area than conventional arithmetic architecture.

• Journal of information and communication convergence engineering
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• v.9 no.4
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• pp.435-440
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• 2011

This paper propose the method of constructing the highly efficiency adder and multiplier systems over finite fields. The addition arithmetic operation over finite field is simple comparatively because that addition arithmetic operation is analyzed by each digit modP summation independently. But in case of multiplication arithmetic operation, we generate maximum k=2m-2 degree of ${\alpha}^k$ terms, therefore we decrease k into m-1 degree using irreducible primitive polynomial. We propose two method of control signal generation for the purpose of performing above decrease process. One method is the combinational logic expression and the other method is universal signal generation. The proposed method of constructing the highly adder/multiplier systems is as following. First of all, we obtain algorithms for addition and multiplication arithmetic operation based on the mathematical properties over finite fields, next we construct basic cell of A-cell and M-cell using T-gate and modP cyclic gate. Finally we construct adder module and multiplier module over finite fields after synthesizing ${\alpha}^k$ generation module and control signal CSt generation module with A-cell and M-cell. Next, we constructing the arithmetic operation unit over finite fields. Then, we propose the future research and prospects.

• East Asian mathematical journal
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• v.35 no.1
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• pp.59-66
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• 2019

In this paper we study implicit-explicit (IMEX) methods combined with a semi-Lagrangian scheme to evaluate the prices of fixed strike arithmetic Asian options under jump-diffusion models. An Asian option is described by a two-dimensional partial integro-differential equation (PIDE) that has no diffusion term in the arithmetic average direction. The IMEX methods with the semi-Lagrangian scheme to solve the PIDE are discretized along characteristic curves and performed without any fixed point iteration techniques at each time step. We implement numerical simulations for the prices of a European fixed strike arithmetic Asian put option under the Merton model to demonstrate the second-order convergence rate.

• Journal of IKEEE
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• v.17 no.3
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• pp.346-351
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• 2013

Low-cost and low-power are important requirements in mobile systems. Thus, when a floating-point arithmetic unit is needed, 24-bit floating-point format can be more useful than 32-bit floating-point format. However, a 24-bit floating-point arithmetic unit can be risky because it usually has lower accuracy than a 32-bit floating-point arithmetic unit. Consecutive floating-point operations are performed in 3D graphic processors. In this case, the verification of the floating-point operation accuracy is important. Among 3D graphic arithmetic operations, the floating-point division is one of the most difficult operations to satisfy the accuracy of $10^{-5}$ which is the required accuracy in OpenGL ES 3.0. No 24-bit floating-point divider, whose accuracy is algebraically verified, has been reported. In this paper, a 24-bit floating-point divider is analyzed and it is algebraically verified that its accuracy satisfies the OpenGL requirement.

• Journal of the Institute of Convergence Signal Processing
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• v.13 no.1
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• pp.19-25
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• 2012

An adaptive system is a well-known method for removing noise from noise-corrupted speech. In this paper, we perform a least mean square (LMS) based on wavelet adaptive algorithm. It establishes the faster convergence rate of as compared to time domain because of eigenvalue distribution width. And this paper provides the basic tool required for the FIR algorithm whose algorithm reduces the arithmetic complexity. We consider a new fast short-length running FIR structure in discrete wavelet adaptive algorithm. We compare FIR algorithm and short-length fast running FIR algorithm (SFIR) to the proposed fast short-length running FIR algorithm(FSFIR) for arithmetic complexities.

• Journal of electromagnetic engineering and science
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• v.9 no.1
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• pp.12-16
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• 2009

This paper presents a new iterative locally one-dimensional [mite-difference time-domain(LOD-FDTD) method that has a simpler formula than the original iterative LOD-FDTD formula[l]. There are fewer arithmetic operations than in the original LOD-FDTD scheme. This leads to a reduction of CPU time compared to the original LOD-FDTD method while the new method exhibits the same numerical accuracy as the iterative ADI-FDTD scheme. The number of arithmetic operations shows that the efficiency of this method has been improved approximately 20 % over the original iterative LOD-FDTD method.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.1-12
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• 2015

We present a local convergence analysis for inexact Newton-like method in a Banach space under weaker Lipschitz condition. The convergence ball is enlarged and the estimates on the error distances are more precise under the same computational cost as in earlier studies such as [6, 7, 11, 18]. Some special cases are considered and applications for solving nonlinear systems using the Newton-arithmetic mean method are improved with the new convergence technique.

• International Journal of Internet, Broadcasting and Communication
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• v.13 no.3
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• pp.118-123
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• 2021

Recently, digital crime is becoming more intelligent, and efficient digital forensic techniques are required to collect evidence for this. In the case of important files related to crime, a specific person may intentionally delete the file. In such a situation, data recovery is a very important procedure that can prove criminal charges. Although there are various methods to recover deleted files, we focuses on the recovery technique using HxD editor. When recovering a deleted file using the HxD editor, check the file structure and access the file data area through calculation. However, there is a possibility that errors such as arithmetic errors may occur when a file approach through calculation is used. Therefore, in this paper, we propose an algorithm that automatically calculates the header and footer of a file after checking the file signature in the root directory for efficient file recovery. If the algorithm proposed in this paper is used, it is expected that the error rate of arithmetic errors in the file recovery process can be reduced.