• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.4
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• pp.375-385
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• 2020

In this paper, a special indefinite inner product, named hyperbolic scalar product, is used and all acquired results have been raised and proved with the proviso that the space is equipped with this indefinite scalar product. The main objective is to be introduced and applied an indefinite oblique projection method, called Indefinite Lanczos J-biorthogonalizatiom process, which in addition to building a pair of J-biorthogonal bases for two used Krylov subspaces, leads to the introduction of a process for solving large non-J-symmetric linear systems, i.e., Indefinite two-sided Lanczos Algorithm for Linear systems.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.7
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• pp.503-512
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• 2001

The general DSP algorithm, like orthogonal transform or filter processing, needs efficient hardware architecture to compute inner product. The typical MAC architecture has high cost of silicon. Because of this reason, the distributed arithmetic without multiplier is widely used for implementing inner product. This paper presents the optimization to reduce required hardware in distributed arithmetic by using extraction method of adder sharing component. The optimization process uses Boltzmann-machine which is one of the neural network. This proposed method can solve problem that is increasing complexity depending on depth of inner product and compose optimal summation-network with the minimum FA and FF in a few time. The designed DCT by using Proposed method is more efficient than a ROM-based distributed arithmetic.

• Herbal Formula Science
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• v.26 no.4
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• pp.319-327
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• 2018

Objectives : Astragali Radix is known as a perennial plant, and it is estimated that there may be differences in the contents and their components depending on the ages. The components of astragali radix may activate differently. Methods : The astragali radix components cultivated in Jecheon( one year ), Korea, Shanxi province( 7 years ), China, Inner Mongolia( 5 years) and Inner Mongolia ( 8 years ) were extracted with pure ethyl alcohol and identified the component molecules. The extracted components of astragali radix were measured the activity of Telomerase for confirmation of their Telomere lengths. Results : The cell activity has been shown the greatest contribution in astragali radix of Inner Mongolia(8 years). Although there is the difference in cell activity between the two products of the 5 and 7 years, the difference between the values was small and the 7 years product was slightly higher than 5 years product. Conclusions : Total Astragaloside contents were highest in the product of Inner Mongolia(8 years), followed by the 7 year product of Shanxi province. Especially, astragaloside and cycloastragenol (TA-65) among the astragali radix components have shown to be increased Telomerase activity in the DNA metabolism of the cells, and the efficacy depends on the ages of growth.

• Transactions of Materials Processing
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• v.6 no.4
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• pp.329-337
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• 1997

Forging of an inner pulley for compressor clutch assembly of car air conditioner is investigated in this study. In cold forging of inner pulley, the design requirements are to keep the same height of the inner rib and the outer one, and to make uniform the hardness distribution in the forged product. Using the rigid-plastic finite element simulation. we design the optimal process conditions, which has a performing operation. Also the final product configuration of forging has to be designed again in view of the metal flow involved in the operation, derived from the finite element simulations. The forged pulley is investigated by checking the hardness distribution and it is noted that the distribution has improved to be even and high enough for industrial application.

• Korean Journal of Remote Sensing
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• v.23 no.6
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• pp.553-558
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• 2007

The equation based on vector inner product by the angles between pairs of two image rays can independently separate the position and pose of a camera. As our second application, the exterior calibration between a camera and a laser range finder is proposed here through analysis of surfaces created by the equation.

• The Transactions of the Korea Information Processing Society
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• v.7 no.12
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• pp.3986-3994
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• 2000

A multiple vector reductive processing occurs during the vector inner product operation ([C] = [A] $\bigodot$,$\square$ [B]) and proceeds at the hardware dyadic pipeline unit. Every scalar result has to be generated with the component merging delay time in the multiple vector reduction($\bigodot$). In this paper we propose a new design method by which the component merging time could be eliminated from the multiple reduction and the scalar results from the reduction($\bigodot$) could be generated nearly in the almost same condensed time as the input components are fel>ded in the dyadic pipeline unitlo) or the output components are drained out of the dyadic pipeline unit($\square$), so called a dedicated chained pipeline unit for only a inner product operation.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.23 no.1
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• pp.33-43
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• 2013

The research on data mining that can manage a large amount of information efficiently has grown with the drastic increment of information. Privacy-preserving data mining can protect the privacy of data owners. There are several privacy-preserving association rule, clustering and classification protocols. A privacy-preserving association rule protocol is used to find association rules among data, which is often used for marketing. In this paper, we propose a privacy-preserving k-bits inner product protocol based on Shamir's secret sharing.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.