• Journal of the Korean School Mathematics Society
• /
• v.16 no.4
• /
• pp.841-862
• /
• 2013

This study analyzed issues in the mathematics curriculum concerning the cognitive development of the vector and inner product concepts in the light of Tall's and Watson's research(Tall, 2004a; Tall, 2004b; Watson et al., 2003; Watson, 2002). Some suggestions in teaching the vector and inner product concepts were elaborated in the terms of these analyses. First, the position vector needs to be represented by an arrow on the coordinate system in order to introduce the component form of a vector represented by a directed line segment. Second, proofs of the vector operation law should be carried out by symbolic manipulations based on the algebraic concept of a vector in the symbolic world. Third, it is appropriate that the inner product is defined as $\vec{a}{\cdot}\vec{b}=a_1b_1+a_2b_2$ (when, $\vec{a}=(a_1,a_2)$, $\vec{b}=(b_1,b_2)$) when it comes to considering the meaning of the inner product relevant to vector space in the formal world. Cognitive growth of concepts of the vector and inner product can be properly induced through revising explanation methods about the concepts in the curriculum in the basis of the above suggestions.

• Proceedings of the Optical Society of Korea Conference
• /
• 1990.02a
• /
• pp.102-111
• /
• 1990

In this thesis, an optical bidirectional inner-product associative memory model using liquid crystal television is proposed and analyzed theoretically and realized experimentally. The LCTV is used as a SLM(spatial light modulator), which is more practical than conventional SLMs, to produce image vector in terms of computer and CCD camera. Memory and input vectors are recorded into each LCTV through the video input connectors of it by using the image board. Two multi-focus hololenses are constructed in order to perform optical inner-product process. In forward process, the analog values of inner-products are measured by photodetectors and are converted to digital values which are enable to control the weighting values of the stored vectors by changing the gray levels of the pixels of the LCTV. In backward process, changed stored vectors are used to produce output image vector which is used again for input vector after thresholding. After some iterations, one of the stored vectors is retrieved which is most similar to input vector in other words, has the nearest hamming distance. The experimental results show that the proposed inner-product associative memory model can be realized optically and coincide well with the computer simulation.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.50 no.11
• /
• pp.124-129
• /
• 2013

This paper proposes a high-performance vector inner product calculation circuit for real-time object recognition based on SVM algorithm. SVM algorithm shows a higher detection rate than other object recognition algorithms. However, it requires a huge amount of computational efforts. Since vector inner product calculation is one of the major operations of SVM algorithm, it is important to implement a high-performance vector inner product calculation circuit for real-time object recognition capability. The proposed circuit adopts the pipeline architecture with six stages to increase the operating speed and makes it possible to recognize objects in real time based on SVM. The proposed circuit was described in Verilog HDL at RTL. For silicon verification, an MPW chip was fabricated using TSMC 180nm standard cell library. The operation of the implemented MPW chip was verified on the test board with test application software developed for the chip verification.

• East Asian mathematical journal
• /
• v.22 no.1
• /
• pp.1-16
• /
• 2006

Some new reverses of the Schwarz inequality in inner product spaces and applications for vector-valued sequnces and integrals are given.

• School Mathematics
• /
• v.10 no.4
• /
• pp.573-581
• /
• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• The Transactions of the Korea Information Processing Society
• /
• v.7 no.12
• /
• pp.3986-3994
• /
• 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 Remote Sensing
• /
• v.23 no.6
• /
• pp.553-558
• /
• 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.

• International Journal of Aeronautical and Space Sciences
• /
• v.16 no.3
• /
• pp.437-444
• /
• 2015

Satellite selection and exclusion techniques have been applied to the global navigation satellite system (GNSS) with the aim of achieving a balance between navigational performance and computational efficiency. Conventional approaches to satellite selection based on the best dilution of precision (DOP) are excessively computational and complicated. This paper proposes a new method that applies a geometric sensitivity index of individual GNSS satellites. The sensitivity index is derived using the inner product of the line of sight (LOS) vector of each satellite. First, the LOS vector is computed, which accounts for the geometry between the satellite and user positions. Second, the inner product of each pair of LOS vectors is calculated, which indicates the proximities of the satellites to one another. The proximity can be determined according to the sensitivity of each satellite. A post-processing test was conducted to verify the reliability of the proposed method. The proposed index and the results of a conventional approach that measures the dilution of precision (DOP) were compared. The test results demonstrate that the proposed index produces results that are within 96% of those of the conventional approach and reduces the computational burden. This index can be utilized to estimate the sensitivity of individual satellites, obtaining a navigation solution. Therefore, the proposed index applies to satellite selection and exclusion as well as to the sensitivity analyses of multiple GNSS applications.

• Journal of Educational Research in Mathematics
• /
• v.25 no.2
• /
• pp.177-188
• /
• 2015

In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.

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