• Communications of Mathematical Education
• /
• v.37 no.1
• /
• pp.65-84
• /
• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.

• Journal of Internet of Things and Convergence
• /
• v.9 no.6
• /
• pp.57-62
• /
• 2023

This research is a comparative analysis of the U.S. S&P 500 index using the volatility breakout strategy against the Buy and Hold approach. The volatility breakout strategy is a trading method that exploits price movements after periods of relative market stability or concentration. Specifically, it is observed that large price movements tend to occur more frequently after periods of low volatility. When a stock moves within a narrow price range for a while and then suddenly rises or falls, it is expected to continue moving in that direction. To capitalize on these movements, traders adopt the volatility breakout strategy. The 'k' value is used as a multiplier applied to a measure of recent market volatility. One method of measuring volatility is the Average True Range (ATR), which represents the difference between the highest and lowest prices of recent trading days. The 'k' value plays a crucial role for traders in setting their trade threshold. This study calculated the 'k' value at a general level and compared its returns with the Buy and Hold strategy, finding that algorithmic trading using the volatility breakout strategy achieved slightly higher returns. In the future, we plan to present simulation results for maximizing returns by determining the optimal 'k' value for automated trading of the S&P 500 index using artificial intelligence deep learning techniques.

• Economic and Environmental Geology
• /
• v.57 no.2
• /
• pp.129-141
• /
• 2024

This study derived production-production multipliers using a regional input-output table and estimated the induced effect of aggregates through the non-metallic minerals sector and the concrete products sector. In deriving the induced effect of aggregates, it is difficult to use the regional input-output table due to the sector classification problem. This study analyzed the non-metallic mineral sector, including aggregates, as aggregates sector, and the concrete products sector, which uses most of the aggregate production. By analyzing this, we attempted to alleviate difficulties caused by sector classification restrictions. In the process of estimating the induced effect, it was assumed that there was a decrease in aggregate production, and in the process of analyzing the concrete products sector, the effect of the decrease in concrete product production due to the decrease in aggregate production, that is, the decrease in production of one unit of aggregate was 0.8511 in the concrete product sector. The analysis was conducted on the premise of a decrease in unit production. Inducing effects within and between regions were calculated for the 17 metropolitan cities and provinces classified by the regional input-output table. The employment effect was also calculated, assuming a 10% production decrease to show differences according to the size of the aggregate and concrete product sectors in each region.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.54 no.7
• /
• pp.21-28
• /
• 2017

Practical models for FPGA architectures which include performance- and/or density-enhancing components such as carry chains, wide function multiplexers, and memory/multiplier blocks are being applied to academic FPGA placement tools which used to rely on simple imaginary models. Previously the techniques such as pre-packing and multi-layer density analysis are proposed to remedy issues related to such practical models, and the wire length is effectively minimized during initial analytic placement. Since timing should be optimized rather than wire length, most previous work takes into account the timing constraints. However, instead of the initial analytic placement, the timing-driven techniques are mostly applied to subsequent steps such as placement legalization and iterative improvement. This paper incorporates the timing driven techniques, which check if the placement meets the timing constraints given in the standard SDC format, and minimize the detected violations, with the existing analytic placer which implements pre-packing and multi-layer density analysis. First of all, a static timing analyzer has been used to check the timing of the wire-length minimized placement results. In order to minimize the detected violations, a function to minimize the largest arrival time at end points is added to the objective function of the analytic placer. Since each clock has a different period, the function is proposed to be evaluated for each clock, and added to the objective function. Since this function can unnecessarily reduce the unviolated paths, a new function which calculates and minimizes the largest negative slack at end points is also proposed, and compared. Since the existing legalization which is non-timing driven is used before the timing analysis, any improvement on timing is entirely due to the functions added to the objective function. The experiments on twelve industrial examples show that the minimum arrival time function improves the worst negative slack by 15% on average whereas the minimum worst negative slack function improves the negative slacks by additional 6% on average.

• The Korean Journal of Nuclear Medicine
• /
• v.32 no.4
• /
• pp.365-373
• /
• 1998

Purpose: The conventional gamma camera is not ideal for scintimammography because of its large detector size (${\sim}500mm$ in width) causing high cost and low image quality. We are developing a small gamma camera dedicated for breast imaging. Materials and Methods: The small gamma camera system consists of a NaI (T1) crystal ($60 mm{\times}60 mm{\times}6 mm$) coupled with a Hamamatsu R3941 Position Sensitive Photomultiplier Tube (PSPMT), a resister chain circuit, preamplifiers, nuclear instrument modules, an analog to digital converter and a personal computer for control and display. The PSPMT was read out using a standard resistive charge division which multiplexes the 34 cross wire anode channels into 4 signals ($X^+,\;X^-,\;Y^+,\;Y^-$). Those signals were individually amplified by four preamplifiers and then, shaped and amplified by amplifiers. The signals were discriminated ana digitized via triggering signal and used to localize the position of an event by applying the Anger logic. Results: The intrinsic sensitivity of the system was approximately 8,000 counts/sec/${\mu}Ci$. High quality flood and hole mask images were obtained. Breast phantom containing $2{\sim}7 mm$ diameter spheres was successfully imaged with a parallel hole collimator The image displayed accurate size and activity distribution over the imaging field of view Conclusion: We have succesfully developed a small gamma camera using NaI(T1)-PSPMT and nuclear Instrument modules. The small gamma camera developed in this study might improve the diagnostic accuracy of scintimammography by optimally imaging the breast.

• Korean small business review
• /
• v.31 no.4
• /
• pp.67-93
• /
• 2009

The purpose of this paper is to explore the relations between financial constraints and dividend smoothing of innovative small and medium sized enterprises(SMEs) listed on Korea Securities Market and Kosdaq Market of Korea Exchange. The innovative SMEs is defined as the firms with high level of R&D intensity which is measured by (R&D investment/total sales) ratio, according to Chauvin and Hirschey (1993). The R&D investment plays an important role as the innovative driver that can increase the future growth opportunity and profitability of the firms. Therefore, the R&D investment have large, positive, and consistent influences on the market value of the firm. In this point of view, we expect that the innovative SMEs can adjust dividend payment faster than the noninnovative SMEs, on the ground of their future growth opportunity and profitability. And also, we expect that the financial unconstrained firms can adjust dividend payment faster than the financial constrained firms, on the ground of their financing ability of investment funds through the market accessibility. Aivazian et al.(2006) exert that the financial unconstrained firms with the high accessibility to capital market can adjust dividend payment faster than the financial constrained firms. We collect the sample firms among the total SMEs listed on Korea Securities Market and Kosdaq Market of Korea Exchange during the periods from January 1999 to December 2007 from the KIS Value Library database. The total number of firm-year observations of the total sample firms throughout the entire period is 5,544, the number of firm-year observations of the dividend firms is 2,919, and the number of firm-year observations of the non-dividend firms is 2,625. About 53%(or 2,919) of these total 5,544 observations involve firms that make a dividend payment. The dividend firms are divided into two groups according to the R&D intensity, such as the innovative SMEs with larger than median of R&D intensity and the noninnovative SMEs with smaller than median of R&D intensity. The number of firm-year observations of the innovative SMEs is 1,506, and the number of firm-year observations of the noninnovative SMEs is 1,413. Furthermore, the innovative SMEs are divided into two groups according to level of financial constraints, such as the financial unconstrained firms and the financial constrained firms. The number of firm-year observations of the former is 894, and the number of firm-year observations of the latter is 612. Although all available firm-year observations of the dividend firms are collected, deletions are made in the case of financial industries such as banks, securities company, insurance company, and other financial services company, because their capital structure and business style are widely different from the general manufacturing firms. The stock repurchase was involved in dividend payment because Grullon and Michaely (2002) examined the substitution hypothesis between dividends and stock repurchases. However, our data structure is an unbalanced panel data since there is no requirement that the firm-year observations data are all available for each firms during the entire periods from January 1999 to December 2007 from the KIS Value Library database. We firstly estimate the classic Lintner(1956) dividend adjustment model, where the decision to smooth dividend or to adopt a residual dividend policy depends on financial constraints measured by market accessibility. Lintner model indicates that firms maintain stable and long run target payout ratio, and that firms adjust partially the gap between current payout rato and target payout ratio each year. In the Lintner model, dependent variable is the current dividend per share(DPS_t), and independent variables are the past dividend per share(DPS_t-1) and the current earnings per share(EPS_t). We hypothesized that firms adjust partially the gap between the current dividend per share(DPS_t) and the target payout ratio(Ω) each year, when the past dividend per share(DPS_t-1) deviate from the target payout ratio(Ω). We secondly estimate the expansion model that extend the Lintner model by including the determinants suggested by the major theories of dividend, namely, residual dividend theory, dividend signaling theory, agency theory, catering theory, and transactions cost theory. In the expansion model, dependent variable is the current dividend per share(DPS_t), explanatory variables are the past dividend per share(DPS_t-1) and the current earnings per share(EPS_t), and control variables are the current capital expenditure ratio(CEA_t), the current leverage ratio(LEV_t), the current operating return on assets(ROA_t), the current business risk(RISK_t), the current trading volume turnover ratio(TURN_t), and the current dividend premium(DPREM_t). In these control variables, CEA_t, LEV_t, and ROA_t are the determinants suggested by the residual dividend theory and the agency theory, ROA_t and RISK_t are the determinants suggested by the dividend signaling theory, TURN_t is the determinant suggested by the transactions cost theory, and DPREM_t is the determinant suggested by the catering theory. Furthermore, we thirdly estimate the Lintner model and the expansion model by using the panel data of the financial unconstrained firms and the financial constrained firms, that are divided into two groups according to level of financial constraints. We expect that the financial unconstrained firms can adjust dividend payment faster than the financial constrained firms, because the former can finance more easily the investment funds through the market accessibility than the latter. We analyzed descriptive statistics such as mean, standard deviation, and median to delete the outliers from the panel data, conducted one way analysis of variance to check up the industry-specfic effects, and conducted difference test of firms characteristic variables between innovative SMEs and noninnovative SMEs as well as difference test of firms characteristic variables between financial unconstrained firms and financial constrained firms. We also conducted the correlation analysis and the variance inflation factors analysis to detect any multicollinearity among the independent variables. Both of the correlation coefficients and the variance inflation factors are roughly low to the extent that may be ignored the multicollinearity among the independent variables. Furthermore, we estimate both of the Lintner model and the expansion model using the panel regression analysis. We firstly test the time-specific effects and the firm-specific effects may be involved in our panel data through the Lagrange multiplier test that was proposed by Breusch and Pagan(1980), and secondly conduct Hausman test to prove that fixed effect model is fitter with our panel data than the random effect model. The main results of this study can be summarized as follows. The determinants suggested by the major theories of dividend, namely, residual dividend theory, dividend signaling theory, agency theory, catering theory, and transactions cost theory explain significantly the dividend policy of the innovative SMEs. Lintner model indicates that firms maintain stable and long run target payout ratio, and that firms adjust partially the gap between the current payout ratio and the target payout ratio each year. In the core variables of Lintner model, the past dividend per share has more effects to dividend smoothing than the current earnings per share. These results suggest that the innovative SMEs maintain stable and long run dividend policy which sustains the past dividend per share level without corporate special reasons. The main results show that dividend adjustment speed of the innovative SMEs is faster than that of the noninnovative SMEs. This means that the innovative SMEs with high level of R&D intensity can adjust dividend payment faster than the noninnovative SMEs, on the ground of their future growth opportunity and profitability. The other main results show that dividend adjustment speed of the financial unconstrained SMEs is faster than that of the financial constrained SMEs. This means that the financial unconstrained firms with high accessibility to capital market can adjust dividend payment faster than the financial constrained firms, on the ground of their financing ability of investment funds through the market accessibility. Futhermore, the other additional results show that dividend adjustment speed of the innovative SMEs classified by the Small and Medium Business Administration is faster than that of the unclassified SMEs. They are linked with various financial policies and services such as credit guaranteed service, policy fund for SMEs, venture investment fund, insurance program, and so on. In conclusion, the past dividend per share and the current earnings per share suggested by the Lintner model explain mainly dividend adjustment speed of the innovative SMEs, and also the financial constraints explain partially. Therefore, if managers can properly understand of the relations between financial constraints and dividend smoothing of innovative SMEs, they can maintain stable and long run dividend policy of the innovative SMEs through dividend smoothing. These are encouraging results for Korea government, that is, the Small and Medium Business Administration as it has implemented many policies to commit to the innovative SMEs. This paper may have a few limitations because it may be only early study about the relations between financial constraints and dividend smoothing of the innovative SMEs. Specifically, this paper may not adequately capture all of the subtle features of the innovative SMEs and the financial unconstrained SMEs. Therefore, we think that it is necessary to expand sample firms and control variables, and use more elaborate analysis methods in the future studies.