• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1101-1111
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• 2008

Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.923-938
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• 2011

Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.137-143
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• 2007

In this paper, a Berstein-Hoeffding type inequality is established for linearly negative quadrant dependent random variables. A condition is given for almost sure convergence and the associated rate of convergence is specified.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.55-63
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• 2001

In this paper, we derive a general strong law of large numbers and a general weak law of large number for normed weighted sums of pairwise negative quadrant dependent random variables with the common distribution function.

• Food Science and Biotechnology
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• v.16 no.4
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• pp.557-564
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• 2007

We prepared caviar analogs encapsulated by calcium-alginate gel membranes as a means to replace higher priced natural caviars. Processing the caviar analogs (beluga type) was optimized by response surface methodology with central composite design. Concentrations of sodium alginate ($X_1$) and $CaCl_2\;(X_2)$ were chosen as the independent variables. In order to compare characteristics of the caviar analogs with the natural caviar, sphericity ($Y_1$), diameter ($Y_2$), membrane thickness ($Y_3$), rupture strength ($Y_4$), rupturing deformation ($Y_5$), and sensory score ($Y_6$) were used as the dependent variables. The sphericity of the caviar analogs showed a similar value to that of natural caviar (over 94%) in the range of independent variables. Generally, the $CaCl_2$ concentration ($X_2$) affected all dependent variables to a greater extent than the sodium alginate concentration ($X_l$), For the multiple response optimization of the 5 dependent variables ($Y_1,\;Y_2,\;Y_4,\;Y_5$, and $Y_6$), the desirability function was defined as the following conditions: target values ($Y_1\;=\;100%,\;Y_2\;=\;3.0\;mm,\;Y_4\;=\;1,470\;g,\;Y_5\;=\;1.1\;mm,\;and\;Y_6\;=\;10\;points$). Membrane thickness ($Y_3$) was eliminated from the dependent variables for multiple response optimization because it could not be measured with an image analyzer. The values of the independent variables as evaluated by multiple response optimization were $X_1\;=\;-0.093$ (78%) and $X_2\;=\;-0.322$ (1.07%), respectively.

• Journal of KIISE:Software and Applications
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• v.31 no.9
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• pp.1131-1141
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• 2004

Cohesion refers to the degree of the relatedness of the elements in a module, and it is widely accepted that the module of higher cohesion is easier to understand, maintain, and reuse. Recently, several cohesion metrics have been proposed to measure the cohesiveness of classes in an object-oriented program. However, the existing cohesion metrics do not consider the characteristics of dependent instance variables that are commonly used in a class and, thus, do not properly reflect the cohesiveness of the class. This paper presents an approach for improving the cohesion metrics by considering the characteristics of the dependent instance variables in an object-oriented program. To demonstrate the importance of the dependent instance variables, a case study has been conducted on a class library.

• The Mathematical Education
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• v.53 no.1
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• pp.93-110
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• 2014

Algebra deals with so general properties about number system that it is called as 'generalized arithmetic'. Observing students' activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1007-1025
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• 2019

In the present work, the complete convergence and complete moment convergence properties for arrays of rowwise extended negatively dependent (END) random variables are investigated. Some sharp theorems on these strong convergence for weighted sums of END cases are established. These main results not only generalize the known corresponding ones of Cai [2], Wang et al. [17] and Shen [14], but also improve them, respectively.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.145-153
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• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.6
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• pp.39-46
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• 2020

Playing an important role in developing the economy and overall developments of the country, commercial banks have to be aware of their crucial presence in order to perform well and contribute significantly. At the same time, as a place to receive deposits, banks are required to be in safe situations to avoid bankruptcy or deal with financial crises. This research seeks to identify the determinants of Capital Adequacy Ratio and Banks' performance as well as the relationship between these two dependent variables. The paper uses 128 observations of 16 Vietnamese commercial banks during the period from 2010 to 2017, with two simultaneous dependent variables CAR and ROE, and independent variables including Return on Assets, Tobin Q, Credit growth, GDP growth, Equity to Deposits, Loans to Deposits, Bank size, Cost to Income, Liquidity risk, Provision for Loan loss ratio, Non-performing loans and Inflation. The results reveal that Capital Adequacy Ratio and Banks' Performance have statistically significant relationship and Credit growth, GDP growth, Equity-to-Deposit ratio and Cost-to-Income ratio all have significant effects on two dependent variables. The findings of this study suggest that commercial banks should control the respective elements in order to maintain adequate level of capital and also create effective performance.