• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.1033-1048
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• 2020

We synthesize the recent work done on conditionally defined Lucas and Fibonacci numbers, tying together various definitions and results generalizing the linear recurrence relation. Allowing for any initial conditions, we determine the generating function and a Binet-like formula for the general sequence, in both the positive and negative directions, as well as relations among various sequence pairs. We also determine conditions for periodicity of these sequences and graph some recurrent figures in Python.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.489-508
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• 2020

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

• 전기의세계
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• v.23 no.1
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• pp.69-72
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• 1974

This paper deals with an analytical design of a feedback regulator with vector input is discrete linear time-invariant systems. We have derived some relations such that the eigenvalues of a system plant with vector input under the time-optimal control strategy can be arbitrarily changed by the characteristics of the minor loop compensator which is indroduced in the feedback path.

• Transactions of the Korean Society of Mechanical Engineers
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• v.1 no.4
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• pp.196-202
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• 1977

The solidification process in a cylinder with finite thickness in studied by explicit finite difference method. The temperature distribution, the solidification front profile and the dischrged latent heat for the process are obtained. It is found that the solidification front profile is almost linear except in the vicinity of the initation of phase change. This result motivates us to use linear relations between the position of solidification and time for approximate calculations.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.3-10
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• 2001

In order to establish the intensity-magnitude relation far the Korean earthquakes, those relations for the earthquakes in the Sino-Korean craton were estimated. In this process, earthquake data of northeastern China region whose geological environment is similar to Korea Peninsula were also utilized. These data were analyzed not only with linear fit, but also with non-linear fit. The fellowing relation, M=0.57 $\times$ 1$_{e}$ + 2.86, seems appropriate for the present, but its validity should be tested more in the future.e.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1177-1187
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• 2014

In the current paper we study absolutely pure representations of quivers. Then over some nice quivers including linear quivers some sufficient conditions guaranteeing a representation to be absolutely pure is characterized. Furthermore some relations between atness and absolute purity is investigated. Finally it is shown that the absolutely pure covering of representations of linear quivers (including $A^-_{\infty}$, $A^+_{\infty}$ and $A^{\infty}_{\infty}$) by R-modules whenever R is a coherent ring exists.

• Water for future
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• v.24 no.3
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• pp.61-70
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• 1991

the relationships between rainfall and runoff are analyzed statistically and modelled using discrete linear transfer function, which can be shown with the relations between input and output in hydrologic system. The procedures of identification, estimation and diagnostic checking of model are proposed, and the suitabilith of assume model is determined by the statistics used in time series analysis.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2003.06a
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• pp.173-176
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• 2003

In this paper, a DLC method is suggested for linear feedback systems to improve the tracking performance when the task of the system is repetitive. DLC can generate the desired control input directly from the previously teamed control inputs corresponding to other output trajectories. It is assumed that all outputs considered in this paper have some relations called "proportionality. " To show the validity and tracking performance of the proposed method, some simulation are performed for the tracking control of a linear system with a PI controller.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.217-222
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• 2012

In this note we investigate some properties of ${\beta}$-algebras and further relations with $B$-algebras. Especially, we show that if ($X$, -, +, 0) is a $B^*$-algebra, then ($X$, +) is a semigroup with identity 0. We discuss some constructions of linear ${\beta}$-algebras in a field $K$.

• East Asian mathematical journal
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• v.38 no.1
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• pp.85-94
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• 2022

Recently, an LWE-based commitment scheme is proposed. Their construction is statistically hiding as well as computationally binding. On the other hand, the construction of related zero-knowledge protocols is left as an open problem. In this paper, we present zero-knowledge protocols with hardness based on the LWE problem. we show how to instantiate efficient zero-knowledge protocols that can be used to prove linear and sum relations among these commitments. In addition, we show how the variant of LWE, spLWE problem, can be used to instantiate efficient zero-knowledge protocols.