• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1167-1179
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• 2022

In this paper, we obtain some subsets of real numbers (ℝ) on which a fractional part function is defined as a real-valued continuous function. This gives rise to the analysis of the continuous properties of the fractional part function as a real-valued function. The analysis of fractional part function is helpful in the study of the dynamics of circle.

• Journal of Mechanical Science and Technology
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• v.20 no.5
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• pp.658-667
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• 2006

Fractional derivative models, which are used to describe the viscoelastic behavior of material, have received considerable attention. Thus it is necessary to put forward the analysis solutions of dynamic systems containing a fractional derivative. Although previously reported such kind of fractional calculus-based constitutive models, it only handles the particularity of rational number in part, has great limitation by reason of only handling with particular rational number field. Simultaneously, the former study has great unreliability by reason of using the complementary error function which can't ensure uniform real number. In this paper, a new approach is proposed for an analytical scheme for dynamic system of a spring-mass-damper system of single-degree of freedom under general forcing conditions, whose damping is described by a fractional derivative of the order $0<{\alpha}<1$ which can be both irrational number and rational number. The new approach combines the fractional Green's function and Laplace transform of fractional derivative. Analytical examples of dynamic system under general forcing conditions obtained by means of this approach verify the feasibility very well with much higher reliability and universality.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.393-401
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• 2014

In this work, we discuss the existence of mild solutions in the ${\alpha}$-norm for some partial functional integrodifferential equations with infinite delay. We assume that the linear part generates an analytic semigroup on a Banach space X and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.181-193
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• 2017

An identification method for determination of the parameters of the rheological models of dampers made of viscoelastic material is presented. The models have two, three or four parameters and the model equations of motion contain derivatives of the fractional order. The results of dynamical experiments are approximated using the trigonometric function in the first part of the procedure while the model parameters are determined as the solution to an appropriately defined optimization problem. The particle swarm optimization method is used to solve the optimization problem. The validity and effectiveness of the suggested identification method have been tested using artificial data and a set of real experimental data describing the dynamic behavior of damper and a fluid frequently used in dampers. The influence of a range of excitation frequencies used in experiments on results of identification is also discussed.

• Journal for History of Mathematics
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• v.27 no.6
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• pp.409-419
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• 2014

In school mathematics, the logarithmic function is defined as the inverse function of an exponential function. And the natural logarithm is defined by the integral of the fractional function 1/x. But historically, Napier had already used the concept of logarithm in 1614 before the use of exponential function or integral. The calculation of the logarithm was a hard work. So mathematicians with arithmetic ability made the tables of values of logarithms and people used the tables for the estimation of data. In this paper, we first take a look at the mathematicians and mathematical principles related to the appearance and the developments of the logarithmic tables. And then we deal with the confusions between mathematicians, raised by the estimation data which were known as proportional parts or mean differences in common logarithmic tables.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.11
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• pp.92-100
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• 2009

In this paper, we analyze the hardware architecture of Low Density Parity Check (LDPC) decoder using Log Likelihood Ration-Belief Propagation (LLR-BP) decoding algorithm. Various design issues that affect the decoding performance and the hardware complexity are discussed and the tradeoffs between the hardware complexity and the performance are analyzed. The message data for passing error probability is quantized to 7 bits and among them the fractional part is 4 bits. To maintain the decoding performance, the integer and fractional parts for the intrinsic information is 2 bits and 4 bits respectively. We discuss the alternate implementation of $\Psi$(x) function using piecewise linear approximation. Also, we improve the hardware complexity and the decoding time by applying overlapped scheduling.

• The KIPS Transactions:PartC
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• v.9C no.3
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• pp.385-398
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• 2002

To accommodate the increasing number of mobile terminals in the limited radio spectrum, wireless systems have been designed as micro/picocellular architectures for a higher capacity. This reduced coverage area of a cell has caused a higher rate of hand-off events, and the hand-off technology for efficient process becomes a necessity to provide a stable service. Population-based Bandwidth Reservation(PBR) Scheme is proposed to provide prioritized handling for hand-off calls by dynamically adjusting the amount of reserved bandwidth of a cell according to the amount of cellular traffic in its neighboring cells. We analyze the performance of the PBR scheme according to the changes of a fractional parameter, f, which is the ratio of request reservation to the total amount of bandwidth units required for hand-off calls that will occur for the next period. The vague of this parameter, f should be determined based on QoS(Quality of Service) requirement. To meet the requirement the value of Parameter(f) must be able to be adjusted dynamically according to the changing traffic conditions. The best value of f can be determined by a function of the average speed of mobile stations, average call duration, cell size, and so on. This paper considers the average call duration and the cell size according to the speed of mobile stations. Although some difference exists as per speed, in the range of 0.4 $\leq$ f $\leq$ 0.6, Blocking Probability, Dropping Probability and Utilization show the best values.

• The Journal of Dong Guk Oriental Medicine
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• v.1
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• pp.55-80
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• 1992

In order to examine that the effect of Sam Hwa San, circulating the vital energy of Sam Cho and controlling body fluid metabolism, gives any influence on renal function, changes in the urine flow, eletrolytes excretion, plasma aldosterone concentration and renin activity were observed after intravenous infusion of the Sam Hwa San extract in rabbit. Also in vitro effect of the herb extract on oxygen consumption in renal cortical slices and ATPase activity in kidney microsomes was measured. The following results were obtained : 1. The urine flow was markedly increased at 10 min after intravenous infusion of the Sam Hwa San extract($0.134{\pm}0.015$ vs. $0.433{\pm}0.046ml/min.kg$), but return ed to normal value after 40 min of infusion. 2. The glomerular filtration rate was significantly increased at 10 min after in travenous infusion of the Sam Hwa San extract, and the renal plasma flow at 10 and 20 min after infusion of the Sam Hwa San extract, following return to normal value. 3. $Na^+$ excretion was significantly increased during 10-40 min after intravenous infusion of the Sam Hwa San extract, although showed the maximal rate at 10-20 min. The fractional $Na^+$ excretion was also increased during 10-40 min. $K^+$ excretion was rapidly increased at 10 min after the intravenous Infusion of the Sam Hwa San extract and then gradually decreased to normal level at 40 min. The fractional $K^+$ excretion was significantly increased during 10-40 min after the intravenous infusion of the Sam Hwa San extract. 4. The plasma aldosterone concentration and renin activity were not altered by the infusion of the Sam Hwa San extract. 5. The ouabain-sensitive oxygen consumption of renal cortical slices was significantly reduced by the Sam Hwa San extract(0.5 and 1.0 vol.%). 6. The Na-K-ATPase activity of renal microsomes was strongly inhibited by the Sam Hwa San extract(0.5 and 1.0 vol.%). These results suggest that the Sam Hwa San causes a strong diuretic effect which results from reduction of Na reabsorption in renal tubule by a direct inhibition of Na-pump and, in part, from all increase in renal blood flow. In clinic, it is considered to obtain the therapeutic effect in body fluid metabolism disharmony to cause the circular disorder of vital energy.

• The Journal of the Petrological Society of Korea
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• v.3 no.1
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• pp.76-93
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• 1994

The Precambrian Hongjesa granite is lithologically zoned from biotite granite in central part to biotite-muscovite granite towards the margin. The X_{Fe}$ (=Fe/(Fe+Mg)) value and the aluminum saturation index of biotite systematically vary as a function of mineral assemblage, and are positively related with those of bulk rock. This relationship as well as the lithological zoning are attributed to the fractional crystallization of the Hongjesa granitic magma. The trace element data corroborate that biotite-muscovite granite is more fractionated than biotite granite. The evolution of the Hongjesa granite is elucidated by using the AFM liquidus topology, where A=$Al_2O_3-CaO-Na_2O-K_2O$; F=FeO+MnO; and M=MgO. At an early magmatic stage where biotite is the only ferromagnesian mineral to crystallize, the X_{Fe}$ value and the alumina content of granitic magma continuously increase.. Muscovite subsequently crystallizes with biotite along the biotitemuscovite cotectic curve where biotite-muscovite granite forms. Local enrichments in Mn and B further crystallize garnet and tourmaline, respectively. The unique zonal pattern characterized by the occurrence of the evolved biotite-muscovite granite at the margin may be accounted for by the passive stoping during the emplacement of the Hongjesa granite. This emplacement may have occurred in continental collision environment, according to the tectonic discrimination diagram using major element chemistry.