• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.835-845
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• 2017

The $GCF_{\epsilon}$ expansion is a new class of continued fractions induced by the transformation $T_{\epsilon}:(0, 1]{\rightarrow}(0, 1]$: $T_{\epsilon}(x)={\frac{-1+(k+1)x}{1+k-k{\epsilon}x}}$ for $x{\in}(1/(k+1),1/k]$. Under the algorithm $T_{\epsilon}$, every $x{\in}(0,1]$ corresponds to an increasing digits sequences $\{k_n,n{\geq}1\}$. Their basic properties, including the ergodic properties, law of large number and central limit theorem have been discussed in [4], [5] and [7]. In this paper, we study the large deviation for the $GCF_{\epsilon}$ expansion and show that: $\{{\frac{1}{n}}{\log}k_n,n{\geq}1\}$ satisfies the different large deviation principles when the parameter ${\epsilon}$ changes in [-1, 1], which generalizes a result of L. J. Zhu [9] who considered a case when ${\epsilon}(k){\equiv}0$ (i.e., Engel series).

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.63-72
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• 2004

It is known that each natural number can be written uniquely as a sum of Fibonacci numbers with suitably increasing indices. In 1960, Daykin showed that the sequence of Fibonacci numbers is the only sequence with this property. Consider here the problem of representing each natural number uniquely as a sum of positive integers taken from certain sequence allowing a fixed number, $\cal{l}\geq2$, of repetitions. It is shown that the $(\cal{l}+1)$-adic expansion is the only such representation possible.

• Journal of Korean Society of Forest Science
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• v.105 no.4
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• pp.463-471
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• 2016

The purpose of this study was to develop allometric equations for identifying the amount of wood and building biomass statistics of L. tulipifera by density, biomass expansion factors and root ratio. For this purpose, total of 40 trees were sampled, which were used consideration the area and the DBH class. As a results, the wood density was $0.43g{\cdot}cm^{-3}$, biomass expansion factors were 1.2, root ratio was 0.2 and uncertainty were 3.9%, 4.6%, 24.1%, respectively. Allometric equations for above ground of L. tulipifera trees were $W=0.060D^{2.524}$. Total and underground allometric equations were $W=0.063D^{2.578}$, $W=0.010D^{2.591}$, respectively.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.2
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• pp.129-135
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• 2015

In this experimental study, the thermal stability values of micrometer-sized silica particle-reinforced epoxy composite specimens were evaluated by measuring their thermal expansion coefficients and Young's moduli. For all specimens used in this study (from the baseline specimen to that containing 70 wt% silica filler), the thermal expansion coefficients and Young's moduli were gradually reduced down to 25% and increased up to 51%, respectively. The results of the experiment were compared with those of certain empirical models. The experimental results of the measurement of thermal expansion coefficients corresponded well with those of Kerner's model, which considers the bulk and shear moduli of the matrix and silica filler. However, the results of the measurement of Young's moduli using the empirical Mori-Tanaka model were observed to match better with those of the experiment. The comparison of the results of the experiment with those of the empirical models demonstrated that a reliable model for measuring the thermal expansion coefficients and Young's moduli of composite specimens needs to consider certain property variations in the composites in addition to volume fraction changes in the filler and matrix.

• Journal of Animal Environmental Science
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• v.15 no.3
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• pp.281-288
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• 2009

The objective of this study is to predict the expansion possibility of treatment capacity in public livestock manure treatment plant (PLMTP) integrated individual farmhouses. According to the treatment efficiency and cost reducing effect, expansion possibility was examined using three cases; (i) decrease of influent concentration from 20,000 mg/L BOD to 1,000 mg/L BOD, (ii) maintenance of low concentration influent with minimum revising existing facilities (BIOSUF) and (iii) maintenance of low concentration influent without revising existing facilities (liquid corrosion method, LCM). In BIOSUF, the treatment capacity increased from 130 ton/day to 300 ton/day. Also, LCM resulted in expansion of treatment capacity from 210 ton/day to 250 ton/day while that of designed concentration influent decreased from 210 ton/day to 190 ton/day. The treatment costs were 14,674 won/ton and 9,929 won/ton for BIOSUF and LCM, respectively. After some revisions, it will be changed to 7,221 won/ton and 8,277 won/ton. Therefore, it must be considered that the livestock manure treats to low concentration and flows into PLMTP for the efficient operation and reducing treatment cost.

• International Journal of Aerospace System Engineering
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• v.6 no.2
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• pp.1-10
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• 2019

In this paper, the probabilistic free vibration analysis of a geometrically coupled cantilever wing with uncertain material properties is carried out using stochastic finite element (SFEM) based on first order perturbation technique. Here, both stiffness and damping of the system are considered as random parameters. The bending and torsional rigidities are assumed as spatially varying second order Gaussian random fields and represented by Karhunen Loeve (K-L) expansion. Here, the expected value, standard deviation, and probability distribution of random natural frequencies and damping ratios are computed. The results obtained from the present approach are also compared with Monte Carlo simulations (MCS). The results show that the uncertain bending rigidity has more influence on the damping ratio and frequency of modes 1 and 3 while uncertain torsional rigidity has more influence on the damping ratio and frequency of modes 2 and 3.

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.154-157
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• 1990

This paper describes a new method of calculating expected energy generation and loss of load probability (L.O.L.P) for electric power system operation and expansion planning. The method represents an equivalent load duration curve (E.L.D.C) as a mixture of cumulants approximation (M.O.C.A), which is the general case of mixture of normals approximation (M.O.N.A). By regarding a load distribution as many normal distributions-rather than one normal distribution-and representing each of them in terms of Gram-Charller expansion, we could improve the accuracy of results. We developed an algorithm which automatically determines the number of distribution and demarcation points. In modelling of a supply system, we made subsets of generators according to the number of generator outage: since the calculation of each subset's moment needs to be processed rapidly, we futher developed specific recursive formulae. The method is applied to the test systems and the results are compared with those of cumulant, M.O.N.A and Booth-Baleriaux method. It is verified that the M.O.C.A method is faster and more accurate than any other methods.

• Archives of Plastic Surgery
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• v.43 no.2
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• pp.197-203
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• 2016

Background The aim of unilateral breast reconstruction after mastectomy is to craft a natural-looking breast with symmetry. The latissimus dorsi (LD) flap with implant is an established technique for this purpose. However, it is challenging to obtain adequate volume and satisfactory aesthetic results using a one-stage operation when considering factors such as muscle atrophy, wound dehiscence and excessive scarring. The two-stage reconstruction addresses these difficulties by using a tissue expander to gradually enlarge the skin pocket which eventually holds an appropriately sized implant. Methods We analyzed nine patients who underwent unilateral two-stage LD reconstruction. In the first stage, an expander was placed along with the LD flap to reconstruct the mastectomy defect, followed by gradual tissue expansion to achieve overexpansion of the skin pocket. The final implant volume was determined by measuring the residual expander volume after aspirating the excess saline. Finally, the expander was replaced with the chosen implant. Results The average volume of tissue expansion was 460 mL. The resultant expansion allowed an implant ranging in volume from 255 to 420 mL to be placed alongside the LD muscle. Seven patients scored less than six on the relative breast retraction assessment formula for breast symmetry, indicating excellent breast symmetry. The remaining two patients scored between six and eight, indicating good symmetry. Conclusions This approach allows the size of the eventual implant to be estimated after the skin pocket has healed completely and the LD muscle has undergone natural atrophy. Optimal reconstruction results were achieved using this approach.

• Transactions of the KSME C: Technology and Education
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• v.3 no.1
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• pp.55-62
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• 2015

The liquefaction to produce LNG (liquefied natural gas) is the only practical way for mass transportation of natural gas across oceans, which accompanies considerable energy consumption in LNG plants. Power generation is one of the effective utilization ways of LNG cold energy which evolves during the vaporization process of LNG with sea water. In this work, performance analysis of two cold energy generation processes, direct expansion and organic Rankine cycles, were carried out by using Aspen HYSYS simulation. The results show that the performance of the organic Rankine cycle is superior to the direct expansion.

• Structural Engineering and Mechanics
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• v.13 no.5
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• pp.491-504
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• 2002

Recently we formulated a 2D hybrid stress element from the 3D Hellinger-Reissner principle for the analysis of thick bodies that are symmetric to the thickness direction. Polynomials have typically been used for all the displacement and stress fields. Although the element predicted the dominant stress and all displacement fields accurately, its prediction of the out-of-plane shear stresses was affected by the very high order terms used in the polynomials. This paper describes an improved formulation of the 2D element using Fourier series expansion for the out-of-plane displacement and stress fields. Numerical results illustrate that its predictions have markedly improved.