• East Asian mathematical journal
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• v.27 no.3
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• pp.339-348
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• 2011

B. C. Berndt [6] has evaluated the transformation formula for a large class of functions that includes and generalizes the classical Dedekind eta-function. In this paper, we consider a twisted version of his formula. Using this transformation formula, we derive modular trans-formation formulas for the generating functions for cranks which were central to deduce K. Mahlburg's results in [11].

• 전기의세계
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• v.15 no.5
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• pp.25-31
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• 1966

This paper derives the useful formulas for computing annual profits, and economical size, locations and regulating values of parallel shunt capacitors in case that they are installed in a distribution line. Inparticular, the derived formulas consider the influence of load variations in order to represent the actual load situations.

• Bulletin of the Korean Mathematical Society
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• v.8 no.1
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• pp.9-15
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• 1971

The purpose of this note is to use primitive recursive functions and predicates similar to those presented by Davis [2] to show the well-known result first proved by Godel in [3] that the well-formed formulas of a pure functional calculus form a recursive set. The technique shown in this paper immediately suggests a unique approach to Theorem proving using a computer.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1131-1144
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• 2022

In this paper, we establish several basic formulas among the double-integral transforms, the double-convolution products, and the inverse double-integral transforms of cylinder functionals on abstract Wiener space. We then discuss possible relationships involving the double-integral transform.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.293-301
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• 2022

The present paper concerns with a study of certain generating functions and summation formulas of generalized Poisson-Charlier polynomials. Some special cases are also discussed.

• Clinical and Experimental Pediatrics
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• v.52 no.9
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• pp.999-1004
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• 2009

Purpose : Glomerular filtration rate (GFR) is a fundamental parameter in assessing renal function and predicting the progression of chronic renal disease. Because the use of serum creatinine has several disadvantages, many studies have investigated the use of cystatin C for estimating GFR. We compared creatinine clearance and GFR with formulas using serum creatinine and cystatin C. Methods : We retrospectively analyzed 211 patients with various renal diseases and classified them into two groups according to creatinine clearance (Group 1: CrCl >$90mL/min/1.73m^2$, Group 2: CrCl <$90mL/min/1.73m^2$). We measured serum creatinine, cystatin C, and creatinine clearance. We calculated GFR using the Schwartz, Counahan, Filler and Lepage, Bokencamp et al, and Grubb et al formulas. Results : GFR determined by the Schwartz formula had the highest correlation to creatinine clearance (r=0.415, P=0.00). GFR determined by various formulas using cystatin C had lower correlation to creatinine clearance (r=0.187, r=0.187, r=0.291). The Schwartz and Counahan formulas showed greater diagnostic accuracy in detecting decreased GFR than cystatin C in group 2 (areas under the curve: Schwartz, 0.596; Counahan, 0.572; Filler, 0.512; Bokencamp, 0.508; and Grubb, 0.514). Conclusion : GFR determined by the Schwartz and Counahan formulas using serum creatinine showed higher correlation coefficient than that determined by formulas using cystatin C. The formulas using cystatin C were not superior to those using serum creatinine in detecting decreased GFR. Cystatin C measurement was not satisfactory for assessing GFR in patients whose renal function was not severely decreased.

• Journal of the Korean GEO-environmental Society
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• v.13 no.4
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• pp.13-26
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• 2012

The deformation modulus of rock masses is a very important design factor for the computation of stability of tunnels and their support systems. Several empirical formulas to estimate the deformation modulus using simple rock classification methods such as RQD or RMR are widely used because field tests to evaluate the deformation modulus are very expensive and time consuming work. However, these formulas can be depended on experiences from the characteristics of local sites in each country. So it is possible that there might be limitations to estimate appropriate deformation modulus in South Korea using the empirical formulas. Therefore, in this study, the applicability of empirical formulas was analyzed by comparing estimated value with the measured value from eight sites in South Korea. The results show that the estimated value based on the empirical formulas partially have tendency to overestimate. Especially, in case of sedimentary rocks, it was too difficult to apply to the empirical formulas because there was no relation ship between estimated value and measured value. For these reasons, additional data from many tests and accurate analyses are necessary to evaluate the estimation method for the deformation modulus considering the local characteristics of rock masses.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-672
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• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• Journal of the Korean Institute of Navigation
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• v.24 no.3
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• pp.123-132
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• 2000

In order to improve the ship maneuverability, It is important to estimate precisely the hydrodynamic coefficients of added mass forces acting on a ship especially in shallow waters, and simple methods for predicting such hydrodynamic forces Is also very desirable. In the previous paper using 3-Dimension potential flow theory, it has been demonstrated that potential calculation is available to estimate added mass coefficients. The present work is aimed at the suggestion of the simplified formulas for predicting the translation and lateral motion of added mass coefficients in shallow water. So, 3-D potential flow theory is also used to calculate the added mass coefficients in deep and shallow waters for Series 60 model which has 5 different kinds of block coefficients (0.6-0.8), SR196 model and T/S HANNARA. After some series computation, simplified formulas for Predicting the added mass force in shallow waters is suggested based on the computation results of Series 60 model. The formulas consist of the combination of principal dimensions and the water depth; d/B, Cb, d/H. The predicted results are compared with the Computation results for SR196 model and T/S HANNARA. The precision of predicted results by simplified formulas are good enough for the practical use. (d/B : draft-Breadth ratio, d/H draft-Water depth ratio, Cb : Block coefficients).

• Journal of Korean Medical classics
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• v.33 no.1
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• pp.51-60
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• 2020

Objectives : To compare the herbal ingredients of the prescriptions in 「Newly Selected Twenty-four Key Formulas applied to Tae-eumin(新定太陰人病應用要藥二十四方)」 chapter of the Shinchuk edition of the 『Donuisusebowon』 and those from the texts of the Four Great Doctors of the Jin Yuan period. Methods : The herbal ingredients of the 『Donuisusebowon』 and those from 『Huangdisuwen Xuanminglunfang(黃帝素問宣明論方)』, 『Lanshimicang(蘭室秘藏)』, 『Suwenbingji Qiyibaomingji(素問病機氣宜保命集)』, 『Shanghan Biaoben Xinfaleicui(傷寒標本心法類萃)』, 『Piweilun(脾胃論)』, 『Neiwai Shangbianhuolun(內外傷辨惑論)』, 『Shanghanzhige(傷寒直格)』, 『Shanghanxinyao(傷寒心要)』, 『Sanxiaolun(三消論)』 were entered into the database. Next, formulas which included the herbal combination pattern of Tae-eumin formula were determined. Results : Among the 27 Tae-eumin formulas including edited versions, those that showed similar pattern among those in the JinYuan texts were the following 12: Gegenjiejitang(葛根解肌湯), Reduohanshaotang(熱多寒少湯), Gegenchengqitang(葛根承氣湯), Gegentaichengqitang(葛根大承氣湯), Gegenshaochengqitang(葛根小承氣湯), Mahuangpobiaotang(麻黃發表湯), Bufeiyuantang(補肺元湯), Zaojiaodahuangtang(皂角大黃湯), Guadisan(瓜蒂散), Shexiangsan(麝香散), Shichangpuyuanzhisan(石菖蒲遠志散), Maimundongyuanzhisan(麥門冬遠志散). Conclusions : Based on the finding that 44.4% of the Shinchuk edition's Tae-eumin formula patterns could be found in the texts of the Four Masters, Dongmu's assertion that about half of the Tae-eumin formulas has been clarified by the doctors of the Song, Yuan, Ming eras could be understood as true.