• 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].

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.231-238
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• 2005

In this paper, we study the arithmetic properties of orders in a quaternion algebra over a dyadic local field and we find the mass formula of orders.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Journal of Microbiology and Biotechnology
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• v.17 no.2
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• pp.364-368
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• 2007

Enterobacter sakazakii may be related to outbreaks of meningitis, septicemia, and necrotizing enterocolitis, mainly in neonates. To reduce the risk of E. sakazakii in baby foods, thermal characteristics for Korean E. sakazakii isolates were determined at 52, 56, and $60^{\circ}C$ in saline solution, rehydrated powdered infant formula, and dried baby food. In saline solution, their D-values were 12-16, 3-5, and 0.9-1 min for each temperature. D-values increased to 16-20, 4-5, and 2-4 min in rehydrated infant formula and 14-17, 5-6, and 2-3 min in dried baby food. The overall calculated z-value was 6-8 for saline, 8-10 for powdered infant formula, and 9-11 for dried baby food. Thermal inactivation of E. sakazakii during rehydration of powdered infant formula was investigated by viable counts. Inactivation of cultured E. sakazakii in infant formula milk did not occur for 20 min at room temperature after rehydration with the water at $50^{\circ}C$ and their counts were reduced by about 1-2 log CFU/g at $60^{\circ}C$ and 4-6 log CFU/ml with the water at 65 and $70^{\circ}C$. However, the thermo stability of adapted E. sakazakii to the powdered infant formula increased more than two times. Considering that the levels of E. sakzakii observed in powdered infant formula have generally been 1 CFU/100 g of dry formula or less, contamination with E. sakazakii can be reduced or eliminated by rehydrating water with at least $10^{\circ}C$ higher temperature than the manufacturer-recommended $50^{\circ}C$.

• Journal of the Korean Geotechnical Society
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• v.37 no.6
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• pp.5-20
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• 2021

In this study, a modified empirical formula for estimating the bearing capacity of the steel pipe prebored and precast pile was proposed by performing 20 cases of real-scale field pile loading tests. The proposed formula will be based on expanded SPT N-value in order to consider the realistic condition of the surrounding soil. The formula is proposed based on a statistic approach of the data points from the field pile loading test, in order to ensure safe engineering practice while finding a reliable formula. The statistical analysis of the data points from the loading test indicated that the existing formula has been underestimated the bearing capacity of the prebored and precast pile. The proposed formula estimates 15% and 20% higher pile End bearing capacity (q_t=230P_driven(kN/m²)) and the shaft resistance (f_max=3.0N_s^E(kN/m²)) compared to the existing formula. The accuracy and the stability of the proposed formula was verified by comparing the estimated results with additional field test data. The verification process showed that the proposed formula was estimated to be more accurate than the existing formula.

• Journal of Environmental Science International
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• v.23 no.11
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• pp.1775-1790
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• 2014

The regional rainfall intensity formula for Gimhae in Gyeongsangnam-do province is developed in this study. The nine points of rainfall observations were selected. In order to demonstrate the accuracy and the versatility of the proposed rainfall intensity formula, three regions under the jurisdiction of the Meteorological Agency near Gimhae, namely Busan, Changwon, Miryang observatories were selected. The present formula can be effectively employed for various design of hydraulic structures in Gimhae area since it is divided into several refined regions.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1197-1222
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• 2010

There is a well-known classical reduction formula by Griffiths and Harris for Littlewood-Richardson coefficients, which reduces one part from each partition. In this article, we consider an extension of the reduction formula reducing two parts from each partition. This extension is a special case of the factorization theorem of Littlewood-Richardson coefficients by King, Tollu, and Toumazet (the KTT theorem). This case of the KTT factorization theorem is of particular interest, because, in this case, the KTT theorem is simply a reduction formula reducing two parts from each partition. A bijective proof using tableaux of this reduction formula is given in this paper while the KTT theorem is proved using hives.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.2
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• pp.116-123
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• 2015

This paper proposed a new formula for predicting acoustic power transmission loss of simple expansion chamber with two internal partitions. Seventeen cases of computational results were performed and the database was constructed for the TL according to the various positions of internal partitions. Using this database, firstly, the formula for the peak values of TL at certain frequencies was developed using the least square estimation. Secondly, the formula for the TL curve could be obtained automatically with the input data of the positions of two internal partitions. The formula of TL developed in this paper showed good agreement with computational results. This formula will be helpful for the positioning of internal partitions to improve TL at target frequencies.

• Journal of Physiology & Pathology in Korean Medicine
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• v.30 no.6
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• pp.385-396
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• 2016

It is a fact that the existing pharmacological research method is difficult to explain the effect and mechanism of action of herbal formula of Korean medicine. We are now very pleased with the development of modern science and the development of a methodology for studying herbal formula characterized by network targets and multi-component therapeutics over the human body. In this review, systems pharmacology or network pharmacology is demonstrated how these are applied to explain the effectiveness of herbal medicine. The post-genomic era provides a unique opportunity for the two fields to understand and benefit from each other. In particular, recent research trends, research methodology, useful databases and results of research on herbal formula are introduced. China already has a policy of scientific development of traditional chinese medicine (TCM) and the development of Chinese medicine industry with a focus on herbal formula research at national level, and in Korea, it is urgent to support and nurture the methodology appropriate to the characteristics of the herbal formula in order to study the safety and efficacy of Korean medicine.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.19 no.3
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• pp.153-161
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• 2016

This paper covers algorithms for the management of regurgitation, constipation and infantile colic in infants. Anti-regurgitation formula may be considered in infants with troublesome regurgitation, while diagnostic investigations or drug therapy are not indicated in the absence of warning signs. Although probiotics have shown some positive evidence for the management of functional gastrointestinal disorders (FGIDs), the evidence is not strong enough to make a recommendation. A partially hydrolyzed infant formula with prebiotics and ${\beta}$-palmitate may be considered as a dietary intervention for functional constipation in formula fed infants. Lactulose has been shown to be effective and safe in infants younger than 6 months that are constipated. Macrogol (polyethylene glycol, PEG) is not approved for use in infants less than 6 months of age. However, PEG is preferred over lactulose in infants >6 months of age. Limited data suggests that infant formula with a partial hydrolysate, galacto-oligosaccharides/fructo-oligosaccharides, added ${\beta}$-palmitate may be of benefit in reducing infantile colic in formula fed infants in cases where cow's milk protein allergy (CMPA) is not suspected. Evidence suggests that the use of extensively hydrolyzed infant formula for a formula-fed baby and a cow's milk free diet for a breastfeeding mother may be beneficial to decrease infantile colic if CMPA is suspected. None of the FGIDs is a reason to stop breastfeeding.