• 충청수학회지
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• 제28권3호
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• pp.491-497
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• 2015

In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter ${\gamma}$ and a weight function H(s, u). We have determined forms of ${\gamma}$ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• 대한수학회논문집
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• 제30권4호
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• pp.439-446
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• 2015

The main objective of this paper is to establish certain explicit expressions for the Humbert functions ${\Phi}_2$(a, a + i ; c ; x, -x) and ${\Psi}_2$(a ; c, c + i ; x, -x) for i = 0, ${\pm}1$, ${\pm}2$, ..., ${\pm}5$. Several new and known summation formulas for ${\Phi}_2$ and ${\Psi}_2$ are considered as special cases of our main identities.

• 대한수학회논문집
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• 제13권2호
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• pp.435-443
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• 1998

Some mathematical constants have been used in evaluating series involving the Zeta function, the origin of which can be traced back to an over two centries old theorem of Christian Goldbach. We show some of the series involving the Zeta function can be evaluated in terms of the Catalan's constant by using the theory of the double Gamma function.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.233-242
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• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.361-378
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• 2020

The most apparent aspect of the present study is to introduce a new sequence space 𝚽^⋆(𝓛_p) derived by double Euler-Totient matrix operator. We examine its topological and algebraic properties and give an inclusion relation. In addition to those, the α-, β(bp)- and γ-duals of the space 𝚽^⋆(𝓛_p) are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.

• 한국지구과학회지
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• 제35권5호
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• pp.362-374
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• 2014

This study investigated the initial mass function (IMF) and star formation history of high-mass stars in the Small Magellanic Cloud (SMC) using a population synthesis technique. We used the photometric survey catalog of Lee (2013) as the observable quantities and compare them with those of synthetic populations based on Bayesian inference. For the IMF slope (${\Gamma}$) range of -1.1 to -3.5 with steps of 0.1, five types of star formation models were tested: 1) continuous; 2) single burst at 10 Myr; 3) single burst at 60 Myr; 4) double bursts at those epochs; and 5) a complex hybrid model. In this study, a total of 125 models were tested. Based on the model calculations, it was found that the continuous model could simulate the high-mass stars of the SMC and that its IMF slope was -1.6 which is slightly steeper than Salpeter's IMF, i.e., ${\Gamma}=-1.35$.

• 대한수학회논문집
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• 제30권3호
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• pp.191-200
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• 2015

Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton [13] presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation [13], the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.

• Journal of Astronomy and Space Sciences
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• 제33권4호
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• pp.247-256
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• 2016

An analysis of light curves and spectra of observed gamma-ray bursts in gamma-ray ranges is frequently demanded because the prompt emission contains immediate details regarding the central engine of gamma-ray bursts (GRBs). We have revisited the relationship between the collimation-corrected peak luminosity and the spectral lag, investigating the lag-luminosity relationships in great detail by focusing on spectral lags resulting from all possible combinations of channels. Firstly, we compiled the opening angle data and demonstrated that the distribution of opening angles of 205 long GRBs is represented by a double Gaussian function having maxima at ~ 0.1 and ~ 0.3 radians. We confirmed that the peak luminosity and the spectral lag are anti-correlated, both in the observer frame and in the source frame. We found that, in agreement with our previous conclusion, the correlation coefficient improves significantly in the source frame. It should be noted that spectral lags involving channel 2 (25-50 keV) yield high correlation coefficients, where Swift/Burst Alert Telescope (BAT) has four energy channels (channel 1: 15-25 keV, channel 2: 25-50 keV, channel 3: 50-100 keV, channel 4: 100-200 keV). We also found that peak luminosity is positively correlated with peak energy.

• 대한본초학회지
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• 제28권6호
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• pp.31-38
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• 2013

Objectives : The purpose of this study was to determine whether NMED-01 or NMED-02 improves laboratory test results in participants with liver function disorder. Methods : This is a randomized, placebo-controlled trial in which participants, treating physicians and data management staff were blinded to treatment group. The study was conducted at Semyung university oriental medicine hospital in Jecheon where participants with high level of serum ${\gamma}$-GTP (60-350 U/L) were enrolled. The intervention consisted of three times daily ingestion of either two capsules of placebo, NMED-01 (NeuMed. co. ltd., Seoul), or NMED-02 (NeuMed. co. ltd., Seoul) for twelve weeks. To evaluate the efficacy and safety of NMED-01 and NMED-02, we primarily evaluated the degree of decrement of serum ${\gamma}$-GPT level among three groups. Secondarily the decrement of serum ALT, AST, and triglyceride level in each group were also evaluated. Adverse effects were monitored during the twelve weeks treatment. Results : The change of ${\gamma}$-GTP level of NMED-01 group was lower than that of placebo group at the end of 12-week administration ($28.1{\pm}38.7U/L$ vs. $9.3{\pm}27.0U/L$, p=0.046). Other variables including AST, ALT, and triglyceride level were not significantly reduced. The decrement of ${\gamma}$-GPT, AST, ALT, and triglyceride level of NMED-02 group was not significant. There were no significant adverse effects or toxicities during treatment period. Conclusions : Participants receiving NMED-01 had improvement in laboratory test results. Despite a modest sample size, our results suggest that NMED-01 are safe and may be potentially effective in improving liver function. However, NMED-02 have lack of a detectable effect in this study.