• Advances in aircraft and spacecraft science
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• 제4권3호
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• pp.281-296
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• 2017

The axial-injection end-burning hybrid rocket proposed twenty years ago by the authors recently recaptured the attention of researchers for its virtues such as no ${\zeta}$ (oxidizer to fuel mass ratio) shift during firing and good throttling characteristics. This paper is the first report verifying these virtues using a laboratory scale motor. There are several requirements for realizing this type of hybrid rocket: 1) high fuel filling rate for obtaining an optimal ${\zeta}$; 2) small port intervals for increasing port merging rate; 3) ports arrayed across the entire fuel section. Because these requirements could not be satisfied by common manufacturing methods, no previous researchers have conducted experiments with this kind of hybrid rocket. Recent advances in high accuracy 3D printing now allow for fuel to be produced that meets these three requirements. The fuel grains used in this study were produced by a high precision light polymerized 3D printer. Each grain consisted of an array of 0.3 mm diameter ports for a fuel filling rate of 98% .The authors conducted several firing tests with various oxidizer mass flow rates and chamber pressures, and analysed the results, including ${\zeta}$ history, using a new reconstruction technique. The results show that ${\zeta}$ remains almost constant throughout tests of varying oxidizer mass flow rates, and that regression rate in the axial direction is a nearly linear function of chamber pressure with a pressure exponent of 0.996.

• 대한수학회보
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• 제50권2호
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• pp.697-704
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• 2013

The function $g{\mapsto}{\zeta}^k_G(g)$ which counts the number of solutions of $x^k=g$ in a finite group G, is not necessarily a character of G. We study this function for the case of dihedral groups and generalized quaternion groups.

• 대한수학회지
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• 제40권6호
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• pp.963-975
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• 2003

The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.29-39
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• 2015

In this paper, we investigate the functional equations of the multiple Dirichlet and Hurwitz L-functions associated with Bernoulli numbers and polynomials attached to Dirichlet character.

• 대한수학회보
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• 제60권6호
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• pp.1651-1672
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• 2023

In 2010, Li-Ye [13, Theorem 0.1] proved that P(ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), Γ"(z)) ≢ 0 in ℂ, where m is a non-negative integer, and P(u₀, u₁, . . . , u_m, v₀, v₁, v₂) is any non-trivial polynomial in its arguments with coefficients in the field ℂ. Later on, Li-Ye [15, Theorem 1] proved that P(z, Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z), ζ(z)) ≢ 0 in z ∈ ℂ for any non-trivial distinguished polynomial P(z, u₀, u₁, . . ., u_n, v) with coefficients in a set L_δ of the zero function and a class of nonzero functions f from ℂ to ℂ ∪ {∞} (cf. [15, Definition 1]). In this paper, we prove that P(z, ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z)) ≢ 0 in z ∈ ℂ, where m and n are two non-negative integers, and P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is any non-trivial polynomial in the m + n + 2 variables u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n with coefficients being meromorphic functions of order less than one, and the polynomial P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is a distinguished polynomial in the n + 1 variables v₀, v₁, . . . , v_n. The question studied in this paper is concerning the conjecture of Markus from [16]. The main results obtained in this paper also extend the corresponding results from Li-Ye [12] and improve the corresponding results from Chen-Wang [5] and Wang-Li-Liu-Li [23], respectively.

• 대한수학회지
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• 제55권5호
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• pp.1207-1220
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• 2018

The generalized hyperharmonic numbers $h^{(m)}_n(k)$ are defined by means of the multiple harmonic numbers. We show that the hyperharmonic numbers $h^{(m)}_n(k)$ satisfy certain recurrence relation which allow us to write them in terms of classical harmonic numbers. Moreover, we prove that the Euler-type sums with hyperharmonic numbers: $$S(k,m;p):=\sum\limits_{n=1}^{{\infty}}\frac{h^{(m)}_n(k)}{n^p}(p{\geq}m+1,\;k=1,2,3)$$ can be expressed as a rational linear combination of products of Riemann zeta values and harmonic numbers. This is an extension of the results of Dil [10] and $Mez{\ddot{o}}$ [19]. Some interesting new consequences and illustrative examples are considered.

• 대한수학회지
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• 제41권2호
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• pp.265-294
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• 2004

In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier-Feynman transforms. Also, we evaluate the conditional Fourier-Feynman transforms of the functions of the forms exp {$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}$\Phi$($\chi$(T)), exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}$\Phi$($\chi$(T)) which are of interest in Feynman integration theories and quantum mechanics.

• 대한수학회지
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• 제43권3호
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• pp.579-591
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• 2006

In this paper we obtain a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for $f(z)\;=\;{\sum}^{\infty}_{k=1}\;P_{nk}(z)$ (the homogeneous polynomial expansion of f) satisfying $n_{k+1}/n_{k}{\ge}{\lambda}>1$ for all $k\;{\in}\;N$, to belong to the weighted Bergman space $$A^p_{\alpha}(B)\;=\;\{f{\mid}{\int}_{B}{\mid}f(z){\mid}^{p}(1-{\mid}z{\mid}^2)^{\alpha}dV(z) < {\infty},\;f{\in}H(B)\}$$. We find a growth estimate for the integral mean $$\({\int}_{{\partial}B}{\mid}f(r{\zeta}){\mid}^pd{\sigma}({\zeta})\)^{1/p}$$, and an estimate for the point evaluations in this class of functions. Similar results on the mixed norm space $H_{p,q,{\alpha}$(B) and weighted Bergman space on polydisc $A^p_{^{\to}_{\alpha}}(U^n)$ are also given.

• Korean Chemical Engineering Research
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• 제47권1호
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• pp.31-37
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• 2009

양쪽성 계면활성제는 등전점 이하의 pH 조건에서 양이온 계면활성제로 작용함으로써 유연력을 나타낼 수 있으며, 등전점 이상의 pH 조건에서는 음이온 혹은 비이온 계면활성제로 작용하여 세정력을 나타낼 수 있다. 따라서 pH에 따른 양쪽성 계면활성제의 특성을 활용하면 한 종류의 계면활성제 분자로 세정력과 유연력을 동시에 발휘할 수 있다. 본 연구에서는 betaine 양쪽성 계면활성제에 대하여 계면활성제의 기본적인 물성(CMC, 표면장력, 계면장력, 접촉각, 점도, 계면활성제 시스템의 상거동 등)을 측정하였으며, 또한 계면활성제 수용액에 대하여 QCM(quartz crystal microbalance) 실험과 zeta potential 측정을 통하여 양쪽성 계면활성제가 양이온 계면활성제에서 음이온 계면활성제로 작용이 전환되는 등전점을 결정하였다. Betaine 계면활성제의 CMC는 약 $10^{-4}mol/L$ 이며, CMC에서의 표면장력은 약 32 mN/m이었다. Spinning drop tensiometer를 사용하여 1 wt% 계면활성제 수용액과 n-decane 오일 사이의 계면장력을 pH 2~10의 조건에서 측정한 결과, 계면장력은 pH 5까지 증가하다가 그 이후 감소하는 경향을 보였으며, 평형에 도달하는 시간도 유사한 경향을 나타내었다. 본 연구에서 사용한 betaine 양쪽성 계면활성제의 등전점을 QCM 실험을 통하여 측정한 결과, 등전점은 pH 3.0~3.3에 존재하였으며, 이 결과는 zeta potential 측정 결과와 동일함을 확인하였다.

• Molecules and Cells
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• 제37권1호
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• pp.66-73
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• 2014

Myeloid-derived suppressor cells (MDSCs) play an important role in impairing the function of T cells. We characterized MDSCs in two chronic hepatitis C (CHC) cohorts: a cross-sectional group that included 61 treatment-naive patients with CHC, 14 rapid virologic response (RVR) cases and 22 early virologic response (EVR) cases; and a longitudinal group of 13 cases of RVR and 10 cases of EVR after pegylated-interferon-${\alpha}$/ribavirin treatment for genotype 1b HCV infection. Liver samples from 32 CHC patients and six healthy controls were subjected to immunohistochemical analysis. MDSCs frequency in treatment-naive CHC was significantly higher than in RVR, EVR, or healthy subjects and was positively correlated with HCV RNA. Patients infected with HCV genotype 2a had a significantly higher frequency of MDSCs than those infected with genotype 1b. Decreased T cell receptor (TCR) ${\zeta}$ expression on $CD8^+$ T cells was significantly associated with an increased frequency of MDSCs in treatment-naive CHC patients and was restored by L-arginine treatment in vitro. Increased numbers of liver arginase-$1^+$ cells were closely associated with the histological activity index in CHC. The TCR ${\zeta}$ chain was significantly downregulated on hepatic $CD8^+$ T cells in CHC. During antiviral follow up, MDSCs frequency in peripheral blood mononuclear cells was directly correlated with the HCV RNA load in the plasma and inversely correlated with TCR ${\zeta}$ chain expression in $CD8^+$ T cells in both RVR and EVR cases. Notably, the RVR group had a higher frequency of MDSCs at baseline than the EVR group. Collectively, this study provides evidence that MDSCs might be associated with HCV persistence and downregulation of CD8 ${\zeta}$ chain expression.