• Journal of the Korean Mathematical Society
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• v.40 no.6
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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.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.915-929
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• 2007

The main result of this paper is to construct the derivative twisted p-adic (h, q)-L-functions at s = 0. We obtain twisted version of Theorem 4 in [17]. We also obtain twisted (h, q)-extension of Proposition 1 in [3].

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.1-10
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• 2007

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim's h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question which was remained in [3].

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1007-1014
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• 2012

We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point 1/2.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.1003-1019
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• 2021

In this paper, we introduce a class of maximal functions along twisted surfaces in ℝⁿ×ℝ^m of the form {(𝜙(|v|)u, 𝜑(|u|)v) : (u, v) ∈ ℝⁿ×ℝ^m}. We prove L^p bounds when the kernels lie in the space L^q (𝕊^n-1×𝕊^m-1). As a consequence, we establish the L^p boundedness for such class of operators provided that the kernels are in L log L(𝕊^n-1×𝕊^m-1) or in the Block spaces B^0,0_q (𝕊^n-1×𝕊^m-1) (q > 1).

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2095-2105
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• 2015

Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

• Applied Microscopy
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• v.18 no.2
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• pp.77-90
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• 1988

The ultrastructure of the excretory duct of the large ampullate gland in the orb web spider, Nephila clavain L. Koch are studied with light and electron microscopes. The excretory ducts of the large ampullate glands connected with the large spinning tubes(spigots) on the anterior spinnerets are basically composed of three superposed types of the layers which are inner cuticles, monolayered epithelial cells and peripheral connective cells. According to the morphological characteristics of the cuticles and internal textures of the epithelial cells, the long excretory ducts are subdivided into three(distal, middle and proximal) portions. Especially, at the distal portion of the ducts near the spinning tubes, the electron lucent subcuticles which had the functions of water removal and orientation of silk fibers are well distributed, whereas at the middle and proximal portions these layers disappeared and instead of these, endocuticles are developed. The endocuticle contains two types of bands, which are electron dense and electron lucent. And along the length of the cuticular stem in the excretory duct, these two alternating bands are twisted spirally. In the cytoplasm of the columnar epithelial cells of the distal portion, rough endoplasmic reticula and Golgj complexes, related to the production of the cuticular materials are well developed. Between the adjacent epithelial cells, specialized septate junctions and desmosomes are formed along the plasma membranes. At the proximal portion of the duct, densely accumulated secretory materials appeared, and these are released to the inner canal by the apocrine secretion.