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SINGULARITY ORDER OF THE RIESZ-NÁGY-TAKÁCS FUNCTION

  • Baek, In-Soo
    • Communications of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.7-21
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    • 2015
  • We give the characterization of H$\ddot{o}$lder differentiability points and non-differentiability points of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) singular function ${\Psi}_{a,p}$ satisfying ${\Psi}_{a,p}(a)=p$. It generalizes recent multifractal and metric number theoretical results associated with the RNT function. Besides, we classify the singular functions using the singularity order deduced from the H$\ddot{o}$lder derivative giving the information that a strictly increasing smooth function having a positive derivative Lebesgue almost everywhere has the singularity order 1 and the RNT function ${\Psi}_{a,p}$ has the singularity order $g(a,p)=\frac{a{\log}p+(1-a){\log}(1-p)}{a{\log}a+(1-a){\log}(1-a)}{\geq}1$.

HORADAM POLYNOMIALS FOR A NEW SUBCLASS OF SAKAGUCHI-TYPE BI-UNIVALENT FUNCTIONS DEFINED BY (p, q)-DERIVATIVE OPERATOR

  • Vanithakumari Balasubramaniam;Saravanan Gunasekar;Baskaran Sudharsanan;Sibel Yalcin
    • Communications of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.461-470
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    • 2024
  • In this paper, a new subclass, 𝒮𝒞𝜇,p,q𝜎 (r, s; x), of Sakaguchitype analytic bi-univalent functions defined by (p, q)-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for |a2| and |a3| are obtained. Fekete-Szegö inequalities for the class are found. Finally, we give some corollaries.

Design and Synthesis of Carbo Analog of Oxetanocin Bisphosphate Derivative as $P2Y_1$ Receptor Antagonist ($P2Y_1$ 수용체 길항제로서의 옥세타노신 카보 유도체의 설계 및 합성)

  • 김혜옥
    • YAKHAK HOEJI
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    • v.43 no.3
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    • pp.328-333
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    • 1999
  • In order to develop selective and competitive and competitive antagonist at the $P2Y_1$ receptor a carbocyclic oxetanocin bisphosphate derivative (7) was synthesized as a bioisostere of the lead, MRS 2179. The synthesis was started from ketene diethylacetal (1) and completed in 6 steps.

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Two pHZ1358 Derivative Vectors for Efficient Gene Knockout in Streptomyces

  • He, Yunlong;Wang, Zhijun;Bai, Linquan;Liang, Jingdan;Zhou, Xiufen;Deng, Zixin
    • Journal of Microbiology and Biotechnology
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    • v.20 no.4
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    • pp.678-682
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    • 2010
  • The deletion of sti from the Streptomyces plasmid pIJ101 made its derivative pHZ1358 an efficient vector for gene disruption and replacement. Here, pHZ1358 was further optimized by the construction of a derivative plasmid pJTU1278, in which a cassette carrying multiple cloning sites and a lacZ selection marker were introduced for convenient plasmid construction in E. coli. In addition, the oriT region of pJTU1278 was also deleted, generating a vector (pJTU1289) that can be used specifically for PCR-targeting. The efficient usage of these vectors was demonstrated by the deletion of the gene involved in avermectin biosynthesis in S. avermitilis.

Physicochemical Characteristics of Cephalosporin Derivative, CKD-604 : Stabilization and Solubilization in Aqueous Media (세팔로스포린계 유도체 CKD-604 물성연구 : 수용액중에서의 안정화 및 가용화)

  • Kwon, Soo-Yeon;Shin, Hee-Jong;Kim, Chong-Kook
    • Journal of Pharmaceutical Investigation
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    • v.29 no.3
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    • pp.205-210
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    • 1999
  • To formulate the parenteral delivery of a new cephalosporin derivative, 7-${\beta}$-[(2)-2-(2-arninothiazol-4-yl)-2methoxyiminoacetamido]- 3- [(2,3-cyclopenteno-4-carbamoyl-l-pyridinium)methyl]- 3-cephem-4-carboxylate sulfate( CKD604), the stability and solubility of CKD-604 in various aqueous media were investigated. The degradation kinetics of CKD-604 in aqueous solutions (ionic strength 0.1, pH 1-8) were studied at $37^{\circ}C$. The observed degradation rates followed pseudo first order kinetics. The pH-rate profile exhibited a minimum degradation rate at pH 5. The Arrhenius activation energy was 14.2 kcal/mol in pH 5 buffer solution. Excellent agreement between the cephalosporins' theoretical pH-rate profile and the experimental data indicated that the degradation pathway of CKD-604 could be predicted according to the general pathway of cephalosporins. The solubility of CKD-604 was 8.16 mg/ml at $25^{\circ}C$. To enhance the solubility and adjust the suitable pH, CKD-604 was solubilized by using sodium ascorbate, ascorbic acid and urea. The compositions were obtained to satisfy optimum pH and concentration, and the total amount of additives was several times of the active ingredient, CKD-604.

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Benzastatin J, a New Demethylated Derivative of Benzastatin B Produced by Controlled Fermentation of Streptomyces nitrosporeus

  • Kim, Won-Gon;Yoo, Ick-Dong
    • Journal of Microbiology and Biotechnology
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    • v.12 no.5
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    • pp.838-840
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    • 2002
  • Feeding experiments of various derivatives of p-aminobenzamide to benzastatins-producing Streptomyces nitrosporeus were performed to observe whether new biosynthetic analogs of benzastatins were produced. The supplementation of p-aminobenzoic acid to the culture medium of Strepromyces nitrosporeus led to the production of benzastatin J, a new demethylated derivative of benzastatin B, while production of benzastatins A and B increased and benzastatins C-G were not detected.

Studies on the constiuents of polygala japonica houttuyn (Polygala japonica houttuyn의 성분연구)

  • 우린근;김제훈
    • YAKHAK HOEJI
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    • v.1 no.1
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    • pp.1-2
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    • 1948
  • The finely powdered entire harbs of Polygala japonica Houttuyn, a drug known as Yong Shin-Cho in Korea, were boiled with methanol and from the filtered extract the methanol was distilled off under diminished pressure and the aqueous solution of the residue was evaporated to dryness after being mixed with ignited magnesia. The dried mass was boiled with absolute alcohol, the filtered clear liquid was evaporated to a small volume and the precipitate Saponin produced by mixing with ether was filtered off. When the filtrate was again evaporated to the thickness of a syrup and allowed to cool for a few days in an ice box, crystalls were separated out in about 5% yield, which formed colorless columns, M. P. 142.deg., from methanol and had the formula $C_{6}$ $H_{12}$ $O_{5}$. On heating it with acetic acid anhybride and sodium acetate, its tetraacetyl derivative $C_{6}$ $H_{8}$ $O_{5}$(C $H_{3}$CO)$_{4}$ was obtained and which formed colorless needles, M. P. 62-5.deg., from ethanol. Their melting points, results of elementar analysis and other characteristics agreed with that of Polygalitol and its derivative. Finally they were proved to be identical with Polygalitol and its derivative, respectively, through determination of mixed melting points with the samples. Polygalitol was isolated from several plants of genus polugala e. g. P. amara, P. vulgaris, P. teunifolia, P. senega etc. The authors added to them another instance of identifying Polygalitol from the plant of genus polygala.olygala.

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Inhibitory Effect of Injinchunggantang-derivative on Hepatic Fibrosis (인진청간탕가미방이 간조직의 섬유화 억제에 미치는 영향)

  • 강경태;김영철;이장훈;우홍정
    • The Journal of Korean Medicine
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    • v.23 no.2
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    • pp.39-56
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    • 2002
  • Objective : The aim of this study is to investigate the inhibitory effect of lnjinchunggantang-derivative on acute and sub-acute hepatic fibrosis induced by $CCl_4$, and to compare the efficiency of lnjinchunggantang-derivative, Salviae Radix and Scirpi Tuber.Zeloariae Rhizoma on acute and sub-acute hepatic fibrosis induced by $CCl_4$. Method : Western blotting for collagen type N, quantitative RT-PCR and gross & histological findings on liver tissue (Hematoxylin & Eosin stain, Reticulin stain, Masson-Trichrome stain) were studied. Results : In the study on collagen type N expression, lnjinchunggantangcderivative, Scirpi Tuber.Zeloariae Rhizoma and Salviae Radix showed inhibitory effect in western blotting. In quantitative RT-PCR assay, lnjinchunggantang-derivative showed inhibitory effect on collagen type N expression in acute hepatic fibrosis model, whereas lnjinchunggantang-derivative, Scirpi Tuber.Zeloariae Rhizoma and Salviae Radix showed inhibitory effect on collagen type N expression in sub-acute hepatic fibrosis model. In the gross findings of acute and sub-acute hepatic fibrosis models,lnjinchunggantang-derivative, Salviae Radix and Scirpi Tuber. Zeloariae Rhizoma showed inhibitory effect on hepatic fibrosis in the order. In the histological findings of acute and sub-acute hepatic fibrosis models in Hematoxylin & Eosin, Reticulin and Masson-Trichrome staining, the liver of $CCl_4$-only group showed atrophy and necrotic change with white nodules whereas that of $CCl_4$+ Injinchunggantang-derivative showed no significant histological change with well preservation of the tone of the tissue, and Scirpi Tuber. Zeloariae Rhizoma and Salviae Radix group showed minimal fibrotic changes. In the scoring system of the extent of the inhibition of the hepatic fibrosis, lnjinchunggantang-derivative group showed statistically significant inhibitory effect(p<0.05) whereas Scirpi Tuber.Zeloariae Rhizoma and Salviae Radix group showed no statistically significant effect in the acute hepatic fibrosis model. In the sub-acute hepatic fibrosis model, lnjinchunggantang-derivative, Scirpi Tuber.Zeloariae Rhizoma and Salviae Radix group showed statistically significant effect (p<0.01). Conclusion : These results show that lnjinchunggantang-derivative, Salviae Radix and Scirpi Tuber.Zeloariae Rhizoma have inhibitory effect in the order on hepatic fibrosis induced by $CCl_4$ by suppressing the expression of collagen type N, ultimately preventing liver cirrhosis. To obtain more credible results in this experiment, developement of a new experimental model more similar to human hepatic fibrosis is still needed.

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On a q-Extension of the Leibniz Rule via Weyl Type of q-Derivative Operator

  • Purohit, Sunil Dutt
    • Kyungpook Mathematical Journal
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    • v.50 no.4
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    • pp.473-482
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    • 2010
  • In the present paper we define a q-extension of the Leibniz rule for q-derivatives via Weyl type q-derivative operator. Expansions and summation formulae for the generalized basic hypergeometric functions of one and more variables are deduced as the applications of the main result.