• Title/Summary/Keyword: Poly (Q)

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THE STUDY ON GENERALIZED (p, q)-POLY-GENOCCHI POLYNOMIALS WITH VARIABLE a

  • H.Y. LEE
    • Journal of Applied and Pure Mathematics
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    • v.5 no.3_4
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    • pp.197-209
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    • 2023
  • In this paper, the generalized (p, q)-poly-Genocchi polynomials with variable a is defined by generalizing it more, and various properties of this polynomial are introduced. To do this, we define a generating function and use the definition to introduce some interesting properties as follows: basic properties, relation between Stirling numbers of the second kind and generalized (p, q)-poly-Genocchi polynomials with variable a and symmetric properties.

SYMMETRIC IDENTITIES FOR DEGENERATE q-POLY-BERNOULLI NUMBERS AND POLYNOMIALS

  • JUNG, N.S.;RYOO, C.S.
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.29-38
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    • 2018
  • In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

ON THE (p, q)-POLY-KOROBOV POLYNOMIALS AND RELATED POLYNOMIALS

  • KURT, BURAK;KURT, VELI
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.45-56
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    • 2021
  • D.S. Kim et al. [9] considered some identities and relations for Korobov type numbers and polynomials. In this work, we investigate the degenerate Korobov type Changhee polynomials and the (p,q)-poly-Korobov polynomials. We give a generalization of the Korobov type Changhee polynomials and the (p,q) poly-Korobov polynomials. We prove some properties and identities and explicit relations for these polynomials.

VARIOUS PROPERTIES OF HIGH-ORDER (p, q)-POLY-TANGENT POLYNOMIALS AND THE PHENOMENA OF THEIR ROOTS

  • JUNG YOOG KANG
    • Journal of applied mathematics & informatics
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    • v.42 no.2
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    • pp.457-469
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    • 2024
  • In this paper, we construct higher-order (p, q)-poly-tangent numbers and polynomials and give several properties, including addition formula and multiplication formula. Finally, we explore the distribution of roots of higher-order (p, q)-poly-tangent polynomials.

A STUDY OF POLY-BERNOULLI POLYNOMIALS ASSOCIATED WITH HERMITE POLYNOMIALS WITH q-PARAMETER

  • Khan, Waseem A.;Srivastava, Divesh
    • Honam Mathematical Journal
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    • v.41 no.4
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    • pp.781-798
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    • 2019
  • This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.

A NOTE ON THE GENERALIZED BERNOULLI POLYNOMIALS WITH (p, q)-POLYLOGARITHM FUNCTION

  • JUNG, N.S.
    • Journal of applied mathematics & informatics
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    • v.38 no.1_2
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    • pp.145-157
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    • 2020
  • In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

IDENTITIES INVOLVING THE DEGENERATE GENERALIZED (p, q)-POLY-BERNOULLI NUMBERS AND POLYNOMIALS

  • JUNG, N.S.
    • Journal of applied mathematics & informatics
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    • v.38 no.5_6
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    • pp.601-609
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    • 2020
  • In this paper, we introduce degenerate generalized poly-Bernoulli numbers and polynomials with (p, q)-logarithm function. We find some identities that are concerned with the Stirling numbers of second kind and derive symmetric identities by using generalized falling factorial sum.

Preparation and Cellular Uptake of Hydrophobic Quantum Dots Encapsulated in Poly-L-Lactic Acid Film (소수성 양자점을 함유한 Poly-L-Lactic Acid film의 제조 및 세포흡수 연구)

  • Lee, Ji-Sook;Woo, Kyoung-Ja;Chung, He-Sson
    • Journal of Pharmaceutical Investigation
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    • v.39 no.1
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    • pp.1-6
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    • 2009
  • To overcome the stability problem of hydrophilic quantum dot (Q-dot), cellular uptake of hydrophobic instead of hydrophilic Q-dot was studied in the hope to find a simple method to use Q-dot as a cellular imaging probe. Hydrophobic Q-dot and poly-L-lactic acid (PLLA) were co-dissolved in chloroform to prepare stable films. Due to the cellular compatibility of PLLA, adherent cells were cultured on the film to observe the degree of Q-dot uptake and cytotoxicity of the prepared films. The results show that Q-dots were absorbed into NIH3T3 and EMT6 cells. Cellular uptake was also observed when hydrophobic Q-dots were coated directly on a glass plate. PLLA/Q-dot film and Q-dot coated on glass plate did not show major cytotoxicity. In vivo tumor model was also used to show the uptake of Q-dot from the PLLA/Q-dot film to the tumor site.

Cellulose Nanocrystals Incorporated Poly(arylene piperidinium) Anion Exchange Mixed Matrix Membranes (셀룰로오스 나노 결정을 도입한 폴리아릴렌 피페리디늄 음이온 교환 복합매질분리막)

  • Da Hye Sim;Young Park;Young-Woo Choi;Jung Tae Park;Jae Hun Lee
    • Membrane Journal
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    • v.34 no.2
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    • pp.154-162
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    • 2024
  • Anion exchange membranes (AEMs) are essential components in water electrolysis systems, serving to physically separate the generated hydrogen and oxygen gases while enabling the selective transport of hydroxide ions between electrodes. Key characteristics sought in AEMs include high ion conductivity and robust chemical and mechanical stability in alkaline. In this study, quaternized Poly(terphenyl piperidinium)/cellulose nanocrystals (qPTP/CNC) mixed matrix membrane was fabricated. The polymer matrix, PTP, was synthesized via super-acid polymerization, known for its excellent ion conductivity and alkaline durability. The qPTP/CNC membrane showed a dense and uniform morphology without significant voids or large aggregates at the polymer-nanoparticle interface. The qPTP/CNC membrane containing 2 wt% CNC demonstrated a high ion exchange capacity of 1.90 mmol/g, coupled with low water uptake (9.09%) and swelling ratio (5.56%). Additionally, the qPTP/CNC membrane showed significantly lower resistance and superior alkaline stability (384 hours at 50℃ in 1 M KOH) compared to the commercial FAA-3-50 membrane. These results highlight the potential of hydrophilic additive CNC in enhancing ion conductivity and alkaline durability of ion exchange membranes.