• Title, Summary, Keyword: multivalent

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ON CERTAIN CLASSES OF MULTIVALENT FUNCTIONS INVOLVING A GENERALIZED DIFFERENTIAL OPERATOR

  • Selvaraj, Chellian;Selvakumaran, Kuppathai A.
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.905-915
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    • 2009
  • Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.

Preparation and in Vitro Release of Melatonin-Loaded Multivalent Cationic Alginate Beads

  • Lee, Beom-Jin;Min, Geun-Hong;Kim, Tae-Wan
    • Archives of Pharmacal Research
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    • v.19 no.4
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    • pp.280-285
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    • 1996
  • The sustained release dosage form which delivers melatonin (MT) in a circadian fashion over 8 h is of clinical value for those who have disordered circadian rhythms because of its short halflife. The purpose of this study was to evaluate the gelling properties and release characteristics of alginate beads varying multivalent cationic species $(Al^{+++}, \; Ba^{++}, \; Ca^{++}, \; Mg^{++}, \; Fe^{+++}, \; Zn^{++})$. The surface morphologies of Ca- and Ba-alginate beads were also studied using scanning electron microscope (SEM). MT, an indole amide pineal hormone was used as a model drug. The $Ca^{++}, \; Ba^{++}, \; Zn^{++}, \; Al^{++}\; and\; Fe^{+++}\; ions\; except\; Mg^{++}$ induced gelling of sodium alginate. The strength of multivalent cationic alginate beads was as follows: $Al^{+++}\llFe^{+++} the induced hydrogel beads were very fragile and less spherical. Fe-alginate beads were also fragile but stronger compared to Al-alginate beads. Ba-alginate beads had a similar gelling strength but was less spherical when compared to Ca-alginate beads. Zn-alginate beads were weaker than Ca- and Ba-alginate beads. Very crude and rough crystals of Ba- and Ca-alginate beads at higher magnifications were observed. However, the type and shape of rough crystals of Ba- and Ca-alginate beads were quite different. No significant differences in release profiles from MT-loaded multivalent cationic alginate beads were observed in the gastric fluid. Most drugs were continuously released upto 80% for 5 h, mainly governed by the passive diffusion without swelling and disintegrating the alginate beads. In the intestinal fluid, there was a significant difference iq the release profiles of MT-loaded multivalent cationic alginate beads. The release rate of Ca-alginate beads was faster when compared to other multivalent cationic alginate beads and was completed for 3 h. Ba-alginate beads had a very long lag time (7 h) and then rapidly released thereafter. MT was continuously released from Feand Zn-alginate beads with initial burstout release. It is assumed that the different release rofiles of multivalent cationic alginate beads resulted from forces of swelling and disintegration of alginate beads in addition to passive diffusion, depending on types of multivalent ions, gelling strength and drug solubility. It was estimated that 0.2M $CaCl_2$ concentration was optimal in terms of trapping efficiency of MT and gelling strength of Ca-alginate beads. In the gastric fluid, Ca-alginate beads gelled at 0.2 M $CaCl_2$ concentration had higher bead strength, resulting in the most retarded release when compared to other concentrations. In the intestinal fluid, the decreased release of Ca-alginate beads prepared at 0.2 M $CaCl_2$ concentration was also observed. However, release profiles of Ca-alginate beads were quite similar regardless of $CaCl_2$ concentration. Either too low or high $CaCl_2$ concentrations may not be useful for gelling and curing of alginate beads. Optimal $CaCl_2$ concentrations must be decided in terms of trapping efficiency and release and profiles of drug followed by curing time and gelling strength of alginate beads.

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STARLIKENESS OF MULTIVALENT MEROMORPHIC HARMONIC FUNCTIONS

  • Murugusundaramoorthy, G.
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.553-564
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    • 2003
  • We give sufficient coefficient conditions for starlikeness of a class of complex-valued multivalent meromorphic harmonic and orientation preserving functions in outside of the unit disc. These coefficient conditions are also shown to be necessary if the coefficients of the analytic part of the harmonic functions are positive and the coefficients of the co-analytic part of the harmonic functions are negative. We then determine the extreme points, distortion bounds, convolution and convex combination conditions for these functions.

Multivalent Harmonic Uniformly Starlike Functions

  • Ahuja, Om;Joshi, Santosh;Sangle, Naveneet
    • Kyungpook Mathematical Journal
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    • v.49 no.3
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    • pp.545-555
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    • 2009
  • In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.

Convolution Properties of Certain Class of Multivalent Meromorphic Functions

  • Vijaywargiya, Pramila
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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    • pp.713-723
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    • 2009
  • The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory.

Supramolecular assembly of peptide molecules for applications in biological multivalent interactions

  • Lim, Yong-Beom;Park, So-Mi;Lee, Eun-Ji;Jeong, Hae-Mi;Ryu, Ja-Hyoung;Yang, Won-Young;Lee, Myong-Soo
    • Proceedings of the Polymer Society of Korea Conference
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    • pp.265-265
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    • 2006
  • Multivalent interactions, which are characterized by the simultaneous binding of multiple ligands on multiple receptors, are prevalent in biological system. We have shown that it is able to make a supramolecular aggregate coated with multiple functional molecules fairly easily by simply mixing one building block. In this particular example, a mannose-coated object was able to agglutinate bacterial cells with cognate binding partners through multivalent interactions. This kind of strategy can be applied in developing materials that can selectively remove pathogens. Supramolecular assembly of this type should be very useful in exploring multivalent biological interactions.

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Redox Reaction of Multivalent Ions in Glass Melts

  • Kim, Kidong
    • Journal of the Korean Ceramic Society
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    • v.52 no.2
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    • pp.83-91
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    • 2015
  • The redox reaction $M^{(x+n)+}+\frac{n}{2}O^{-2}{\rightleftarrows}M^{x+}+\frac{n}{4}O_2$ of multivalent ions in glass melts influences the melting process and final properties of the glass including the fining (removal of bubbles), infrared absorption and homogenization of melts, reaction between metal electrodes and melts or refractory and melts, and transmission and color of glass. In this review paper, the redox behaviors that occur frequently in the glass production process are introduced and the square wave voltammetry (SWV) is described in detail as an in situ method of examining the redox behavior of multivalent ions in the melt state. Finally, some voltammetry results for LCD glass melts are reviewed from the practical viewpoint of SWV.

Inclusion and Subordination Properties of Multivalent Analytic Functions Involving Cho-Kwon-Srivastava Operator

  • PATEL, JAGANNATH;SAHOO, ASHOK KUMAR
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.1031-1051
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    • 2015
  • The object of the present paper is to derive some inclusion and subordination results for certain classes of multivalent analytic functions in the open unit disk, which are defined in terms of the Cho-Kwon-Srivastava operator. Some interesting corollaries are derived and the relevant connection of the results obtained in this paper with various known results are also pointed out.

On Certain Class of Multivalent Functions Involving the Cho-Kwon-Srivastava Operator

  • Shenan, Jamal Mohammad
    • Kyungpook Mathematical Journal
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    • v.52 no.1
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    • pp.21-32
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    • 2012
  • In this paper a new subclass of multivalent functions with negative coefficients defined by Cho-Kwon-Srivastava operator is introduced. Coefficient estimate and inclusion relationships involving the neighborhoods of p-valently analytic functions are investigated for this class. Further subordination result and results on partial sums for this class are also found.

Differential Sandwich Theorem for Multivalent Meromorphic Functions associated with the Liu-Srivastava Operator

  • Ali, Rosihan M.;Chandrashekar, R.;Lee, See-Keong;Swaminathan, A.;Ravichandran, V.
    • Kyungpook Mathematical Journal
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    • v.51 no.2
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    • pp.217-232
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    • 2011
  • Differential subordination and superordination results are obtained for multivalent meromorphic functions associated with the Liu-Srivastava linear operator in the punctured unit disk. These results are derived by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained.