• Title, Summary, Keyword: growth order

Search Result 6,438, Processing Time 0.057 seconds

SLOWLY CHANGING FUNCTION ORIENTED GROWTH MEASUREMENT OF DIFFERENTIAL POLYNOMIAL AND DIFFERENTIAL MONOMIAL

  • Biswas, Tanmay
    • Korean Journal of Mathematics
    • /
    • v.27 no.1
    • /
    • pp.17-51
    • /
    • 2019
  • In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*$-order, relative $_pL^*$-lower order and differential monomials, differential polynomials generated by one of the factors.

ZEROS OF SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH COEFFICIENTS OF SMALL LOWER GROWTH

  • Wang, Sheng
    • Bulletin of the Korean Mathematical Society
    • /
    • v.40 no.2
    • /
    • pp.235-241
    • /
    • 2003
  • It is proved that the product of any two linearly independent meromorphic solutions of second order linear differential equations with coefficients of small lower growth must have infinite exponent of convergence of its zero-sequences, under some suitable conditions.

A FRACTIONAL-ORDER TUMOR GROWTH INHIBITION MODEL IN PKPD

  • Byun, Jong Hyuk;Jung, Il Hyo
    • East Asian mathematical journal
    • /
    • v.36 no.1
    • /
    • pp.81-90
    • /
    • 2020
  • Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

ON SOME GROWTH ANALYSIS OF COMPOSITE ENTIRE AND MEROMORPHIC FUNCTIONS FROM THE VIEW POINT OF THEIR RELATIVE (p, q)-TH TYPE AND RELATIVE (p, q)-TH WEAK TYPE

  • Biswas, Tanmay
    • Korean Journal of Mathematics
    • /
    • v.26 no.1
    • /
    • pp.23-41
    • /
    • 2018
  • The main aim of this paper is to prove some results related to the growth rates of composite entire and meromorphic functions on the basis of their relative (p, q)-th order, relative (p, q)-th lower order, relative (p, q)-th type and relative (p, q)-th weak type where p and q are any two positive integers.

COMPARATIVE GROWTH ANALYSIS OF DIFFERENTIAL MONOMIALS AND DIFFERENTIAL POLYNOMIALS DEPENDING ON THEIR RELATIVE pL* - ORDERS

  • Biswas, Tanmay
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.31 no.1
    • /
    • pp.103-130
    • /
    • 2018
  • In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*-order$, relative $_pL^*-lower$ order and differential monomials, differential polynomials generated by one of the factors.

MEASURES OF COMPARATIVE GROWTH ANALYSIS OF COMPOSITE ENTIRE FUNCTIONS ON THE BASIS OF THEIR RELATIVE (p, q)-TH TYPE AND RELATIVE (p, q)-TH WEAK TYPE

  • Biswas, Tanmay
    • The Pure and Applied Mathematics
    • /
    • v.26 no.1
    • /
    • pp.13-33
    • /
    • 2019
  • The main aim of this paper is to establish some comparative growth properties of composite entire functions on the basis of their relative (p, q)-th order, relative (p, q)-th lower order, relative (p, q)-th type, relative (p, q)-th weak type of entire function with respect to another entire function where p and q are any two positive integers.

THE GROWTH OF ENTIRE FUNCTION IN THE FORM OF VECTOR VALUED DIRICHLET SERIES IN TERMS OF (p, q)-TH RELATIVE RITT ORDER AND (p, q)-TH RELATIVE RITT TYPE

  • Biswas, Tanmay
    • Korean Journal of Mathematics
    • /
    • v.27 no.1
    • /
    • pp.93-117
    • /
    • 2019
  • In this paper we wish to study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of (p, q)-th relative Ritt order, (p, q)-th relative Ritt type and (p, q)-th relative Ritt weak type where p and q are integers such that $p{\geq}0$ and $q{\geq}0$.