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6970 results in Mathematical modeling and methods

Page 10 of 349

  • BRANCHING TECHNIQUE FOR A BI-OBJECTIVE TWO-STAGE ASSIGNMENT PROBLEM

  • EKTA JAIN, KALPANA DAHIYA, VANITA VERMA
  • Journal:
    The ANZIAM Journal / Volume 64 / Issue 2 / April 2022
    Published online by Cambridge University Press:
    15 August 2022, pp. 183-204

  • We discuss a bi-objective two-stage assignment problem (BiTSAP) that aims at minimizing two objective functions: one comprising a nonlinear cost function defined explicitly in terms of assignment variables and the other a total completion time. A two-stage assignment problem deals with the optimal allocation of n jobs to n agents in two stages, where $n_1$ out of n jobs are primary jobs which constitute Stage-1 and the rest of the jobs are secondary jobs constituting Stage-2. The paper proposes an algorithm that seeks an optimal solution for a BiTSAP in terms of various efficient time-cost pairs. An algorithm for ranking all feasible assignments of a two-stage assignment problem in order of increasing total completion time is also presented. Theoretical justification and numerical illustrations are included to support the proposed algorithms.

  • FULLY 3D FLUID OUTFLOW FROM A SPHERICAL SOURCE

  • Part of
  • LAWRENCE K. FORBES, STEPHEN J. WALTERS
  • Journal:
    The ANZIAM Journal / Volume 64 / Issue 2 / April 2022
    Published online by Cambridge University Press:
    10 August 2022, pp. 149-182
    • Article
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  • We consider fully three-dimensional time-dependent outflow from a source into a surrounding fluid of different density. The source is distributed over a sphere of finite radius. The nonlinear problem is formulated using a spectral approach in which two streamfunctions and the density are represented as a Fourier-type series with time-dependent coefficients that must be calculated. Linearized theories are also discussed and an approximate stability condition for early stages in the outflow is derived. Nonlinear solutions are presented and different outflow shapes adopted by the fluid interface are investigated.

Mathematical Methods and Physical Insights
  • An Integrated Approach
  • Alec J. Schramm
  • Published online:
    15 July 2022
    Print publication:
    16 June 2022
  • Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions ('By the Ways') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many taking advantage of Mathematica, to test and deepen comprehension.

  • AN ANALYTICAL APPROXIMATION FOR CONVERTIBLE BONDS

  • Part of
  • JOANNA GOARD
  • Journal:
    The ANZIAM Journal / Volume 64 / Issue 2 / April 2022
    Published online by Cambridge University Press:
    20 June 2022, pp. 135-148

  • This paper looks at adapting the method of Medvedev and Scaillet for pricing short-term American options to evaluate short-term convertible bonds. However unlike their method, we provide explicit formulae for the coefficients of our series solution. This means that we do not need to solve complicated recursive systems, and can efficiently provide fast solutions. We also compare the method with numerical solutions, and find that it performs extremely well, giving accurate bond prices as well as accurate optimal conversion prices.

Page 10 of 349