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O. Bamidele Awojoyogbe,Karem Boubaker 한국물리학회 2009 Current Applied Physics Vol.9 No.1
This paper proposes a solution to Bloch NMR flow equations in biomedical fluid dynamics using a new set of real polynomials. In fact, the authors conjugated their efforts in order to take benefit from similarities between independent Bloch NMR flow equations yielded by a recent study and the newly proposed characteristic differential equation of the m-Boubaker polynomials. The main goal of this study is to establish a methodology of using mathematical techniques so that the accurate measurement of blood flow in human physiological and pathological conditions can be carried out non-invasively and becomes simple to implement in medical clinics. Specifically, the polynomial solutions of the derived Bloch NMR equation are obtained for use in biomedical fluid dynamics. The polynomials represent the T2-weighted NMR transverse magnetization and signals obtained in terms of Boubaker polynomials, which can be an attractive mathematical tool for simple and accurate analysis of hemodynamic functions of blood flow system. The solutions provide an analytic way to interpret observables made when the rF magnetic fields are designed based on the Chebichev polynomials. The representative function of each component is plotted to describe the complete evolution of the NMR transverse magnetization component for medical and biomedical applications. This mathematical technique may allow us to manipulate microscopic blood (cells) at nanoscale. We may be able to theoretically simulate nano-devices that may travel through tiny capillaries and deliver oxygen to anemic tissues, remove obstructions from blood vessels and plaque from brain cells, and even hunt down and destroy viruses, bacteria, and other infectious agents. This paper proposes a solution to Bloch NMR flow equations in biomedical fluid dynamics using a new set of real polynomials. In fact, the authors conjugated their efforts in order to take benefit from similarities between independent Bloch NMR flow equations yielded by a recent study and the newly proposed characteristic differential equation of the m-Boubaker polynomials. The main goal of this study is to establish a methodology of using mathematical techniques so that the accurate measurement of blood flow in human physiological and pathological conditions can be carried out non-invasively and becomes simple to implement in medical clinics. Specifically, the polynomial solutions of the derived Bloch NMR equation are obtained for use in biomedical fluid dynamics. The polynomials represent the T2-weighted NMR transverse magnetization and signals obtained in terms of Boubaker polynomials, which can be an attractive mathematical tool for simple and accurate analysis of hemodynamic functions of blood flow system. The solutions provide an analytic way to interpret observables made when the rF magnetic fields are designed based on the Chebichev polynomials. The representative function of each component is plotted to describe the complete evolution of the NMR transverse magnetization component for medical and biomedical applications. This mathematical technique may allow us to manipulate microscopic blood (cells) at nanoscale. We may be able to theoretically simulate nano-devices that may travel through tiny capillaries and deliver oxygen to anemic tissues, remove obstructions from blood vessels and plaque from brain cells, and even hunt down and destroy viruses, bacteria, and other infectious agents.
REMARKS ON RECURRENCE FORMULAS FOR THE APOSTOL-TYPE NUMBERS AND POLYNOMIALS
IREM KUCUKOGLU,YILMAZ SIMSEK 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.4
In this paper, by differentiating the generating functions for one of the family of the Apostol-type numbers and polynomials with re- spect to their parameters, we present some partial differential equations including these functions. By making use of these equations, we provide some new formulas, relations and identities including these numbers and polynomials and their derivatives. Furthermore, by using a col- lection of the generating functions for the aforementioned family and their functional equations, we investigate the numbers and polynomials belonging to this family and their relationships with other well-known special numbers and polynomials including the Apostol-Bernoulli num- bers and polynomials of higher order, the Apostol-Euler numbers and polynomials of higher order, the Frobenius-Euler numbers and polyno- mials of higher order, the λ-array polynomials, the λ-Stirling numbers, and the λ-Bernoulli numbers and polynomials.
Some identities involving the degenerate Bell-Carlitz polynomials arising from differential equation
서종진,유천성 한국전산응용수학회 2020 Journal of applied mathematics & informatics Vol.38 No.5
In this paper we define a new degenerate Bell-Carlitz polynomials. It also derives the differential equations that occur in the generating function of the degenerate Bell-Carlitz polynomials. We establish some new identities for the degenerate Bell-Carlitz polynomials. Finally, we perform a survey of the distribution of zeros of the degenerate Bell-Carlitz polynomials.
DIFFERENTIAL EQUATIONS ASSOCIATED WITH TWISTED (h, q)-TANGENT POLYNOMIALS
RYOO, CHEON SEOUNG The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.3
In this paper, we study linear differential equations arising from the generating functions of twisted (h, q)-tangent polynomials. We give explicit identities for the twisted (h, q)-tangent polynomials.
Differential equations containing 2-variable mixed-type Hermite polynomials
J.Y. Kang 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.3
In this paper, we introduce the 2-variable mixed-type Hermite polynomials and organize some new symmetric identities for these polynomials. We find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials.
DIFFERENTIAL EQUATIONS AND ZEROS FOR NEW MIXED-TYPE HERMITE POLYNOMIALS
JUNG YOOG KANG The Korean Society for Computational and Applied M 2023 Journal of applied mathematics & informatics Vol.41 No.4
In this paper, we find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials. Moreover, we observe the structure and symmetry of the zeros of the 2-variable mixed-type Hermite equations.
J.Y. Kang,C.S. Ryoo 한국전산응용수학회 2022 Journal of applied mathematics & informatics Vol.40 No.3
In this paper, we study differential equations arising from the generating functions of the geometric polynomials. We give explicit identities for the geometric polynomials. Finally, we investigate the zeros of the geometric polynomials by using computer.
DIFFERENTIAL EQUATIONS ASSOCIATED WITH MAHLER AND SHEFFER-MAHLER POLYNOMIALS
Kim Taekyun,Kim Dae San,Kwon Hyuck-In,Ryoo Cheon Seoung 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.1
In this paper, we study linear differential equations arising from the generating functions of Mahler and Sheffer-Mahler polynomials. We give explicit identities for the Mahler and Sheffer-Mahler polynomials. In addition, we investigate the zeros of the Sheffer- Mahler polynomials with numerical methods.
REVISIT NONLINEAR DIFFERENTIAL EQUATIONS ASSOCIATED WITH EULERIAN POLYNOMIALS
Kim, Dae San,Kim, Taekyun Korean Mathematical Society 2017 대한수학회보 Vol.54 No.4
In this paper, we present nonlinear differential equations arising from the generating function of the Eulerian polynomials. In addition, we give explicit formulae for the Eulerian polynomials which are derived from our nonlinear differential equations.
NONLINEAR DIFFERENTIAL EQUATIONS AND LEGENDRE POLYNOMIALS
김태균,김대산,장관우 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.1
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre polynomials.