Name: ADESINA, Olufemi Adeyinka

Date and Place of Birth:1st August, 1969, Lagos.

State of Origin: Ogun.

Nationality: Nigerian.

Present Postal Address: Department of Mathematics,

Obafemi Awolowo University, Ile-Ife, Nigeria. 220005.

Office: Mathematics Building Rm. 14

Tel: +234-8066066540

E-mail: oadesina@oauife.edu.ng

        Education:

a)       Obafemi Awolowo University, Ile-Ife, Ph.D. Mathematics, 2006.

b)       Obafemi Awolowo University, Ile-Ife, M.Sc. Mathematics, 1999.

c)       Ogun State University, Ago-Iwoye, B.Sc. (Hons.) Mathematics, 1995.

 Distinction and Awards:

(a)            Scholarships:

(i)             Obafemi Awolowo University Postgraduate Scholarship.

(ii)            Federal Government of Nigeria Scholarship for Postgraduate Studies.

(b)             Awards: Honours Award for Outstanding Youth Corps Member (Ondo State) 1996.

(c)            Postdoctoral Experience: Ford Foundation Research Postdoctoral Fellowship at the African Institute of Mathematical Science, Muizenberg, Cape Town, South Africa, 2007.

 Work Experience in Obafemi Awolowo University:

(i)         Professor                                                            (October 2011- Present). 

(ii)        Reader                                                                (October 2008- September 2011).  

(iii)       Senior Lecturer                                                   (October 2006 - September 2008).

(iv)       Lecturer I                                                            (October 2003 - September 2006).

(v)        Lecturer II                                                            (October 2001 - September 2003).

(vi)       Assistant Lecturer                                               (October 1999 - September 2001).

(vii)     Graduate Assistant                                               (October 1997 - September 1999).

As a teacher, I have been able to advance and diffuse knowledge through teaching of several Mathematics courses for over fifteen years. During this period, I have demonstrated a high level of competence in all professional aspects of teaching, such as construction of courses, classroom presentation, tutorials, assignments and grading; innovation in the classroom; commitment to teaching; evidence of intensive and sustained attention to the teaching and learning process; instilling in students the desire to be lifelong learners, and availability to students.

I have also been able to undertake in a responsible manner, the academic and administrative tasks assigned to me. As the Vice-Dean, Students’ Affairs, I have been involved in the positive reorganization and refocusing the activities in the Division, especially, as it relates to the troubled students’ body. I organized large groups of diverse students and students’ organizations into effectively working together on issues. I have edited a refereed conference proceeding. Together with a few colleagues, I participated in leading capacity in the organization of conferences at the departmental and faculty levels. I wrote articles and spoke to diverse audiences on the issues I have represented.

Membership of professional bodies:

(i)                  Member, American Mathematical Society.

(ii)                 Member, Nigerian Mathematical Society.

(iii)                 Member, Quality Control Society of Nigeria.

(iv)                 Member, Research Group in Mathematical Inequalities and Applications. Victoria, Australia.

(v)                  Member, International Society of Difference Equations.

(vi)                 Member, Groupe Interafricain de Research en Analyse Geometrie et Applications.

(vii)                Member, Grupo Ecuaciones Diferenciales de Orden Mayor y Applicaciones (Higher Order Differential Equations and Applications Group),  Colombia.

Review activities:

As a service to the global scientific community, I serve actively as a reviewer to the following reputable journals:

  • Ife Journal of Science;
  • Journal of the Nigerian Mathematical Society;
  • Zentralblatt MATH, (Germany);
  • American Mathematical Society’s Mathematical Review, (United States);
  • Applied Mathematics and Computations, [Elsevier] (United States);
  • Journal of Applied Mathematics Letters, [Elsevier] (United States);
  • Journal of Computers and Mathematics with Applications, [Elsevier] (United States);
  • Journal of the Franklin Institute, [Elsevier] (United States);
  • Afrika Matematika, [Springer]
  • Abstract and Applied Analysis [Hindawi]
  • Journal of Advanced Research in Dynamical and Control Systems, (United States);
  • Journal of Nonlinear Studies, (United States);
  • Journal of Mathematical Communications, (Hungary);
  • Filomat (Serbia);
  • Selcuk Journal of Applied Mathematics, (Turkey);
  • Journal of Applied Mathematics and Informatics, (South Korea);
  • Bulletin of the Malaysian Mathematical Society, (Malaysia).

Research Experience:

Almost every evolutionary phenomenon encountered in the real world has qualitative behaviour(s) understood in one or another sense. From the theoretical viewpoint, the concept of these behaviours is an underlying principle in numerous practical problems modeled by various kinds of differential equations. Our research activities focus essentially on higher order nonlinear differential equations (with and without delays) with special emphasis on the qualitative behaviour of solutions of these equations. These can be classified into the search for the following properties of solutions of considered nonlinear differential equations:

 

a)       Boundedness of Solutions;

b)       Exponential Stability of Solutions;

c)       Periodic Solutions;

d)       Almost Periodic Solutions;

e)       Uniformly Dissipative Solutions;

f)        Convergence of Solutions;

g)       Existence of Limiting Regimes;

h)       Stability of Solutions

i)         Square Integrable Solutions.

j)        Non-Resonant Oscillations.

In this direction, nonlinear equations of third, fourth, fifth and nth orders have been investigated extensively. The study of whichever property varies with the considered equations. The method of investigation also varies. These methods can be divided into:

(i) Frequency Domain: This involves the study of position of the characteristic polynomial roots in the complex plane. The equations are reduced to a first order system; transfer functions obtained, which are then used in obtaining matrix inequalities. The method is used in studying properties a, b, c, d and e above.

(ii) Lyapunov: This involves constructing a suitable positive definite Lyapunov function whose derivative is negative definite. Lyapunov function in this regard involves finding the system of closed surfaces that contain the origin and are converging to it. The vector field of motion equations should be directed inside the areas limited by such surfaces. If a solution gets into such area limited by the surface, then it will never leave it again. These surfaces form level surfaces of a Lyapunov function. The method is used in studying properties f, g and h above.

(iii) Exponential Dichotomy: The norm of the projection onto the stable subspace of any orbit in the system decays exponentially as t tends to positive infinity and the norm of the projection onto the unstable subspace of any orbit decays exponentially as t tends to negative infinity and furthermore that the stable and unstable subspaces are conjugate. The method is used in studying property d above.

(iv) Functional Analytic and Topological:This depends on the employment of Leray-Schauder continuation technique to study the spectral properties associated with nonlinear functions of concerned equations. The method is used in studying property j above.

(v) Square Integrable: Measurable functions that are square-integrable, in the sense of the  Lebesgue integral, forms a vector space which is a Hilbert space, provided functions which are equal almost everywhere are identified. The method is used in studying property i) above.

We have systematically and progressively used the frequency domain method to study uniform dissipative and some qualitative properties of solutions (boundedness, exponential stability, periodicity and almost periodicity) for varieties of third, fourth and fifth-ordered differential equations with various combinations of non-linear terms with and without delays. In the case of fifth order equations, our attempt using this method is the first in the literature. The analysis involved increases with the order of the equation and the number of the nonlinear function present. The equations that were investigated are important in both theory and practice; because they can be applied to model automatic controls in electronic systems realized by means of R-C filters and also find applications in some three loop electric circuit problems. They are also used in modeling of mathematical problems in economics, epidemiology and biology. Obtained results in this direction have enhanced active research into fifth-order non-linear differential equations, which had hitherto been relatively quiet due to the obvious difficulty in tackling odd ordered differential equations; and also throw more lights on the behaviour of solutions of lower and higher analogous of these equations. The computations and analysis required for the derivation of our results were facilitated by novel advanced techniques.

We have also been able to show for the first time in the literature that convergence results and existence of limiting regime in the sense of Demidovich are provable, for some fifth order nonlinear differential equations with the restoring function and other nonlinear terms not necessarily differentiable. In this direction, the not necessarily differentiable nonlinear functions are only required to satisfy some increment ratios that lie in a closed sub interval of the Routh-Hurwitz interval. The convergence property of systems that are stable is important both theoretically and in applications since; small perturbations from the equilibrium point imply that the trajectory will return to it when time goes to infinity. In some applications, it is still not sufficient to know that the trajectories will converge to the equilibrium point at infinite time; but there is a need to estimate how fast the trajectories approach the equilibrium point. The concept of exponential stability has also been used for this purpose. Knowing when a system is exponentially stable provides an explicit bound on the trajectory state at any time.

Criteria that generalized and improved existing results on some third and fourth order non-linear differential equations with different forcing terms have been obtained. In particular, on third order equations, existence of bounded and $L^2$-solutions for some continuous square integrable functions have been obtained. We introduced a forcing term and a more a general sector condition on the non-linear term which is differentiable, for a certain Lurie system, and obtained exponential stability, periodicity, almost periodicity and dissipativity results on the solution. By using the method of exponential dichotomy and the Schauder fixed point theorem, known results on almost periodic solutions to nth order nonlinear differential equations are improved and generalized.

 We have also paid close attention to the behaviour of stochastic delay differential equations. Of particular interest is the investigation of the effect of stabilization on small departures from deterministic differential equations when the underlying deterministic equation has known asymptotic behaviour. Further investigation in this direction is ongoing.

Recently, we used the weighted residual method to solve a certain nonlinear fifth order boundary value problems arising in viscoelastic fluid flows.

We have successfully presented some of these results for intellectual scrutiny before experts in the field both within and outside the country through conferences, workshops and seminars. The abstract of our published papers have been indexed in the American Mathematical Reviews in the U.S. and in Europe by Zentralblatt fur Mathematik.