On generalized integral inequalities with applications in bio-mathematics and physical sciences

Pelen, Neslihan Nesliye
In this thesis, applications of generalized integral inequalities especially on biomathematics and physics are studied. Application on Biomathematics is about the predatorprey dynamic systems with Beddington DeAngelis type functional response and application on physics is about water percolation equation. This thesis consists 6 chapters. Chapter 1 is introductory and contains the thesis structure. Chapter 2 is about under which conditions the two dimensional predator-prey dynamic system with Beddington DeAngelis type functional response is permenent and globally attractive. Chapter 3 is about the same type dynamic system but with impulses. In that chapter under which conditions the dynamic system has at least one periodic solution is investigated. To get the result we use Continuation Theorem. Using impulse on this type of dynamic system is also important. Because we can model the real life much better by this way. In Chapter 4, the predator-prey dynamic system with Beddington DeAngelis type functional response on periodic time scales in shifts is studied. In this chapter, first we prove which kind of periodic time scales in shifts should be used to find there is at least one δ±-periodic solution for the given system. Then again by using Continuation Theorem we get the desired result. In Chapter 5, first we generalize the Constantin’s Inequality on Nabla and Diamond-α calculus on time scales. Then by using a topological transversality theorem and using the generalization of Constantin’s Inequality on Nabla Calculus, we have showed that the vwater percolation equation on nabla time scales calculus has solution. This solution is unique and bounded. The last chapter is the summary of what we have done in this thesis. As a result, since this study is on time scales, the findings are also important on the discrete and continuous case.


Some Inequalities Between Pairs of Marginal and Joint Bayesian Lower Bounds
Bacharach, Lucien; Chaumette, Eric; Fritsche, Carsten; Orguner, Umut (2019-01-01)
In this paper, tightness relations (or inequalities) between Bayesian lower bounds (BLBs) on the mean-squared-error are derived which result from the marginalization of a joint probability density function (pdf) depending on both parameters of interest and extraneous or nuisance parameters. In particular, it is shown that for a large class of BLBs, the BLB derived from the marginal pdf is at least as tight as the corresponding BLB derived from the joint pdf. A Bayesian linear regression example is used to i...
On the Krall-type polynomials on q-quadratic lattices
Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01)
In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
Isomorphism classes of elliptic curves over finite fields of characteristic two
Kırlar, Barış Bülent; Akyıldız, Ersan; Department of Mathematics (2005)
In this thesis, the work of Menezes on the isomorphism classes of elliptic curves over finite fields of characteristic two is studied. Basic definitions and some facts of the elliptic curves required in this context are reviewed and group structure of elliptic curves are constructed. A fairly detailed investigation is made for the isomorphism classes of elliptic curves due to Menezes and Schoof. This work plays an important role in Elliptic Curve Digital Signature Algorithm. In this context, those isomorphi...
Evaluation of Hypersingular Integrals on Curvilinear Surface Elements
Selcuk, Gokhun; Koç, Seyit Sencer (2016-04-15)
In this study finite part integrals are utilized for evaluation of hypersingular and nearly-hypersingular surface integrals on curvilinear elements. These integrals are related to the second derivative of the free space Green' function and arise in the solution of electric field integral equation (EFIE) via locally corrected Nystriim (LCN) method. The curvilinear elements are represented by the Taylor series expansion of the surface function around the observation point. The hypersingular integral, defined ...
On Lyapunov inequality in stability theory for Hill's equation on time scales
Atici, FM; Guseinov, GS; Kaymakcalan, B (Springer Science and Business Media LLC, 2000-01-01)
In this paper we obtain sufficient conditions for instability and stability to hold for second order linear Delta -differential equations on time scales with periodic coefficients.
Citation Formats
N. N. Pelen, “On generalized integral inequalities with applications in bio-mathematics and physical sciences,” Ph.D. - Doctoral Program, Middle East Technical University, 2015.