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Let (M, J, g) be a metallic pseudo-Riemannian manifold equipped with a metallic structure J and a pseudo-Riemannian metric g. The paper deals with interactions of Codazzi couplings formed by conjugate connections and tensor structures. The presence of Tachibana operator and Codazzi couplings presents a new characterization for locally metallic pseudo-Riemannian manifold. Also, a necessary and sufficient condition under which a non-integrable metallic pseudo-Riemannian manifold is a quasi metallic pseudo-Riemannian manifold is derived. Finally, it is introduced metallic-like pseudo-Riemannian m ...More
Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings.
Keywords: dual numbers; dual absolute value; ...More
Let L4 be a 4-dimensional Lorentzian space with the sign (−,,,). The aim of this study is to investigate the other missing algebraic forms of the constraint manifolds of 2C and 3C spatial open chains in L4. For this purpose, firstly, we obtain the structure equations of a spatial open chain using the equations of open chains of the Lorentz plane and Lorentz sphere. After then, using these structure equations, we search the algebraic forms of the constraint manifolds of 2C and 3C spatial open chains in Lorentzian 3-space with respect to the causal characters of the first link and the axis of ro ...More
The numerical solution of linear Volterra-Stieltjes integral equations of the second kind by using the generalized trapezoid rule is established and investigated. Also, the conditions on estimation of the error are determined and proved. A selected example is solved employing the proposed method.
The problem of minimum-energy control in the integro-differential linear systems with Fredholm integral was solved using the N.N. Krasovskii method of the problem of moments. An explicit solution of the boundary problem for the integro-differential equation was established using the K.A. Kasymov method.
Sufficient conditions for the boundedness on the half-axis of all solutions of the fourth-order linear Volterra integro-differential equation are established. Moreover, it is shown that the corresponding linear homogeneous and inhomogeneous differential equations can have unbounded solutions on the half-axis. Illustrative examples are given.
In this paper, we construct a method to find approximate solutions to fractional differential equations involving fractional derivatives with respect to another function. The method is based on an equivalence relation between the fractional differential equation and the Volterra-Stieltjes integral equation of the second kind. The generalized midpoint rule is applied to solve numerically the integral equation and an estimation for the error is given. Results of numerical experiments demonstrate that satisfactory and reliable results could be obtained by the proposed method.
The optimal control problem is investigated for oscillation processes, described by integro-differential equations with the Fredholm operator when functions of external and boundary sources non-linearly depend on components of optimal vector controls. Optimality conditions having specific properties in the case of vector controls were found. A sufficient condition is established for unique solvability of the nonlinear optimization problem and its complete solution is constructed in the form of optimal control, an optimal process, and a minimum value of the functional.
Based on a new approach, we show that finding solutions for a class of systems of linear (respectively, nonlinear) Fredholm integral equations of the third kind with multipoint singularities is equivalent to finding solutions of systems of linear (respectively, nonlinear) Fredholm integral equations of the second kind with additional conditions. We study the existence, nonexistence, uniqueness, and nonuniqueness of solutions for this class of systems of Fredholm integral equations of the third kind with multipoint singularities.
Sebahattin BALCI | Meerim İmaş Kızı | Fahreddin ABDULLAYEV
We study the order of growth of the moduli of arbitrary algebraic polynomials in the weighted Bergman space A(p)(G, h), p > 0, in regions with zero interior angles at finitely many boundary points. We obtain estimates for algebraic polynomials in bounded regions with piecewise smooth boundary.