The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.
Millions of lives might be saved if stained tissues could be detected quickly. Image classification algorithms may be used to detect the shape of cancerous cells, which is crucial in determining the severity of the disease. With the rapid advancement of digital technology, digital images now play a critical role in the current day, with rapid applications in the medical and visualization fields. Tissue segmentation in whole-slide photographs is a crucial task in digital pathology, as it is necessary for fast and accurate computer-aided diagnoses. When a tissue picture is stained with eosin and hematoxylin, precise tissue segmentation is especially important for a successful diagnosis. This kind of staining aids pathologists in disti
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This study focuses on studying an oscillation of a second-order delay differential equation. Start work, the equation is introduced here with adequate provisions. All the previous is braced by theorems and examplesthat interpret the applicability and the firmness of the acquired provisions
Oscillation criterion is investigated for all solutions of the first-order linear neutral differential equations with positive and negative coefficients. Some sufficient conditions are established so that every solution of eq.(1.1) oscillate. Generalizing of some results in [4] and [5] are given. Examples are given to illustrated our main results.
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EDIRKTO, an Implicit Type Runge-Kutta Method of Diagonally Embedded pairs, is a novel approach presented in the paper that may be used to solve 4th-order ordinary differential equations of the form . There are two pairs of EDIRKTO, with three stages each: EDIRKTO4(3) and EDIRKTO5(4). The derivation techniques of the method indicate that the higher-order pair is more accurate, while the lower-order pair provides superior error estimates. Next, using these pairs as a basis, we developed variable step codes and applied them to a series of -order ODE problems. The numerical outcomes demonstrated how much more effective their approach is in reducing the quantity of function evaluations needed to resolve fourth-order ODE issues.
The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.