The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

Aннотация

В статье представлены явления полисемии и омонимии в специализированной терминосистеме, а именно в геодезической терминологии; определены предпосылки и причины возникновения полисемии и омонимии в профессиональном языке в области геодезии и кадастра; установлены различия и взаимосвязь между понятиями омонимия и полисемия; выделены главных типы полисемантических тер

Bipedal robotic mechanisms are unstable due to the unilateral contact passive joint between the sole and the ground. Hierarchical control layers are crucial for creating walking patterns, stabilizing locomotion, and ensuring correct angular trajectories for bipedal joints due to the system’s various degrees of freedom. This work provides a hierarchical control scheme for a bipedal robot that focuses on balance (stabilization) and low-level tracking control while considering flexible joints. The stabilization control method uses the Newton–Euler formulation to establish a mathematical relationship between the zero-moment point (ZMP) and the center of mass (COM), resulting in highly nonlinear and coupled dynamic equations. Adaptiv

Abstract: The use of indirect, all-ceramic restorations has grown in popularity among dentists. Studies have demonstrated that for indirect ceramic restorations to be effective over time, cement and ceramic must be bonded in a stable manner. Chemical, mechanical, and laser irradiation are among the methods used to precondition ceramic surfaces in order to increase bond strength.The objective of the study: This study was performed to investigate the roughness values and surface topography of lithium disilicate glass-ceramic treated with conventional methods and different Er,Cr:YSGG, and fractional CO₂ laser conditioning parameters.Material and methods:<

The acceptance sampling plans for generalized exponential distribution, when life time experiment is truncated at a pre-determined time are provided in this article. The two parameters (α, λ), (Scale parameters and Shape parameters) are estimated by LSE, WLSE and the Best Estimator’s for various samples sizes are used to find the ratio of true mean time to a pre-determined, and are used to find the smallest possible sample size required to ensure the producer’s risks, with a pre-fixed probability (1 - P^*). The result of estimations and of sampling plans is provided in tables.

Key words: Generalized Exponential Distribution, Acceptance Sampling Plan, and Consumer’s and Producer Risks

Title: Arabic Manuscript, Concepts and Terms and Their Impact on Determining Its Historical beginnings and extension of its existence.

Researcher: Dr. Atallah Madb Hammadi Zubaie.

Bn the name of Allah Most Merciful

The interest in manuscripts and rules  of their investigation and dissemination appeared soon, and the speech in editing terms and concepts appeared in sooner time.  When looking at the classified books  in the Arab manuscripts , we find the books of the first generation  did not allude definition for this term  , but rather  focused on  the importance of manuscripts and their  existence locations, indexing, care, and verification rules. The  reason for this is that the science of Arabic manuscrip