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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

Nuclear structure of 20,22Ne isotopes has been studied via the shell model with Skyrme-Hartree-Fock calculations. In particular, the transitions to the low-lying positive and negative parity excited states have been investigated within three shell model spaces; sd for positive parity states, spsdpf large-basis (no-core), and zbme model spaces for negative parity states. Excitation energies, reduced transition probabilities, and elastic and inelastic form factors were estimated and compared to the available experimental data. Skyrme interaction was used to generate a one-body potential in the Hartree-Fock calculations for each selected excited states, which is then used to calculate the single-particle matrix elements. Skyrme interac

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

In this research , we study the inverse Gompertz distribution (IG) and estimate the  survival function of the distribution , and the survival function was evaluated using three methods (the Maximum likelihood, least squares, and percentiles estimators) and choosing the best method estimation ,as it was found that the best method for estimating the survival function is the squares-least method because it has the lowest IMSE and for all sample sizes

Water has a great self-generating capacity that can neutralize the polluting interventions carried out by humans. However, if human activities continue this uncontrolled and unsustainable exploitation of this resource, this regenerating capacity shall fail and it will be jeopardized definitively. Shatt Al-Arab River in South of Iraq. It has an active role in providing water for irrigation, industry, domestic use and a commercial gateway to Iraq. in the last five years Shatt Al-Arab suffered from a rise in pollutants due to the severe decline in sewage networks, irregular networks and pesticide products, as well as the outputs of factories and companies that find their way to water sources and lead to a widespread collapse of water quality.

In this research , we study the inverse Gompertz distribution (IG) and estimate the  survival function of the distribution , and the survival function was evaluated using three methods (the Maximum likelihood, least squares, and percentiles estimators) and choosing the best method estimation ,as it was found that the best method for estimating the survival function is the squares-least method because it has the lowest IMSE and for all sample sizes