The purpose of this paper is to give some results theorems , propositions and corollaries concerning new algebraic systems flower , garden and farm with accustomed algebraic systems groupoid , group and ring.

Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an ef

The flow in a manifolds considered as an advanced problem in hydraulic engineering applications. The objectives of this study are to determine; the uniformity qn/q1 (ratio of the discharge at last outlet, qn to the discharge at first outlet, q₁) and total head losses of the flow along straight and rectangular loop manifolds with different flow conditions. The straight pipes were with 18 m and 19 m long and with of 25.4 mm (1.0 in) in diameter each. While, the rectangular close loop configuration was with length of 19 m and with diameter of 25.4 mm (1.0 in) also. Constant head in the supply tank was used and the head is 2.10 m. It is found that outlets spacing and manifold configuration are the main factors aff

The new complexes including Cu(II), Co(II), Ni(II), Pt(IV), and Pd(II) metals with 4,4'-(((1E,1'E)-1,4-phenylenebis(methaneylylidene))bis(azaneylylidene))bis(5-(4-chlorophenyl)-4H-1,2,4-triazole-3-thione) have been synthesized of utilizing us polystyrene (PS) photostability. The supplement (0,5 w / v%) was for the production of polystyrene ( PS) in the form of tetrahydrofuran (THF). Polystyrene films were exposing irradiation (250 – 380 nm) absorption light intensity of 6.02 x 10-9 ein dm-3 s-1 at room temperature, through the changes that occur to each of viscosity average molecular weight (Mv), main chain scission (S), degree of polymerization (DPn), weight loss %, hydroxyl index (lOH), carbonyl index (ICo) determined the photo stabiliz

This paper presents a novel idea as it investigates the rescue effect of the prey with fluctuation effect for the first time to propose a modified predator-prey model that forms a non-autonomous model. However, the approximation method is utilized to convert the non-autonomous model to an autonomous one by simplifying the mathematical analysis and following the dynamical behaviors. Some theoretical properties of the proposed autonomous model like the boundedness, stability, and Kolmogorov conditions are studied. This paper's analytical results demonstrate that the dynamic behaviors are globally stable and that the rescue effect improves the likelihood of coexistence compared to when there is no rescue impact. Furthermore, numerical simul

The load shedding  scheme has been extensively implemented as a fast solution for unbalance conditions. Therefore, it's crucial to investigate supply-demand balancing in order to protect the network from collapsing and to sustain stability as possible, however its implementation is mostly undesirable. One of the solutions to minimize the amount of load shedding is the integration renewable energy  resources, such as wind power, in the electric power generation could contribute significantly to minimizing power cuts as it is ability to positively improving the stability of the electric grid. In this paper propose a method for shedding the load base on the priority demands with incorporating the wind po