This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

The study was conducted from November 2021 to May 2022 at the three study sites within the Baghdad governorate. The study aims to identify the impact of human activities on the Tigris River, so an area free of human activities was chosen and represented the first site. A total of 48 types were diagnosed, 6204 ind/m3 spread over three sites. The following environmental indicators were evaluated: Constancy Index (S), Relative abundance index (Ra), Richness Index (between 17.995 and 23.251), Shannon Weiner Index (0.48-1.25 bit/ind.), Uniformity Index (0.124 -0.323). The study showed that the highest percentage recorded was for the phylum Annileda 34%; and the stability index shows that taxes (Stylaria sp., Aoelosoma sp., Branchinra sowerby, Ch

The study explores the use of ergative verbs in constructing clauses and their impact on the backgrounding of the agent's role in two selected short stories. Contrary to hypothesis No. 1, the research indicates that changes in sentence patterns don't affect the meaning of the process. Additionally, hypothesis No. 2 is refuted as the middle structure is found to highlight the agent's role in the science fiction short story, Terra Infirmum, rather than concealing it as hypothesized for "The Invisible Man." The analysis uncovers that writers utilize ergative processes to narrate stories in various ways, including transitive/active voice, intransitive/active voice, and transitive/passive voice. Furthermore, the findings suggest that writers emp

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

Undesirable growth of potato (Solanum tuberosum L.) crop under an excessive N fertilizer application is the main obstacle presently. This research was conducted to investigate the response of different potato cultivars; Russet Burbank, Shepody, and Superior, and its qualitative characteristics under a series of N rates. Six rates of N fertilization (0–280 kg ha−1) were applied on 11 sites in a randomized complete block design, with four replications. Sites with ≥30 g kg−1 of soil organic matter (OM) produced total tuber yield, marketable yield, and tuber weight per plant 39.5, 45.2, and 54.9%, respectively, higher than sites with ≤30 g kg−1 of OM. Tubers specific gravity increased by 0.18% in the sites with ≥30 g kg−1 of OM.

The paper presents a highly accurate power flow solution, reducing the possibility of ending at local minima, by using Real-Coded Genetic Algorithm (RCGA) with system reduction and restoration. The proposed method (RCGA) is modified to reduce the total computing time by reducing the system in size to that of the generator buses, which, for any realistic system, will be smaller in number, and the load buses are eliminated. Then solving the power flow problem for the generator buses only by real-coded GA to calculate the voltage phase angles, whereas the voltage magnitudes are specified resulted in reduced computation time for the solution. Then the system is restored by calculating the voltages of the load buses in terms

   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