This research delves into the examination of weak solutions for boundary value problems associated with nonlinear partial differential equations. Utilizing the variational method, we explore the conditions necessary and sufficient for the existence and uniqueness of these weak solutions. Furthermore, we provide practical demonstrations by solving specific examples of nonlinear problems involving partial differential equations. The study concludes with an analysis of the benefits and limitations inherent in employing the variational method for such investigations.
This work deals with the application of the “Method of Undetermined Coefficient” in solving nonhomogeneous linear differential equations with constant coefficients as an alternative to the method to “Variation of Parameters”. Its treatment covers up to the fourth-order nonhomogeneous linear DEs. It has carefully explained the steps and procedures involved in finding the complementary and particular solutions which are usually combined to obtain the general solutions. It also discusses the limitations or the extent to which this method under consideration can be applied.
The study assessed the flood vulnerability of the Asafo Sewerage treatment site within the Kumasi Metropolitan Assembly in Ghana using the HEC-RAS model 1- and 100-year floods. Three distinct scenarios (S1, S2 and S3) relating to the point where the Gee River join the Subin River and another that combined scenario 1 with a built levee (S1+Levee), were tested to ascertain the most effective way of preventing floodwaters from entering the treatment site. The result depicts a direct relationship between flood inundation are-as and designed streamflow for the different return periods within the treatment site, with the natural regime already experiencing inundation at least once a year. The observed flood inundation could be due to the low ground elevations and the natural depression created by the diversions of the Gee and Subin Rivers from their natural state within the treatment site. Adopting S2 would increase the extent of inundation from the natural regime by 12.28-19.38% for 1-100-year floods within the treatment site. The results re-vealed a significant decrease in the 1-year flood extent under S3 (71.58%) and S1+Levee (94.94%), despite a slight rise under S1 (3.24%). The extent of inundations during the 100-year flood was estimated to drop by 38.99%, 40.40%, and 97.01%, S1, S3 and S1+Levee, respectively. The treatment site recorded low flood depths (0.00-0.60 m) and velocities (0.00-1.00 m/s), whilst high flood depths (> 1.0 m) and velocities (> 4.0 m/s) were within the main Subin River channel. It is worth noting that not all the inundated areas within the treatment site are susceptible to high-risk levels, with most of the designated high and very high flood-risk zones located within the main river channels of the Subin and Gee Rivers. The aged, Children, buildings and small vehicles are generally safe within the treatment site due to its low level of susceptibility. Based on the study, S1+Levee is considered the best option to adopt for reducing the amount of flooding within the treatment site, followed by S3 and S1 in that order.
Development of circle in four steps hypothesis HA verification BE. According Euclidean geometry, pythagorion theorima, and the solution of Deinostratus, The construction give us questions: where is the mistake, and ancient civilization use that application in them construction, as pyramids, Parthenon, astrolavos, Minoan analogical calculator,mechanism of Antikytheron, and how useful can be to our time.
Energy conservation is paramount importance for natural gas especially considering high oil prices as any wastage of energy leads to increased production cost. Several tools are available to assess a design of natural gas consumption this study about a technique framework to reduce natural gas Consumption. The purpose of this study to distribute the production of natural gas for various consumers, Each with certain chemical composition and properties of natural gas which satisfy the customer demand and reduce the consumption of the natural gas at the network grid. The Using Machine learning (ML) to handle the input data for more efficiently with different algorithms with natural gas maneuver reducing gas consumption and maximize daily production