In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO₂ as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H₂O₂, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest deg

The uptake of Cd(II) ions from simulated wastewater onto olive pips was modeled using artificial neural network (ANN) which consisted of three layers. Based on 112 batch experiments, the effect of contact time (10-240 min), initial pH (2-6), initial concentration (25-250 mg/l), biosorbent dosage (0.05-2 g/100 ml), agitation speed (0-250 rpm) and temperature (20-60ºC) were studied. The maximum uptake (=92 %) of Cd(II) was achieved at optimum parameters of 60 min, 6, 50 mg/l, 1 g/100 ml, 250 rpm and 25ºC respectively.

Tangent sigmoid and linear transfer functions of ANN for hidden and output layers respectively with 7 neurons were sufficient to present good predictions for cadmium removal efficiency with coefficient of correlatio

Schiff base obtained from the reaction (Trimethoprim) with (sodiumpyruvate ) to produce the ligand [NaL], the reaction was carried out in methanol as a solvent under reflux. The prepared ligand [NaL] was characterized by FT-IR, UV-Vis spectroscopy, 1H,13C-NMR spectra, mass spectra, and melting point.A new mixed ligand complexes have been prepared between ( 8- hydroxyquinolone) and the ligand [NaL] withMn(II).Co(II),Ni(II),Cu(II), (Zn(II) ,(Cd(II)and Pd(II). All the complexes were characterized by spectroscopic methods (FT-IR, UV-Vis spectroscopy), chloride content and melting point ,molar conductance and magnetic susceptibility.These measure- ments showed octahedral geometry around(,Mn2+, Co2+, Ni2+, Cu2+, Zn2+ and Cd2+) ions and square pla

Background: Fluoridated acrylic resin material can present more stable properties when compared with conventional one.The most widely used fluoride –containing substance added to dental resin materials is sodium fluoride (Naf). This study evaluated the effect of Naf in different concentration to the acrylic resin denture base material and its effect on tensile strength ,modules of elasticity with long –term water immersion (after 4 months immersion in de-ionized water) Materials and methods: Eighty specimens from dumbbells shaped metal pattern for tensile strength test were preparedaccording to ISO 527: 1993 plastic –Determination tensile properties ,in dimensions(60mm, 12mm, 3 ± 0.2mm) length, width and depth respec

Introduction: This study was designed to examine the effects of addition of the combination of polymerized polymethyl methacrylate (PMMA) and zirconia (ZrO2) particles to heat cure PMMA resin on impact strength, surface hardness, and roughness. Methods: The 70% (w/w) of polymerized PMMA powder (particle size: 0.70mm) was mixed with 30% (w/w) of zirconia powder (ZrO2) (1mm) to produce PMMA-ZrO2 filler. Ninety acrylic specimens created were divided into three groups containing 0% wt (Control group), 2% wt, and 4% wt, PMMA-ZrO2 filler. Ten specimens were used for impact strength, surface hardness and roughness test, blindly. Data were analyzed via oneway ANOVA and the Tukey post hoc test using R 3.6.3. Results: There was statistically signific

After this systematic presentation of the phenomenon of rotation of formulas, ie the construction of the verb and the verb, and the narrated narratives therein differed among the readers, it became clear to us how the difference was clear between reading and the other, and how readers have varied in their readings of the verb, As we have noted through our modest research that the phenomenon of building the verb for the actor and the effect have included the act of both past and present tense, and not limited to a specific time, and this difference in reading was not limited to a particular environment, but beyond To more than one environment This is evidenced by the readings of various readers from the environment of Kufa, Basra, Mecca,