This study presents a mathematical model describing the interaction of gut bacteria in the participation of probiotics and antibiotics, assuming that some good bacteria become harmful through mutations due to antibiotic exposure. The qualitative analysis exposes twelve equilibrium points, such as a good-bacteria equilibrium, a bad-bacteria equilibrium, and a coexisting endemic equilibrium in which both bacteria exist while being exposed to antibiotics. The theory of the Sotomayor theorem is applied to study the local bifurcation around all possible equilibrium points. It’s noticed that the transcritical and saddle-node bifurcation could occur near some of the system’s equilibrium points, while pitchfork bifurcation cannot be accrued at

Background: evaluate the effects of three different intracoronal bleaching agents on the shear bond strengths (SBS) and failure site of stainless steel and monocrystalline (sapphire) orthodontic brackets bonded to endodontically treated teeth using light cured orthodontic adhesive in vitro. Materials and methods: Eighty extracted sound human upper first premolars were selected, endondontically treated and randomly divided equally (according to the type of the brackets used) into two main groups (n = 40 per group). Each main group were subdivided (according to the bleaching agent used) into four subgroups 10 teeth each; as following : control (un bleached) group, hydrogen peroxide group (Hp) 35%, carbamide peroxide group (CP) 37% group and s

Dairy wastewater generally contains fats, lactose, whey proteins, and nutrients. Casein precipitation causes the effluent to decompose into a dark, strong-smelling sludge. Fluid waste contains soluble organic matter, suspended solids, and gaseous organic matter, which cause undesirable taste and smell, grant tone and turbidity, and advance eutrophication, which plays an essential role in increasing biological oxygen demand (BOD) in water. It also contains detergents and disinfecting agents from the rinses and washing processes, which increase the need for chemical oxygen (COD). One of the characteristics of dairy effluents is their relatively high temperature, high organic contents, and wide pH range, so the discharge of wastewater into

The implementation of the concept of project scheduling in the organizations generally requires a set of procedures and requirements, So, most important of all is the understanding and knowledge of the tools and techniques which are called the methods of scheduling projects. Consequently, the projects of the municipality administration in the holy governorate of Karbala suffer from the problem of delaying their projects and chaos in the ways of implementation. To provide assistance to this directorate and to demonstrate how to schedule projects using one of the advanced scientific methods that proved their ability to schedule any project and its potential to accelerate the time of completion, as well as ease of use and effectiven

In parallel with the shell model using the harmonic oscillator's single-particle wave functions, the Hartree-Fock approximation was also used to calculate the neutron skin thickness, the mirror charge radii, and the differences in proton radii for ¹³O-¹³B and ¹³N-¹³C mirror nuclei. The calculations were done for both mirror nuclei in the psdpn model space. Depending on the type of potential used, the calculated values of skin thickness are affected. The symmetry energy and the symmetry energy's slope at nuclear saturation density were also determined, and the ratio of the density to the saturation density of nuclear matter and the symmetry energy has a nearly linear correlation. The mirror ener

Nonlinear time series analysis is one of the most complex problems ; especially the nonlinear autoregressive with exogenous variable (NARX) .Then ; the problem of model identification and the correct orders determination considered the most important problem in the analysis of time series . In this paper , we proposed splines  estimation method for model identification , then we used three criterions for the correct orders determination. Where ; proposed method used to estimate the additive splines for model identification , And the rank determination depends on the additive property  to avoid the problem of curse dimensionally . The proposed method is one of the nonparametric methods , and the simulation results give a

This study concerns the role of activated carbon (AC) from palm raceme as a support material for the enhancement of lipase-catalyzed reactions in an aqueous solution, with deep eutectic solvent (DES) as a co-solvent. The effects of carbonization temperature, impregnation ratio, and carbonization time on lipase activity were studied. The activities of Amano lipase from Burkholderia cepacia (AML) and lipase from the porcine pancreas (PPL) were used to investigate the optimum conditions for AC preparation. The results showed that AC has more interaction with PPL and effectively provides greater enzymatic activity compared with AML. The optimum treatment conditions of AC samples that yield the highest enzymatic activity were 0.5 (NaOH (

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient