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

     The bubble columns are widely used as a two or three phase reactor in industrial chemical process such as absorption, biochemical reactions, coal liquefaction, etc. To design such a column, two main parameters should be taken in consideration, the gas hold-up (), and the liquid phase mass transfer coefficient K_La. The study includes the effect of gas velocity and the addition of alcohols on gas hold-up and mass transfer coefficient in bubble column with draught tube when the length of the column is 1.5m and the ratio of the draught tube diameter to the column diameter equals 0.5 and the air dispersion into the base of the draught tube using a multi hole tuyere is equivalent to a diameter of 0.15 mm and

Alien fish species have negative effects on the abundance, diversity and richness of native fish species in southern Iraq. The numbers of alien fish species are constantly increasing due to the entry of invasive species. This has resulted in shifts in the historical composition of fish community structure and scarcity of some native species which represent the keystone in the building of fish populations.

    Fish samples were monthly collected from three sites in southern Iraq (Al-Chibyaish marsh, the lower parts of Euphrates River, and the northern part of Shatt Al-Arab River) from April 2017 to June 2018. A total of 14,853 individuals of fish were sampled, which represented 26 species, 24 genera and 13 families

The trading banks in Iraq invest their funds according to regulations imposed by the Central Bank in Iraq in different financial fields like stock exchanges, acquire stocks as assets that could be sold at any time as well as make loans and contributing in corporations establishment also magnitude foreign capital through direct contacts with foreign exchange markets.

We can summarize the problem of this paper as shortage in mathematical models that used in studying and analyzing these investments and according to this problem we used (a constructed mathematical model ) consists of three major indicators: profitability of total investment assets which is divided into three sub-indicators: owners equity risk indicator, debits risk i

Background: Osteoarthritis (OA) currently seems
inevitable and unavoidable for a large swath of the
population .its etiology relates to a strong ,but
complex ,non mendelian genetic basis ,combined
with mechanical and metabolic factors that cause
molecular alterations the end results of which
affect the whole joint .Glucosamine and
chondrotin sulfate alone or in combination may be
of benefit to a subgroup of individuals who have
knee pain due to OA.
Glucosamine has been shown to alter cartiage turn
over in patients with OA undergoing physical
training
Aim of the study: To find the validity of
glucosamine chondrotin sulfate in treatment of
grade 1 and 2 OA.
Methods: the sample of 280 patients

Amino acids have the role in the process of proteins synthesis. They are an essential source of nitrogen atoms that have a role in the pathways of synthetic reaction pathways. The carbon skeletons of the amino acids are the source of energy in addition to their role as precursors in the paths of interactions. The amino acids analysis for the brain of the quail bird in different stage of development (10-16 days of incubation) in addition to the hatching stage (17th day) and the adult. Materials and Methods: Amino Acids Analysis The amino acids were separated from the embryos and adult brains of the quail bird Coturnix coturnix and were diagnosed based on standard amino acids, using high performance liquid chromatographic device (H.P.L.C.). R

The settlement rate and pore water pressure dissipation rate are mainly controlled by the permeability of soil. Both laboratory and field tests show that the permeability is varied during the loading and consolidation process. It is known that consolidation process is accompanied by decrease in void ratio which leads to decrease in the coefficient of permeability. The importance of the decrease of the coefficient of permeability on the time rate of settlement and pore water pressure needs to be investigated.
This paper takes into account the change in coefficient of permeability during consolidation and studies its effect on consolidation characteristics of a clay layer. The finite element method is used in the analysis and the packag

The research aimed to identify "the effectiveness of educational-learning design according to the model of brain compatibility in achievement among firstmiddle grade students in mathematics", in schools affiliated with the Second Karkh Directorate of Education. To achieve the goal of research, the following zero hypothesis has been formulated: " There is no statistically significant difference at the semantic level (05.0) between the average scores of experimental group students who will study with design accreditation (educational - learning) according to the brain compatibility model and the grades of control group students who will study in the usual way in the achievement thinking test". The research community, which is represented by