This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

In the present paper, an eco-epidemiological model consisting of diseased prey consumed by a predator with fear cost, and hunting cooperation property is formulated and studied. It is assumed that the predator doesn’t distinguish between the healthy prey and sick prey and hence it consumed both. The solution’s properties such as existence, uniqueness, positivity, and bounded are discussed. The existence and stability conditions of all possible equilibrium points are studied. The persistence requirements of the proposed system are established. The bifurcation analysis near the non-hyperbolic equilibrium points is investigated. Numerically, some simulations are carried out to validate the main findings and obtain the critical values of th

The derivation of 5^th order diagonal implicit type Runge Kutta methods (DITRKM5) for solving 3^rd special order ordinary differential equations (ODEs) is introduced in the present study. The DITRKM5 techniques are the name of the approach. This approach has three equivalent non-zero diagonal elements. To investigate the current study, a variety of tests for five various initial value problems (IVPs) with different step sizes h were implemented. Then, a comparison was made with the methods indicated in the other literature of the implicit RK techniques. The numerical techniques are elucidated as the qualification regarding the efficiency and number of function evaluations compared with another literature of the implic

ABSTRACTBackground : Acne vulgaris is a
common skin disease, affecting more than 85% of
adolescents and often continuing into adulthood.
People between 11 and 30 years of age and up to
5% of older adults. For most patients acne remains
a nuisance with occasional flares of unsightly
comedones, pustules and nodules. For other less
fortunate persons, the sever inflammatory response
to Propionibacterium acnes (P.acnes) results in
permanent
Methods: Disfiguring scars. (1, 2) Stigmata of sever
acne cane lead to social ostracism, withdrawal
from society and severe psychologic
depression (1-4).
Result Pathogenesis of acne Traditionally, acne
has been thought of as a multifactorial disease of
the fo

The self-awareness interactions reflects with emotions,assess the child in respect to its relations with the social standards; they are not merely simply reactions , but rather they connect with his moral behavior and other 's thinks. When the self- awareness gets developed with emotions within the child , the latter become highly sensitive, causing him prone to be blamed . AS a result , the children test the self –awareness interactions with emotions and in age 3 years , where the self –awareness interactions with emotion clearly link to the self- assessment. The children in stage of kindergarten could not describe the self-awareness interactions accurately ; they test it under different circumstances in comparison to the youngest o

The childhood stage is considered the most important stage of all the stages through
the human being’s life. In this stage the human being will be more affected by the various
factors that surround him/her. The first five years of his/her life leave a great impact not only
on the human being personality, but also on his/her whole life. Therefore, it is worthwhile tobe concerned with and focus at the raising up and the teaching of the child during the
childhood stage.
The mission of raising up children in this era - the era of globalization and information
bursting or news flooding – has become a very difficult or even an impossible mission.
Furthermore, not only in the Arabic world, but also all over the world, t

The research objectives, to build a measure of the level of tactical performance of volleyball players applying for the Iraqi Premier League for the 2018-2019 season. The nature of the research problem, then the researchers determined the research sample in the deliberate manner of the players of the Iraqi clubs for the Premier League (B, A). The researchers adopted the entire community as a sample for the research, and the number (156) players distributed over (13) clubs and divided the sample into (12)players an exploratory experiment player representing (the police club) and (100) player representing the construction sample and after a maximum period of two months has passed since applying the scale to the construction sample the researc

        Recently, some prostate cancer patients have acquired resistance to the second -generation drugs (anzalutamide and apalutamide) prescribed for the treatment of this disease due to the emergence of the F876L mutation, which represents a challenge to modern medicine. In this study, a new series of 2-thiohydantoin derivatives were prepared through the reaction of different derivatives of maleimide (1c-4c) with isothiocyanate derivatives. The prepared compounds were diagnosed using FT-IR,¹H-NMR ,¹³C-NMR, Mass spectra. The prepared series compounds has been studied against prostate cancer cells. The MTT assay was used to determine the activity of the prepared compounds against prostate cancer cells. The da