Let  be a metric space and  be a continuous map. The notion of the  -average shadowing property ( ASP )  for a continuous map on  â€“space is introduced  and the relation between the ASP and average shadowing property(ASP)is investigated. We show that if  has ASP, then   has ASP for every . We prove that if a map  be pseudo-equivariant with dense set of periodic points and has the ASP,  then  is weakly mixing. We also show that if   is a expansive pseudo-equivariant homeomorphism that has the ASP and  is topologically mixing,  then  has a  -specification. We obtained that the identity map  on  has the ASP  if and only if th

Praise be to God, who said: {And establish prayer and pay zakat and lend to God a good loan, and whatever good you put forward for yourselves you will find with God. It is better and greater in reward. Ask forgiveness of God. Indeed, God is Forgiving, Most Merciful. May blessings and peace be upon Muhammad, the servant of God, and His Messenger, may God bless him and grant him peace, who said: “Islam is built on five Testifying that there is no god but God and that Muhammad is the Messenger of God, establishing prayer, paying zakat, Hajj, and fasting Ramadan” ().
Now that follows: Islamic law aims to make man happy in this world and the afterlife, starting with faith in God Almighty until the end of the legal obligations. This is

Given that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier “tick,” studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease’s incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution’s qualitative attributes is included. According to the established basic reproductio

Background: The healing of a sutured tendon in the hand usually occur with an unwanted amount of scarring that defeat good results. Many variables has been studied over many decades; timing of repair M’as a matter of debate. Zone II is the area where those variables mostly affect the results of treatment.
Objective: To study and evaluate the results of early or delayed repair under the effects of our local variables.
Method: Prospective study of 85 patients, which had flexor tendon repair at zone II by primary repair, delayed primary repair and tendon graft.
Results: Results showed a primary repair ended with better functional results than those with delayed repair and than those with tendon graft. Excellent & good results

The legal system of found property is considered as a reason or method of preliminary acquisition of ownership, as well as two other reasons, that is to say, the fixture of personal chattels, and the adverse possession, resting on the principles of equity, and included within the English common law of customary origins, which is unwritten and based upon judicial precedents of the English courts, equity and later legislations. It is worth-bearing in mind that the found property is the lost property on which the finder enjoys more rights than all other people, except its original owner. It is also worth-mentioning that the treasure trove is considered as found property in the English law. and it is any object at least 300 years old when fo

    In this paper, we introduce the concept of s.p-semisimple module. Let S be a semiradical property, we say that a module M is s.p - semisimple if for every submodule N of M, there exists a direct summand K of M such that K ≤ N and N / K has S. we prove that a module M is s.p - semisimple module if and only if for every submodule A of M, there exists a direct summand B of M such that A = B + C and C has S. Also, we prove that for a module M is s.p - semisimple if and only if for every submodule A of M, there exists an idempotent e ∊ End(M) such that e(M) ≤ A and (1- e)(A) has S. 

Narcissus tazetta, a member of the Amaryllidaceae family, is known to be rich in bioactive metabolites such as alkaloids, phenolics and flavonoids, which have been found in nearly every species in this family. N. tazetta cultivated in Iraq, had not previously been studied for its active components; thus, the current study used phytochemical screening and phenolic compounds estimation, both qualitatively and quantitatively. Results showed that the plant alcoholic extract was rich in alkaloids, polyphenols and flavonoids besides tannins, polysaccharides and saponins. Qualitatively; TLC and HPLC chromatogram for total phenolics and flavonoids compounds revealed the presence of Gallic acid (GA), Caffeic acid (CA), Paracumar

     Fractional calculus has paid much attention in recent years, because it plays an essential role in many fields of science and  engineering, where the study of stability theory of fractional differential equations emerges to be very important. In this paper, the stability of fractional order ordinary differential equations will be studied and introduced the backstepping method. The Lyapunov function  is easily found by this method. This method also gives a guarantee of stable solutions for the fractional order differential equations. Furthermore it gives asymptotically stable.

      Some necessary and sufficient conditions are obtained that guarantee the oscillation of all solutions of two types of neutral integro-differential equations of third order. The integral is used in the sense of Riemann-Stieltjes. Some examples were included to illustrate the obtained results

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach