Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

    A mounted specimen of a mustelid animal deposited in the Kurdistan Museum of Natural History, Salahaddin University, Erbil proved to be Mustela erminea (Linnaeus, 1758) and represents a new record for the mammalian fauna of Iraq. Its measurements and some biological noted are provided. Also, two passerine birds; the Red-headed bunting, Emberiza bruniceps Brandt, 1841(Family, Emberizidae) and the Variable wheatear, Oenanthe picata (Blyth, 1847) (Family, Muscicapidae) were recorded for the first time in Iraq. Furthermore, the tree frog Hyla savignyi Audouin, 1829 was found in two locations north east of Iraq with spotted dorsum and having interesting behavior in having the capabil

A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of ri

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings

A study of some mite species of alfalfa. wheat, and barley was conducted in central Iraq.
The mites were extracted using a tullgren funnel method. Twelve species were recorded. 10 of
them belong to suborder Trombidiformes and 2 belong to suborder Sarcoptiforms. Three
mites, Irnpar(pes hystricinus, Scutacarus longitarsus, and Rhizoglyphus echin opus are new
records for Iraqi mite fauna, and 11 are new host records in alfalfa soil.

The Old World Screwworm Fly Chrysomya bezziana is a new insect pest on cattles and other domestic recor¬ded for the first from Iraq. It was first observed in cow's vagina in September of 1996 in Shaikh Hammed (Tarmiya), near Baghdad city. Chrysomya bezziana Villeneuve is well known as one of the most important insect pests of livestock. Its larvae infest living tissues by causing myiasis. In a wide range of worm-blooded host species (Spradbery and Vanningham, 1980; Spradbery and Kirk. 1992). It is widely dist¬ributed species over an extensive area of tropical and subtropical Africa, the Arabian Gulf countries, Iran. Indian subcontinent. South-East Asia. Indonesia, and as far east as Papua New Guinea (Zurapt, 1965; Djalayer et al. 1978;

The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl

       In this work, the fractional damped Burger's equation (FDBE) formula    = 0,