The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see [10, 11]), and studdied for example in [5] and [12]. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and other familiar concepts. Also in spinor bundles, we introduce a covariant derivation along multivector fields and call it the Clifford covariant derivation of that spinor bundle, which is related to its structure and has a natural relation to its Dirac OPERATOR.

We study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic Thom forms and distributional Thom currents, dual to different types of submanifolds. We show that the harmonic Thom form associated to a symplectic submanifold is nowhere vanishing. We also construct symplectic smoothing OPERATORs which preserve the harmonicity of distributional currents and using these OPERATORs, construct harmonic Thom forms for co-isotropic submanifolds, which unlike the harmonic forms associated with symplectic submanifolds, are supported in an arbitrary tubular neighborhood of the manifold.

The Schwarz inequality and Jensen’s one are fundamental in a Hilbert space. Regarding a sesquilinear map B(X, Y ) = Y*X as an OPERATORvalued inner product, we discuss OPERATOR versions for the above inequalities and give simple conditions that the equalities hold.

This study is a critical discourse analysis of Reader's Choice. The objectives of the research are to investigate the extent of ideological evasiveness and biases in this book, as well as to show whether the book may be suitable for being used as a textbook. To this end, four reading comprehension texts were chosen randomly from the book. These texts are: "The Midnight Visitor", "Sonar for the Blind", "Pockety Women Unite?", and "The 800 th Lifetime". The discursive structures of these texts have been studied according to HODGE and Kress's (1996) framework that consists of four features: naming, nominalization, active vs. passive sentences, and actional vs. relational sentences. The frequency of discursive structures have been measured in these texts. The results show that there was no evasive and biased structure in the book. Furthermore, according to the factors that have been focused in this study, the book proved to be a suitable textbook.

Background and Objectives: Resistance among bacterial isolates is the leading cause of increased mortality and morbidity worldwide. Carbapenems once thought to be effective are becoming ineffective mostly due to the emergence of carbapenemase. This study was designed to determine in vitro efficacy of Modified HODGE test for detection of carbapenemase production in Gram negative rods.Material and Methods: The study was done in the Department of Microbiology, Armed Forces Institute of Pathology Rawalpindi Pakistan from January 2010 to December 2010. A total of 200 Gram negative rods from different clinical samples were taken. Those isolates which showed intermediate or susceptible zones i.e 16 mm-21mm on disc diffusion were included in the study. These isolates were then subjected to Modified HODGE test.Result: Out of 200 isolates, 138 (69%) were positive for carbapenemase production by Modified HODGE test. Out of 138 MHT positive organisms, the frequency of E. coli was 38%, followed by Pseudomonas aeruginosa (30%), Klebsiella pneumoniae (17%), Acinetobacter baumannii (12%), Citrobacter diversus (2%) and Enterobacter agglomerans (1.4%).Conclusion: Modified HODGE test is a simple test which can be performed in the routine lab for detection of carbapenemases in isolates showing intermediate or sensitive zone diameter on disc diffusion.

Any notion of purity is normally defined in terms of solvability of some set of equations. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair (A, M), for a category A and a class M of monomorphisms in a category A. In this paper we take A to be the category Act-S of S-acts, for a semigroup S, and Msp to be the class of CspI-pure monomorphisms and study some categorical and algebraic properties of this class concerning the closure OPERATOR CspI.