On Analytical Review of Conjugate and Reflexive Spaces | Asian Research Journal of Current Science

In this review, we started by considering a normed space , its dual and bi-dual spaces. We define functionals on , as those functionals that are bounded linear functionals and then establish a corresponding unique bounded linear functional that defines a canonical mapping of  into  such that is linear, injective and preserves norm. By this, isomorphism is established so that reflexive maps are realized. In the cause of this work, we invoked the idea of compact topological space and operators mapped on them. We also discussed separable spaces as it relates to this topic. The work was rounded up in section three by discussing the Tychonoff’s theorem as it relates to the weak topology in conjugate spaces, adjoint operators and conjugate spaces of  and .

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On Application of Set Theory to Some Aspects of Real Analysis and Topology | Asian Journal of Pure and Applied Mathematics

Set as a collection of mathematical elements makes more meaning in classical analysis and topology. There are diverse forms of its existence and operations. In the course of this work, we discussed its various operations such as union intersection complementation and its various algebras. The application of the various algebra in real analysis and metric space topology was peripherally discussed. Conclusively, we discovered that set is an all round player in analytical and topology mathematics.

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On Analysis of Extreme Values for Functions of Several Variables | Asian Journal of Pure and Applied Mathematics

Extreme values for functions or systems of functions in this paper x-rays either maxima or minima and to do this, we determine either a maxima or minima for any given function such that derivatives of such a function must be evaluated and tested under given conditions. To achieve these results were put into use as guide. Such results include the Lagrange’s methods and the sign of a quadratic expression of n-variables. The use of this analysis was extended to finding maxima/minima for systems of equations.

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SEROLOGICAL AND MOLECULAR DIAGNOSIS OF Toxoplasma gondii | BIONATURE

This study aimed to determine the immune status of pregnant women at the Central Hospital of Ain Naâdja (HCA) in Algeria. For this purpose, the identification of anti-Toxoplasma immunoglobulins IgG and IgM by ELFA test was carried out in 393 patients, as well as the comparison of the serological profile for the mother-child, serum-aqueous humor pairs by the Western Blot (WB) assay. Parasite search was done by standard PCR on placenta samples using JW62/JW63 primer. The results obtained from 393 serums collected showed that: 40.96% of the pregnant women having a serological profile in favor of an old Toxoplasmosis, and 59.03% were not immunized (P<0.05). Serological comparison by WB analysis of the pairs revealed that 90.1% of the couples possessing the same serological profile (negative), and 9.09% were positive (congenital toxoplasmosis) (P<0.05). To conclude, The PCR performed on placentas showed a high level of specificity for diagnosis. It allows early diagnosis and should be recommended for identification of congenital infection.

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Chemical Control of Insect Pests by Reduced Doses and Effect on Leaf Components in Alfalfa (Medicago sativa L.) | Asian Journal of Research and Review in Agriculture

Control insect pests in modern agroecosystems are essential for the environment and biodiversity. In this regard, the aim of the study was to determine the effects of Biscaya (thiacloprid 240 g/L), applied alone and with 1/5 and 2/5 reduced doses in a mix with the mineral oil Akarzine on pea aphid, Acyrthosiphon pisum Harr. and alfalfa plant bug, Adelphocoris lineolatus Goeze mortality, plastid pigments and total nitrogen content on alfalfa plants. It was found that mineral oil Akarzine exhibited an insecticidal effect from the first to the seventh day, including after treatment. Akarzine, combined with 1/5 and 2/5 reduced doses of Biscaya, helped to prolong the toxic action of the insecticide and provided a significantly lower density of pea aphid and alfalfa plant bug. Factor days after treatment had a dominant influence and a significant effect on the efficacy - 66.5%. The total pigment content in leaves was statistically reduced after the treatments except for combined Biscaya in the 2/5 reduced dose and Akarzine. The combination retained the green and yellow pigments, did not reduce the photosynthesis efficiency of the plant. The use of Akarzine with Biscaya in 1/5 reduced dose led to the highest nitrogen fixation in alfalfa. The mixture of Acarzine and Biscaya in 1/5 reduced dose was marked by a high protective effect against insect pests, good physiological state of the plants, improved photosynthesis and high nitrogen content

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On the Review of Riemann’s Line and Double (Surface) Integrals | Asian Research Journal of Current Science

In this review, we started by considering a normed space , its dual and bi-dual spaces. We define functionals on , as those functionals that are bounded linear functionals and then establish a corresponding unique bounded linear functional that defines a canonical mapping of  into  such that is linear, injective and preserves norm. By this, isomorphism is established so that reflexive maps are realized. In the cause of this work, we invoked the idea of compact topological space and operators mapped on them. We also discussed separable spaces as it relates to this topic. The work was rounded up in section three by discussing the Tychonoff’s theorem as it relates to the weak topology in conjugate spaces, adjoint operators and conjugate spaces of  and .

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On a Review of the Sobolev Space | Journal of Pure and Applied Mathematics

Sobolev, an aspect of Functional Analysis has since the middle of nineteenth century been very useful in many areas of pure mathematics such as Ordinary Differential Equation, Numerical Analysis etc. and now developed into what is known as Sobolev Space. Due to its growing relevance in analytical mathematics, this review paper becomes important in that it displays exciting theoretic definitions and results in the Sobolev Space with impressive details on the Real Index, integration by part, special inequalities and the Embedding Theorem, while towards the end of the work was conclusion in the form of a mathematical remark.

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