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In the present work, a unification of certain functions of mathematical physics is proposed and its properties are studied. The proposed function unifies Lommel function, Struve function, the Bessel-Maitland function and its generalization, Dotsenko function, generalized Mittag-Leffler function etc. The properties include absolute and uniform convergence, differential recurrence relation, integral representations in the form of Euler-Beta transform, Mellin-Barnes transform, Laplace transform and Whittaker transform. The special cases namely the generalized hypergeometric function, generalized Laguerre polynomial, Fox H-function etc. are also obtained.
Objective: To evaluate the role of chromohysteroscopy in improving diagnostic accuracy of endometrial biopsy in cases of AUB. Design: Cross sectional interventional study. Materials and Methods: This study was conducted on 60 women with AUB in Dept. of Obst. & Gyne at King George Medical University, Lucknow over a period of one year. All cases underwent diagnostic hysteroscopy followed by chromohysteroscopy using 2% methylene blue dye. Hysteroscopic guided biopsy was taken from stained and unstained areas followed by an endometrial aspiration biopsy from whole uterine cavity. The histopathology results of three samples were compared and analyzed in relation with staining pattern and type of AUB. Data analysis was done on SPSS version 15 of windows 2007. Results: Out of 60 cases, 11cases were found to have non hormonal pathology after chromohysterosopic biopsy. Eight (72.72%) cases were diagnosed by stained endometrial tissue, one (9.09%) by unstained tissue and three (27.27%) by endometrial aspiration. The diagnostic ability of stained tissue biopsy was significantly higher (p = 0.006) than unstained biopsy and endometrial aspiration. Conclusion: Chromohysteroscopy is a simple and effective technique for diagnosing endometrial pathology in cases of AUB.
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of ？as it is required to prove the desired result.