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Polylogarithms and Subordination of Some Cubic Polynomials
Manju Yadav,Sushma Gupta,Sukhjit Singh 경북대학교 자연과학대학 수학과 2024 Kyungpook mathematical journal Vol.64 No.1
Let V3(z, f) and σ^(1)3(z, f) be the cubic polynomials representing, respectively, the 3rd de la Vall´ee Poussin mean and the 3rd Ces`aro mean of order 1 of a power series f(z). If K denotes the usual class of convex univalent functions in the open unit disk centered at the origin, we show that, in general, V3(z, f) /< σ^(1)3(z, f), for all f ∈ K. Making use of polylogarithms, we identify a transformation, Λ : K → K , such that V3(z, Λ(f))< σ^(1)3(z, Λ(f)) for all f ∈ K . Here ‘<’ stands for subordination between two analytic functions.
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Sarita Magu,Deepak Singh,Rohtas Kanwar Yadav,Manju Bala 대한척추외과학회 2015 Asian Spine Journal Vol.9 No.5
Study Design: Prospective study. Purpose: To compare magnetic resonance imaging (MRI) findings with clinical profile and neurological status of the patient and to correlate the MRI findings with neurological recovery of the patients and predict the outcome. Overview of Literature: Previous studies have reported poor neurological recovery in patients with cord hemorrhage, as compared to cord edema in spine injury patients. High canal compromise, cord compression along with higher extent of cord injury also carries poor prognostic value. Methods: Neurological status of patients was assessed at the time of admission and discharge in as accordance with the American Spine Injury Association (ASIA) impairment scale. Mean stay in hospital was 14.11±5.74 days. Neurological status at admission and neurological recovery at discharge was compared with various qualitative cord findings and quantitative parameters on MRI. In 27 patients, long-term follow-up was done at mean time of 285.9±43.94 days comparing same parameters. Results: Cord edema and normal cord was associated with favorable neurological outcome. Cord contusion showed lesser neurological recovery, as compared to cord edema. Cord hemorrhage was associated with worst neurological status at admission and poor neurological recovery. Mean canal compromise (MCC), mean spinal cord compression (MSCC) and lesion length values were higher in patients presenting with ASIA A impairment scale injury and showed decreasing trends towards ASIA E impairment scale injury. Patients showing neurological recovery had lower mean MCC, MSCC, and lesion length, as compared to patients showing no neurological recovery (p <0.05). Conclusions: Cord hemorrhage, higher MCC, MSCC, and lesion length values have poor prognostic value in spine injury patients.
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