Eigenvalue hypothesis for multi-strand braids

Computing polynomial form of the colored HOMFLY-PT for non-arborescent knots obtained from three or more strand braids is still an open problem. One of the efficient methods suggested for the three-strand braids relies on the eigenvalue hypothesis which uses the Yang-Baxter equation to express the answer through the eigenvalues of the ${\cal R}$-matrix. In this paper, we generalize the hypothesis to higher number of strands in the braid where commuting relations of non-neighbouring $\mathcal{R}$ matrices are also incorporated. By solving these equations, we determine the explicit form for $\mathcal{R}$-matrices and the inclusive Racah matrices in terms of braiding eigenvalues (for matrices of size up to 6 by 6). For comparison, we briefly discuss the highest weight method for four-strand braids carrying fundamental and symmetric rank two $SU_q(N)$ representation. Specifically, we present all the inclusive Racah matrices for representation $[2]$ and compare with the matrices obtained from eigenvalue hypothesis.Comment: 23 page

Ocular doppler imaging: opening a new window in decoding glaucoma

Background: In the aetiopathogenesis of multifactorial glaucoma autoregulation of ocular blood flow plays an important role as failure of autoregulation may lead to progression of disease. Aim of this study to understand this better this study was designed to investigate the quantum of these abnormalities and their likely role in pathogenesis and prognosis of primary open angle glaucoma(POAG).Methods: This is a case control study design which involved 67 POAG patients and 67 matched controls. The parameters assessed includes peak systolic velocity(PSV), end diastolic velocity(EDV) and resistive index(RI) of ophthalmic artery(OA) and central retinal artery(CRA) of patients having POAG with age and sex matched healthy subjects. The data obtained was statistically analysed using IBM SPSS 21.Results: The study showed decreased PSV of 31.7 cm/s vs 42.7 cm/s(p=0.0001) and EDV11.7 cm/s vs 19.8 cm/s(p=0.002) with increased RI 0.63 vs 0.53(p=0.000) in  OA and PSV of 15.2 cm/s vs 21.4 cm/s(p=0.001) and EDV4.7 cm/s vs 11.7 cm/s(p=0.003) with increased RI 0.69 vs 0.45(p=0.000) in CRA in both eyes in POAG patients as compared to healthy controls.Conclusion: The study has shown the promising application of ocular Doppler in evaluating POAG patients. However, more such studies are needed with larger study sample and on follow up basis for better understanding glaucoma hemodynamics and applicability of ocular Doppler in management of glaucoma

Optimization on Manufacturing Processes at Indian Industries Using TOPSIS

Evaluation and optimization of multi-criteria with multiple alternatives have been essential activities for decision-making process. TOPSIS (Technique for order of preference by similarity to ideal solution), a multi-criteria decision-making (MCDM) technique, has been adopted in the past for research & decision-making and ranking of alternatives by optimizing input parameters to get the maximum overall output from the system. This study aims to explore the context, reasons, and particular advantages of using TOPSIS in the materials science and engineering field for realizing goals of competitive supply chains (SCs). This study has reviewed and analyzed research papers from the approach of systematic review of the literature. This study has presented a conceptual framework to emphasize the antecedents and consequences of using the TOPSIS methodology for output optimization in the materials science and engineering industry that can improve the competitiveness of SCs. This study found that TOPSIS based methodologies have been used in eleven types of industries in India, indicating the prowess of TOPSIS methodology. The results of TOPSIS have compared very well with other MCDM methods that are relatively more difficult and cumbersome. This study will help the engineers, practitioners, academicians, researchers, and SC managers with the application approach of TOPSIS for output optimization in various fields