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ObjectiveTo analyze the characteristics of the intestinal microbiota of polycystic ovarian syndrome with insulin resistance (PCOS-IR) and explore the possible mechanism of modified Banxia Xiexin Decoction in the treatment of PCOS-IR.MethodsA total of 17 specific pathogen-free (SPF) female Sprague–Dawley (SD) rats, aged 21 days, were selected and randomly divided into the control group (group Z, n = 6), model group (group M, n = 6), and treatment group (group A, n = 5). Letrozole combined with a high-fat diet was used to induce the PCOS-IR model. Rats in group A were treated with modified Banxia Xiexin Decoction for 2 weeks after the end of modeling; then the characteristics of reproductive, metabolic, inflammatory, and intestinal microbiota were compared among three groups.ResultsThe PCOS-IR model had an imbalance of intestinal microbiota, and the enriched microbiota was mainly class Coriobacteria, order Clostridiales, and genus Clostridium_sensu_stricto_1. Modified Banxia Xiexin Decoction can regulate the disorder of intestinal microbiota diversity, significantly increase the abundance of phyla Verrucomicrobiota Proteobacteria and genera Akkermansia and Blautia, and decrease the abundance of genus Clostridium_sensu_stricto_1.ConclusionGenus Clostridium_sensu_stricto_1 might be the pivotal pathogenic bacteria of PCOS-IR. Modified Banxia Xiexin Decoction may ameliorate PCOS-IR by regulating intestinal microbiota imbalance and improving metabolic disorders.

In this paper, we construct the real representation matrix of canonical hyperbolic quaternion matrices and give some properties in detail. Then, by means of the real representation, we study linear equations, the inverse and the generalized inverse of the canonical hyperbolic quaternion matrix and get some interesting results.

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