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Optimal power flow (OPF) is a fundamental tool for analyzing the characteristics of bipolar DC distribution network (DCDN). However, existing OPF models face challenges in reflecting the power distribution and exchange of bipolar DCDN directly since its decision variables are voltage and current. This paper addresses this issue by establishing a convex OPF model that can be used for the planning and operation of bipolar DCDN. First, the power flow characteristics of bipolar DCDN are revealed through power injection-based equations, upon which the original OPF model is established. Next, the original OPF model undergoes a transformation into a convex OPF model based on second-order cone programming (SOCP) through variable substitution, secondorder cone relaxation, McCormick relaxation, and first-order Taylor expansion, respectively. Finally, the sequence bound tightening algorithm (STBA) is employed to tighten the boundaries of McCormick envelopes in each iteration to ensure the exactness of the convex OPF model. The effectiveness of this novel OPF model for bipolar DCDN is verified through two case studies, i.e., capacity configuration of distributed generation (DG) and operation optimization of bipolar DCDN., Comment: 10 pages, 13 figures, under review in IEEE transactions on power systems

We prove that the octonionic polynomials V l 1 ⊗, l k ⊗k are independent of the associative orders ⊗ k . This improves the octonionic Taylor type theorem.

The quaternionic Cauchy-Szeg�� kernel of the Hardy space $\mathcal{H}^2(\mathcal{U}_n)$ on the quaternionic Siegel half space $\mathcal{U}_n$ is derived and the Hardy spaces on the octonionic Siegel half space is investigated., 17 pages, has been submitted to journal for publication

Objectives To investigate if calcineurin pathway is involved in cardiac fibroblasts proliferation, transdifferentiation and apoptosis induced by mechanical stretch. Methods Primary cardiac fibroblasts from 1- to 2-day-old Sprague-Dawley rats were isolated by trypsinization and purified by differential anchoring velocity technology. The cultured cells of passage 2-3 were divided into: control group, mechanical stretch group (MS group), calcineurin siRNA + mechanical stretch group (CaN-siRNA + MS group), FK506 + mechanical stretch group (FK506 + MS group), calcineurin overexpression + mechanical stretch group (CaN-overex + MS group). Calcineurin and downstream NFAT3 expressions were determined by western blot. Cardiac fibroblasts proliferation was determined by cell counting kit-8 and detection of proliferating cell nuclear antigen (PCNA), cell transdifferentiation was measured by alpha-smooth muscle actin (alpha-SMA) through western blot and apoptosis by Bax/Bcl-2. Results Mechanical stretch promoted cardiac fibroblasts proliferation, as well as upregulation of alpha-SMA and increased Bax/Bcl-2 ratio, overexpression of calcineurin could promote more cardiac fibroblasts adverse remodelling similar to those induced by mechanical stretch. Pretreatment with calcineurin-siRNA lentivirus significantly attenuated cardiac fibroblasts proliferation, transdifferentiation and apoptosis when later stimulated by mechanical stretch, whereas pretreatment with FK506, a calcineurin inhibitor, only moderately inhibited cardiac fibroblasts proliferation and apoptosis with no obvious effect on cell transdifferentiation. Conclusions This study demonstrates that mechanical stretch promoted cardiac fibroblasts proliferation, transdifferentiation and apoptosis via activating calcineurin/NFAT3, thus abolishing the calcineurin pathway might be beneficial for reversing myocardial fibrosis.