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Weerakoon and Fernando [A variant of Newton's method with accelerated third-order convergence, Appl. Math. Lett. 13 (2000) 87–93] were resorted on a trapezoidal quadrature rule to derive an arithmetic mean Newton method with third-order convergence of the iterative scheme to solve nonlinear equations. Different quadrature methods have been developed, which form a special class of third-order iterative schemes requiring three evaluations of functions on [ f (x n) , f ′ (x n) , f ′ (y n) ] per iteration, where y n is generated from the first Newton step. As an extension of these methods, we derive a new family of iterative schemes by using a new weight function H to generalize the quadrature methods, of which (x n + 1 − x n) f ′ (x n) / H signifies an approximate area under the curve f ′ (x) between x n and x n + 1 . Then, a generalization of the midpoint Newton method is obtained by using another weight function, which is based on three evaluations of functions on [ f (x n) , f ′ (x n) , f ′ ((x n + y n) / 2) ] per iteration. The sufficient conditions of these two weight functions are derived, which guarantee that the convergence order of the proposed iterative schemes is three. [ABSTRACT FROM AUTHOR]

We report the synthesis of two carbazole-thiophene-based conjugated microporous polymers (Cz-3Th and Cz-4Th CMPs) with different degrees of planarity for photocatalytic hydrogen evolution from water. Depending upon the building linker's planarity, we found that the porous structure, hydrogen-evolution rate, and photocatalytic stability of the resultant CMPs varied. [ABSTRACT FROM AUTHOR]

Antiplatelet therapy is the first-line management for noncardioembolic transient ischemic attack (TIA) and acute ischemic stroke (IS). Herein, we review the safety and efficacy of antiplatelet therapies in patients with IS and TIA, primarily focusing on the acute stage. We discuss current antiplatelet monotherapy and the factors influencing efficacy and continuation rate according to clinical trial data. Aspirin remains the most commonly used first-line antiplatelet agent for preventing noncardioembolic stroke recurrence, and clopidogrel, cilostazol, and ticagrelor are feasible alternatives. Various short-term dual antiplatelet therapies (including clopidogrel-aspirin and ticagrelor-aspirin combination therapy) for minor stroke and high-risk TIA are also reviewed. For selected patients with specific stroke etiologies, short-term dual antiplatelet therapy with aspirin combined with clopidogrel or ticagrelor can significantly reduce the risk of stroke. However, insufficient evidence supports the benefits of triple antiplatelet therapy for recurrent noncardioembolic stroke prevention, and this treatment substantially increases the rate of bleeding complications. Keyword: antiplatelet therapy, acute ischemic stroke, secondary prevention, transient ischemic attack.