In this paper, we first investigate the thermodynamic features of the black hole with a coulomb-like field.Moreover, we obtain the geometric description of the black hole thermodynamics. We find that for the black hole with a coulomb-like field the Weinhold geometry is flat, whereas its Ruppeiner geometry is curved. For the heat capacity and curvature calculation shows the Ruppeiner geometry has a transition point.
Let E be a nonempty closed uniformly convex and 2-uniformly smooth Banach space with dual E * and A : E * → E be Lipschitz continuous monotone mapping with A −1 (0) = ∅. A new semi-implicit midpoint rule (SIMR) with the general contraction for monotone mappings in Banach spaces is established and proved to converge strongly to x * ∈ E, where J x * ∈ A −1 (0). Moreover, applications to convex minimization problems, solution of Hammerstein integral equations, and semi-fixed point of a cluster of semi-pseudo mappings are included.
Adopting the anomaly cancellation method, initiated by Robinson and Wilczek recently, this paper discusses Hawking radiation from the dilaton—(anti) de Sitter black hole. To save the underlying gauge and general covariance, it introduces covariant fluxes of gauge and energy-momentum tensor to cancel the gauge and gravitational anomalies. The result shows that the introduced compensating fluxes are equivalent to those of a 2-dimensional blackbody radiation at Hawking temperature with appropriate chemical potential.
In this paper, we introduce a proximal point iterative algorithm with general errors for monotone mappings in Banach spaces. We prove that the proposed algorithm converges strongly to a proximal point for monotone mappings. Our theorems in this paper improve and unify most of the results that have been proposed for this important class of nonlinear mappings. MSC: 47H09; 47H10; 47L25
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