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Abstract: The sub-elliptic obstacle problem arises in various branches of the applied sciences, e.g., in mechanical engineering and robotics, mathematical finance, image reconstruction and neurophysiology. In the recent paper [Donatella Danielli, Nicola Garofalo, Sandro Salsa, Variational inequalities with lack of ellipticity. I. Optimal interior regularity and non-degeneracy of the free boundary, Indiana Univ. Math. J. 52 (2) (2003) 361–398; MR1976081 (2004c:35424)] it was proved that weak solutions to the sub-elliptic obstacle problem in a Carnot group belong to the Folland–Stein (optimal) Lipschitz class (the analogue of the well-known interior local regularity for the classical obstacle problem). However, the regularity of the free boundary remained a challenging open problem. In this paper we prove that, in Carnot groups of step , the free boundary is (Euclidean) near points satisfying a certain thickness condition. This constitutes the sub-elliptic counterpart of a celebrated result due to Caffarelli [Luis A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math. 139 (3–4) (1977) 155–184; MR0454350 (56 #12601)]. [Copyright &y& Elsevier]

Abstract: The hybrid power flow analysis (PFA) is an analytic method proposed for the effective prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the PFA algorithm and statistical energy analysis (SEA) coupling concepts. This paper presents the hybrid boundary condition on 3-D case for hybrid PFA in addition to 1-D and 2-D cases which are derived in the other companion paper, and formulates the hybrid power flow finite-element method (PFFEM) including coupling loss factor (CLF) of SEA to extend the application area of hybrid PFA to built-up structures. To verify the derived boundary condition and hybrid PFFEM, numerical analyses were successfully performed for various analytic models and reverberance factors. [Copyright &y& Elsevier]

This paper is concerned with Wold-type decomposition for regular operators whose orbits under any vector satisfy some growth conditions. Several results on left invertible operators close to isometries are extended. We also give numerous results on the Moore–Penrose inverse for regular operators in this particular setting. [ABSTRACT FROM AUTHOR]

In this paper, we give a formal solution of some nonlinear evolution equations. By the formal solution, we can obtain the blow-up solution of the heat equations, even in the supercritical case. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we give new characterization of the classical Morrey space. Complementary global Morrey-type spaces are introduced. It is proved that for particular values of parameters these spaces give new pre-dual space of the classical Morrey space. We also show that our new pre-dual space of the Morrey space coincides with known pre-dual spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we explore constacyclic self-dual codes over . We first characterize constacyclic self-dual codes over of any length. Then we determine the structure of η-constacyclic self-dual codes over , where or . This structure is used to find some constacyclic self-dual codes over . [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the uniqueness of meromorphic functions in the unit disc and consider the relation between the Borel points and shared-values of meromorphic functions in an angular domain. [Copyright &y& Elsevier]

Abstract: In this paper, we focus on the computation of stress resultants of a floating elastic plate using the Mindlin plate theory. The proposed method makes use of the linear wave theory and shallow-draft assumption. However, the usual Kirchhoff theory is replaced by the Mindlin theory for the plate. For a single frequency, the coupled water-plate problem is solved using a higher-order-coupled finite element–boundary element method. The solutions for the stress-resultants computed using the proposed method are more satisfactory than these based on the Kirchhoff plate theory. [Copyright &y& Elsevier]

Abstract: In the present paper, motivated by Stević''s iteration method, we show the stability result of the following unified iterative scheme for a ϕ-strongly pseudocontractive selfmapping T. This stability result implies the stability of Stević''s iteration scheme naturally. [Copyright &y& Elsevier]

Abstract: In this paper, we define concepts of crowns and quasi-crowns, valid in an arbitrary schurian algebra, and which generalise the corresponding concepts in an incidence algebra. We show first that a triangular schurian algebra is strongly simply connected if and only if it is simply connected and contains no quasi-crown. We then prove that the absence of quasi-crowns in a triangular schurian algebra implies the existence of a multiplicative basis. [Copyright &y& Elsevier]

Abstract: In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds. [Copyright &y& Elsevier]

Abstract: Let be a Galois extension of number fields and let be an abelian variety defined over . In this paper we establish the relation between the irreducible characters of the Galois group and the simple factors of the restriction of scalars of from to . Then we derive some equivalences of Birch and Swinnerton–Dyer conjectures. [Copyright &y& Elsevier]

A mixed partition of PG(2n-1,q2) is a partition of the points of PG(2n-1,q2) into (n-1)-spaces and Baer subspaces of dimension 2n-1. In (Bruck and Bose, J. Algebra 1 (1964) 85) it is shown that such a mixed partition of PG(2n-1,q2) can be used to construct a (2n-1)-spread of PG(4n-1,q) and hence a translation plane of order q2n. In this paper, we provide several new examples of such mixed partitions in the case when n=2. [Copyright &y& Elsevier]

In this paper, we study a 2D dissipative Klein–Gordon equation with periodic boundary condition. The existence and uniqueness of a time-periodic solution is proved by the Galerkin method and Leray–Schauder fixed point theorem. [Copyright &y& Elsevier]