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Abstract: The classes of -Wright-convex functions and -Jensen-convex functions are compared with each other. It is shown that for any odd natural number the first one is the proper subclass of the second one. To reach this aim new tools connected with measure theory are developed. [Copyright &y& Elsevier]

Abstract: We consider a class of planar self-affine tiles T that are generated by the lower triangular expanding matrices and the product-form digit sets. We give necessary and sufficient conditions for T to be connected and disk-like. Also for the disconnect case, we give a condition that enumerates the number of connected components of T. [Copyright &y& Elsevier]

Abstract: Assume that is a measure space and , . We prove that is either or a σ-porous subset of . This dichotomy depends on properties of μ and the sign of the number . [Copyright &y& Elsevier]

Abstract: The Feichtinger conjecture, if true, would have as a corollary that for each set and , there is a partition of such that for each , is a Riesz sequence. In this paper, sufficient conditions on sets and are given so that can be uniformly partitioned into Riesz sequences. [Copyright &y& Elsevier]