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In this paper we study the existence of Lelong numbers of m -subharmonic currents of bidimension ( p , p ) on an open subset of C n , when m + p ≥ n . In the special case of m -subharmonic function φ , we give a relationship between the Lelong numbers of d d c φ and the mean values of φ on spheres and balls. As an application we study the integrability exponent of φ . We express the integrability exponent of φ in terms of volume of sub-level sets of φ and we give a link between this exponent and its Lelong number. [ABSTRACT FROM AUTHOR]

Let S be a pure bounded rationally multicyclic subnormal operator on a separable complex Hilbert space H and let M z be the minimal normal extension on a separable complex Hilbert space K containing H . Let b p e ( S ) be the set of bounded point evaluations and let a b p e ( S ) be the set of analytic bounded point evaluations. We show a b p e ( S ) = b p e ( S ) ∩ I n t ( σ ( S ) ) . The result affirmatively answers a question asked by J. B. Conway concerning the equality of the interior of b p e ( S ) and a b p e ( S ) for a rationally multicyclic subnormal operator S . As a result, if λ 0 ∈ I n t ( σ ( S ) ) and d i m ( k e r ( S − λ 0 ) ⁎ ) = N , where N is the minimal number of cyclic vectors for S , then the range of S − λ 0 is closed, hence, λ 0 ∈ σ ( S ) ∖ σ e ( S ) . [ABSTRACT FROM AUTHOR]

Let A t , k ( n ) denote the number of partition k -tuples of n where each partition is t -core. In this paper, we establish formulas of A t , k ( n ) for some values of t and k by employing the method of modular forms, which extends Wang's result for t = 3 and k = 2 , 3 . [ABSTRACT FROM AUTHOR]

We consider a variation of the Lévy–Steinitz theorem where one rearranges only a small number of terms. In particular, we study the set of obtainable rearrangements of a multidimensional series by a permutation σ : ω → ω such that { n ∈ ω : σ ( n ) ≠ n } ∈ I for some proper ideal I ⊂ P ( ω ) . [ABSTRACT FROM AUTHOR]

For any real number β>1, we denote by Tβ the β-transformation on the unit interval [0,1] given by Tβ(x)=βx-βx, where denotes the integer part of We consider the size of the set of β>1 where the orbit of 1 under Tβ ultimately has a positive distance from a given point in [0,1]. For any x0∈[0,1] and any (β0,β1)(1,∞), we obtain the set of β∈(β0,β1) such that x0 is not an accumulation point of the orbit of 1 under Tβ with full Hausdorff dimension. Specifically,dimH{β∈(β0,β1):liminfn→∞|Tβn1-x0|>0}=1. This is a generalization of the result of Schmeling for the case where x0=0 and (β0,β1)=(1,∞). [ABSTRACT FROM AUTHOR]

We establish a pre-order principle. From the principle, we obtain a very general set-valued Ekeland variational principle, where the objective function is a set-valued map taking values in a quasi-ordered linear space and the perturbation contains a family of set-valued maps satisfying certain property. From this general set-valued Ekeland variational principle, we deduce a number of particular versions of set-valued Ekeland variational principle, which include many known Ekeland variational principles, their improvements and some new results. [ABSTRACT FROM AUTHOR]

We investigate the existence and number of limit cycles in a class of general planar piecewise linear systems constituted by two linear subsystems with node–node dynamics. Using the Liénard-like canonical form with seven parameters, some sufficient and necessary conditions for the existence of limit cycles are given by studying the fixed points of proper Poincaré maps. In particular, we prove the existence of at least two nested limit cycles and describe some parameter regions where two limit cycles exist. The main results are applied to the PWL Morris–Lecar neural model to determine the existence and stability of the limit cycles. [ABSTRACT FROM AUTHOR]

Abstract: We show that the Riemann zeta function has only countably many self-intersections on the critical line, i.e., for all but countably many the equation has at most one solution . More generally, we prove that if is analytic in a complex neighborhood of and locally injective on , then either the set is countable, or the image is a loop in . [Copyright &y& Elsevier]

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 the solutions to the prescribed scalar curvature equation on a four-dimensional Riemannian manifold M. We prove an upper bound for the supremum of all the solutions on every compact subset K of M, provided that all the solutions on M are bounded from below by a positive number. [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]

Abstract: In this paper, some new generalized contractive type conditions for a pair of mappings in metric space are defined. Some common fixed point results for these mappings are presented. [Copyright &y& Elsevier]