Let Rn be the set of all permutations of length n which avoid 132. In this paper we study the statistics last descent (“ldes”), first descent (“fdes”), last rise (“lris”), and first rise (“fris”) on the set Rn. In particular, we prove that the bistatistic (“fris”,“lris”) on the set of all permutations Rn\{n . . . 21} and the bistatistic (“n− ldes”,“n− fdes”) on the set of all permutations of Rn...

In this note we give a generalization of a result of Aronszajn and Smith [l] concerning sections of exceptional sets for the spaces of Bessel potentials on Rn of L2 functions and restrictions of functions in these spaces. For the sake of completeness we recall briefly the relevant definitions and theorems. We refer for details to [2]. Throughout this paper we will be concerned with functions de...

Let 0 < q < ∞ and Lqloc(R n) = {f q is locally integrable on Rn}. Suppose f ∈ Lloc(R), B = B(x0, r) = {x ∈ Rn : |x − x0| < r} denotes a ball of Rn centered at x0 and having radius r, write fB = |B|−1 ∫ B f(x)dx and f #(x) = supx∈B |B|−1 ∫ B |f(x) − fB|dx < ∞. f is said to belong to BMO(R n), if f# ∈ L∞(Rn) and define ||f ||BMO = ||f||L∞ . Let T be the Calderón-Zygmund singular integral operator...

In this study, the effects of the size and Chinese traditional processing (including elutriation, water cleaning, acid cleaning, alkali cleaning) on realgar nanoparticles (RN)-induced antitumor activity in human osteosarcoma cell lines (MG-63) and hepatoma carcinoma cell lines (HepG-2) were investigated. The human normal liver cell line (L-02) was used as control. RN was prepared by high-energy...

PURPOSE The study was to compare the oncologic and functional outcomes of partial nephrectomy (PN) and radical nephrectomy (RN) for pathologically proven T1b renal cell carcinoma using pair-matched groups. MATERIALS AND METHODS We reviewed our prospectively maintained database for RN and PN in T1b renal tumors surgically treated between 1999 and 2011 at five institutions in Korea. Of 611 pati...

Let hp , 1 1, where p ∈ Rn with ‖ p‖ = o ( ap/p ) . © 2006 Elsevier Inc. All rights reserved.

where q ∈ C((, ),R), e = (e, . . . , eN )T ∈ C((, ),RN ), N ≥ , and the nonlinear term f (t,u) ∈ C((, )×RN \ {},RN ). We are mainly motivated by the recent excellent works [–], in which singular periodic systems were extensively studied. Let R+ denote the set of vectors of RN with positive components. For a fixed vector v ∈R+ , we say that system (.) presents a singularity at the o...

Fixing a complete Riemannian metric g on Rn, we show that a local diffeomorphism f : Rn → Rn is bijective if the height function f · v (standard inner product) satisfies the Palais-Smale condition relative to g for each for each nonzero v ∈ Rn. Our method substantially improves a global inverse function theorem of Hadamard. In the context of polynomial maps, we obtain new criteria for invertibi...

We investigate the global boundedness of Fourier integral operators with amplitudes in general Hörmander classes Sρ,δm(Rn), ρ,δ∈[0,1] and non-degenerate phase functions arbitrary rank κ∈{0,1,…,n−1} on Besov-Lipschitz Bp,qs(Rn) Triebel-Lizorkin Fp,qs(Rn) order s 0<p≤∞, 0<q≤∞. The results that are obtained all up to end-point sharp also applied regularity Klein-Gordon-type oscillatory integrals a...

UNLABELLED The red nucleus (RN) is a pair of small gray matter structures located in the midbrain and involved in muscle movement and cognitive functions. This retrospective study aimed to investigate the metabolism of human RN and its correlation to other brain regions. METHODS We developed a high-resolution semiconductor PET system to image small brain structures. Twenty patients without ne...