In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

Sufficient (almost necessary) conditions are given on the weight functions u(·), v(·) for Φ−1 2 [ ∫ Rn Φ2 ( C2(Msf)(x) ) u(x)dx ] ≤ Φ−1 1 [ C1 ∫ Rn Φ1(|f(x)|)v(x)dx ] to hold when Φ1, Φ2 are φ-functions with subadditive Φ1Φ 2 , and Ms (0 ≤ s < n), is the usual fractional maximal operator. §

We combine methods from convex analysis, based on a function of Simon Fitzpatrick, with a fine recent idea due to Voisei, to prove maximality of the sum of two maximal monotone operators in Banach space under various natural transversality conditions.

BACKGROUND A high level of strength is inherent in elite soccer play, but the relation between maximal strength and sprint and jumping performance has not been studied thoroughly. OBJECTIVE To determine whether maximal strength correlates with sprint and vertical jump height in elite male soccer players. METHODS Seventeen international male soccer players (mean (SD) age 25.8 (2.9) years, he...

Physiology is often considered a challenging course for students. It is up to teachers to structure courses and create learning opportunities that will increase the chance of student success. In an undergraduate exercise physiology course, concept maps are assigned to help students actively process and organize information into manageable and meaningful chunks and to teach them to recognize the...

In this note we improve the known L p-bounds for Bochner-Riesz operators and their maximal operators.

We review recent progress in the gauging of maximal supergravity theories.

Let X be a Tychonoff space and A a subalgebra of C(X) containing C∗(X). Suppose that CK(X) is the set of all functions in C(X) with compact support. Kohls has shown that CK(X) is precisely the intersection of all the free ideals in C(X) or in C∗(X). In this paper we have proved the validity of this result for the algebra A. Gillman and Jerison have proved that for a realcompact space X, CK(X) i...

PURPOSE To analyze the load-, force-, and power-velocity relationships and determine the load that optimizes power output on the pull-up exercise. METHODS Eighty-two resistance-trained men (age 26.8 ± 5.0 y; pull-up 1-repetition maximum [1-RM; normalized per kg of body mass] 1.5 ± 0.34) performed 2 repetitions with 4 incremental loads (range 70-100%1-RM) in the pull-up exercise while mean pro...

We investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal Kähler metric are parallel w.r.t. the Levi-Civita connection. In the general Riemannian case a formal metric with ma...