In this paper we prove a duality between k-noncrossing partitions over [n] = {1, . . . , n} and k-noncrossing braids over [n − 1]. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to tangled-diagrams [6]. We give a combinatorial interpretation of the bijection in terms of the contraction of arcs of tangled-diagrams. Furthermore it induces by re...

Consider two coaxial round circles with the same radius. A mathematical model of a tiny liquid drop trapped between them are constant mean curvature (CMC) surfaces because CMC surface is critical point area for all variations that preserve enclosed volume and satisfy given boundary condition. said to be stable if second variation any such nonnegative. In this paper, we judge stability one perio...

Two forms of a sampling theorem for concentric circles are established for a bandlimited two-dimensional (2-D) function. The location of the samples is prescribed either on equidistant circles or on the roots of the Bessel function J0( ). Both methods give comparable results, however, the number of samples required for their numerical evaluation is significantly less for the root-sampling formu...

Globevnik [G] answered the question in the affirmative for rotation invariant families. Agranovsky and Globevnik [AG] resolved the question for families of circles when f is a rational or real-analytic functions of two real variables. Ehrenpreis [E2] independently found solution for the circles of constant radii with centers on a line and real-analytic functions. In [T] we obtain the affirmativ...

Fig. 1. Regression analysis (regression line – continuous – and 95% prediction interval – dashed lines) to evaluate commutability of IRMM BCR-304 (triangle) and NIST SRM 956c (black circles) between direct potentiometry and colorimetry assays for serum lithium. Gray circles identify native serum samples. Commutability of two JCTLM-listed secondary reference materials for two commercial lithium ...

In this paper, we study the flexibility of embeddings of bouquets of circles on the projective plane and the Klein bottle. The numbers (of equivalence classes) of embeddings of bouquets of circles on these two nonorientable surfaces are obtained in explicit expressions. As their applications, the numbers (of isomorphism classes) of rooted one-vertex maps on these two nonorientable surfaces are ...