We notice that two combinatorial interpretations of the well-known Catalan numbers Cn = (2n)!/n!(n+1)! naturally give rise to a recursion for Cn. This recursion is ideal for the study of the congruences of Cn modulo 2 r, which attracted a lot of interest recently. We present short proofs of some known results, and improve Liu and Yeh’s recent classification of Cn modulo 2 r. The equivalence Cn ...

A rapid and sensitive electrospray ionization tandem mass spectrometric (ESI-MS-MS) procedure was developed for the determination of cyanide (CN(-)). CN(-) in biological fluids was reacted with NaAuCl(4) to produce dicyanogold, Au(CN)(2)(-), which was extracted with methyl isobutyl ketone (MIBK). One microliter of the extract was injected directly into an ESI-MS-MS instrument. Quantification of...

In the first part of this research, extensive speciesdependent cyanide recoveries studies were performed using the approved standard methods available for determination of free cyanide. The data obtained show that serious problems are associated with both the CATC (cyanide amenable to chlorination) and WAD (weak and dissociable cyanide) methods. In the second part, a novel flow injection gas-di...

We give some inequalities of capacity in Gaussian channel with or without feedback. The nonfeedback capacity Cn,Z(P ) and the feedback capacity Cn,FB,Z(P ) are both concave functions of P . Though it is shown that Cn,Z(P ) is a convex function of Z in some sense, Cn,FB,Z(P ) is a convex like function of Z.

For each fixed pair α, c > 0 let INDEPENDENT SET (m ≤ cn) and INDEPENDENT SET (m ≥ n2 ) − cn) be the problem INDEPENDENT SET restricted to graphs on n vertices with m ≤ cn or m ≥ n2 )− cn edges, respectively. Analogously, HAMILTONIAN CIRCUIT (m ≤ n + cn) and HAMILTONIAN PATH (m ≤ n + cn) are the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with m ≤ n + cn edges. For ea...

A study has been made of the influence of two pools of caseinophosphopeptides (CPPs) obtained from α(s)- and β-casein (CN) fractions, and of three specific CPPs (β-CN(1-25)4P, α(s1)-CN(64-74)4P and α(s2)-CN(1-19)4P), on iron bioavailability (ferritin synthesis) and zinc bioavailability (retention, transport and uptake of zinc) in Caco-2 cells. α-CPP and β-CPP pools did not improve ferritin synt...

Currently, no reliable noninvasive methods exist for monitoring the severity of in vivo cyanide (CN) toxicity, treatment, and resulting physiological changes. We developed a broadband diffuse optical spectroscopy (DOS) system to measure bulk tissue absorption and scattering. DOS was used to optically monitor CN toxicity and treatment with sodium nitrite (NaNO2). To perform experiments, the DOS ...

A two-sided sequence (cn)n∈Z with values in a complex unital Banach algebra is a cosine sequence if it satisfies cn+m + cn−m = 2cncm for any n,m ∈ Z with c0 equal to the unity of the algebra. A cosine sequence (cn)n∈Z is bounded if supn∈Z ‖cn‖ < ∞. A (bounded) group decomposition for a cosine sequence c = (cn)n∈Z is a representation of c as cn = (b n +b−n)/2 for every n ∈ Z, where b is an inver...