We extend a classical construction on symmetric functions, the superization process, to several combinatorial Hopf algebras, and obtain analogs of the hook-content formula for the (q, t)-specializations of various bases. Exploiting the dendriform structures yields in particular (q, t)-analogs of the Björner-Wachs q-hook-length formulas for binary trees, and similar formulas for plane trees.

•At high hCG levels in molar pregnancies, a "hook effect" can cause an artificially negative value.•Delay in diagnosis of a molar pregnancy due to the "hook effect" can lead to severe complications.•Suspicion of a molar pregnancy should be communicated so a diluted sample is used to quantify hCG.

We present a bijective proof of the hook length formula for rooted trees based on the ideas of the bijective proof of the hook length formula for standard tableaux by Novelli, Pak and Stoyanovskii [10]. In section 4 we present another bijection for the formula. MR Subject Classification: 05A05,05A15

uterine leiomyomas/fibroids are the most common pelvic tumors of the female genital tract. the initiators remaining unknown, estrogens and progesterone are considered as promoters of fibroid growth. fibroids are monoclonal tumors showing 40-50% karyo-typically detectable chromosomal abnormalities. cytogenetic aberrations involving chromosomes 6, 7, 12 and 14 constitute the major chromosome abno...

— We find two new hook length formulas for binary trees. The particularity of our formulas is that the hook length h v appears as an exponent. Consider the set B (n) of all binary trees with n vertices. It is well-known that the cardinality of B (n) is equal to the Catalan number (see, e.g., [9, p.220]): (1) T ∈B(n) 1 = 1 n + 1 2n n. For each vertex v of a binary tree T ∈ B (n) the hook length ...

BACKGROUND The purposes of the present study were morphometric characterization of rostellar hooks of Taenia multiceps and to investigate the association of hook length variation and the variability within two mitochondrial genes of sheep isolates of the parasite. METHODS Up to 4500 sheep brains were examined for the presence of C. cerebralis. Biometric characters based on the larval rostella...

Tripterygium wilfordii Hook. f. is a traditional Chinese herb (Murphy, 2006; Qiu et al., 2003). The extract of Tripterygium wilfordii Hook. f. has been widely applied to the treatment of immune-related diseases, such as rheumatoid arthritis (RA), nephritis, and systemic lupus erythematosus (SLE) (Chang et al., 1999; Wang et al., 2000). Extracts of Tripterygium wilfordii Hook. f. have been shown...

Quantitative data on the mechanical performance of upper-limb prostheses are very important in prostheses development and selection. The primary goal of this study was to objectively evaluate the mechanical performance of adult-size voluntary opening (VO) prosthetic terminal devices and select the best tested device. A second goal was to see whether VO devices have improved in the last two deca...

Motility in the photosynthetic bacterium Rhodobacter sphaeroides is achieved by the unidirectional rotation of a single subpolar flagellum. In this study, transposon mutagenesis was used to obtain nonmotile flagellar mutants from this bacterium. We report here the isolation and characterization of a mutant that shows a polyhook phenotype. Morphological characterization of the mutant was done by...

Purified and crude flagellar isolates from cells of Bacillus pumilus NRS 236 were treated with acid, alcohol, acid-alcohol, or heat, and were examined electron microscopically in negatively stained and shadow-cast preparations. Under certain conditions, each of these agents causes the flagella to break between the proximal hooks and the spiral filaments. In such preparations, filaments are seen...