The hook-length formula is a well known result expressing the number of standard tableaux of shape λ in terms of the lengths of the hooks in the diagram of λ. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing more than the fundamental theorem of algebra. This proof was suggested by a q, t-analog of the hook formula given ...

A probabilistic algorithm, called the q-hook walk, is defined. For a given Young diagram, it produces a new one by adding a random box with probabilities, depending on a positive parameter q. The corresponding Markov chain in the space of infinite Young tableaux is closely related to the knot invariant of Jones, constructed via traces of Hecke algebras. For q = 1, the algorithm is essentially t...

A method for preparing bacterial flagellar hook structures is described. The method involves isolating intact flagella from a mutant which makes thermally labile flagellar filaments and heat-treating them to disaggregate the filament preferentially. The resulting hook preparation can be separated and purified by velocity and isopycnic centrifugation. The purified hooks sediment at a relative S ...

This paper summarises key findings from several experiments to determine the most effective branch line weighting options for pelagic longline fisheries. Initial (0-2 m deep) and overall sink rates of a range of line weighting options – each comprising a different combination of weight and leader length (distance between hook and weight) – were compared and several options identified that offer...

We treated 16 patients with acute and chronic acromioclavicular dislocations type III and V by open reduction and fixation using a Hook plate (AO). Plate removal was performed 7 months later on average (range 3 1/2 - 13). A clinical and radiological follow-up was performed after a mean time interval of 29 months (range, 11-40) from the date of plate removal. The L'Insalata scoring system was us...

11 1951, Paul S. Dwyer pnblishcd I,inenr Comptntions, perhaps the first hook dcvoted cntirely to numerical linear algebra.' Digital conipiiting was in its infancy, and Dwyer focused on computation with tncchanical calculators. Nonctheless, the hook was state of the art. Figurc 1 reproduces a pagc of thc book dealing with Gaussian elimination. In 1954, Alston S. Householder published Prim+ p b n...

Effects of the kampo medicine yokukansan on gene expression of the cystine/glutamate antiporter system Xc-, which protects against glutamate-induced cytotoxicity, were examined in Pheochromocytoma cells (PC12 cells). Yokukansan inhibited glutamate-induced PC12 cell death. Similar cytoprotective effects were found in Uncaria hook. Experiments to clarify the active compounds revealed that geissos...

This study describes a new technique called the "fish hook" technique for the treatment of bony mallet finger. This technique catches the dorsal fragment with a bent K-wire shaped like a fish hook. Transarticular fixation is performed with another K-wire. This technique does not directly penetrate the bone fragment to prevent fragment comminution. This study included 26 patients with mallet fin...

UNLABELLED Boden et al. suggested syndesmosis fixation was not necessary in distal pronation external rotation (PER) ankle fractures if rigid bimalleolar fracture fixation is achieved and was not necessary with deltoid ligament injury if the fibular fracture is no higher than 4.5 cm of the tibiotalar joint. We asked whether height of the fibular fracture with or without medial stability predict...