Peter Borwein has conjectured that certain polynomials have non-negative coefficients. In this paper we look at some generalizations of this conjecture and observe how they relate to the study of generating functions for partitions with prescribed hook differences. A combinatorial proof of the generating function for partitions with prescribed hook differences is given.

Five new spirobifuranocoumarins, dahuribirins A-E (1-5) and two new bifuranocoumarins, dahuribirins F and G (6 and 7) were isolated from Japanese Bai Zhi (the root of Angelica dahurica Benth. et Hook. var. dahurica Benth. et Hook.) and their structures were established by chemical and spectral means.

We report the development of chimeric DNA binding peptides comprising a DNA binding fragment of natural transcription factors (the basic region of a bZIP protein or a monomeric zinc finger module) and an AT-Hook peptide motif. The resulting peptide conjugates display high DNA affinity and excellent sequence selectivity. Furthermore, the AT-Hook motif also favors the cell internalization of the ...

Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9. figshare.c.3850918. & 2017 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Can hook-bending be let off the hook? Bending/u...

A simple fixed-hook driving appliance is described, suitable for upper-limb amputees, and its function compared with that of the commonly available ball-and-cup device. The hook is reliable, safe and inexpensive. An attachment is also described which fits on to gear levers, allowing the use of the driving appliance to change gears manually.

BACKGROUND Clavicular hook plates are effective fixation devices for distal clavicle fractures and severe acromioclavicular joint dislocations. However, increasing number of studies has revealed that subacromial portion of the hook may induce acromial bony erosion, shoulder impingement, or even rotator cuff damage. By sonographic evaluation, we thus intended to determine whether the presence of...

Secure attachment to host tissues is essential for survival and reproduction in parasitic organisms. The production of elaborate attachment structures must be costly, however, and investments in attachment should be approximately proportional to the likelihood that a parasite will be dislodged. In the present study, relative investments in attachment as a function of body size and the type of h...

We study integral ratios of hook products of quotient partitions. This question is motivated by an analogous question in number theory concerning integral factorial ratios. We prove an analogue of a theorem of Landau that already applied in the factorial case. Under the additional condition that the ratio has one more factor on the denominator than the numerator, we provide a complete classific...

A partial order is defined on partitions by the removal of rim hooks of a given length. This poset is isomorphic to a product of Young lattices, guaranteeing rim hook versions of Schensted correspondences. Analogous results are given for shifted shapes. 1. Main Results A shape (Young diagram) is a finite order ideal of the lattice P = {(k, l) : k, l ≥ 1}. Shapes form the so-called Young lattice...