Partitions, the partition function p(n), and hook lengths of their Ferrers–Young diagrams are important objects in combinatorics, number theory, representation theory. For positive integers n t, we study $$p_t^\mathrm{e}(n)$$ (resp. $$p_t^\mathrm{o}(n)$$ ), partitions with an even odd) t-hooks. We limiting behavior ratio $$p_t^\mathrm{e}(n)/p(n)$$ , which also gives $$p_t^\mathrm{o}(n)/p(n)$$ s...

The photonic hook (PH) is new type of curved light beam which has promising applications in various fields such as nanoparticle manipulation, super-resolution imaging, etc. Herein, we proposed a approach utilizing patchy microcylinders for the generation PHs. Numerical simulation based on finite-difference time-domain method was used to investigate field distribution characteristics By rotating...

statement of problem: a recent technique (mbt) has been introduced for easy and efficient orthodontic treatment by means of straight wire fixed appliances. although this technique has many advantages, in space closure stage causes up righting problem in upper incisors, which should be adjusted by applying additional torque in anterior region. purpose: the purpose of this clinical trial was to d...

AIM We present a series of 16 patients who underwent occipitocervical fixation with occipital bone hooks used as a substitute for occipital screws for the treatment of occipitocervical instability. MATERIAL AND METHODS In this technique; instrumentation was started following the decompression with insertion of screws into lateral masses. At the occipital level, two symmetrical burr holes were...

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...

The effects of circle hooks on blue shark Prionace glauca catch in a pelagic longline fishery were assessed in fishing experiments on two research essels in the western North Pacific off the coast of Japan from May to September 2005. We used conventional tuna hooks (standard Japanese ook size; 3.8 sun) and two sizes of circle hooks (4.3 sun and 5.2 sun) for each fishing operation and compared c...