Phenylated polyimides: Diels-Alder reaction of biscyclopentadienones with dimaleimides

A series of phenylated polydihydrophthalimides has been synthesized by the Diels-Alder reactions of 3,3′-(oxydi-p-phenylene)bis(2,4,5-triphenylcyclopentadienone) and 3,3′-(p-phenylene)bis(2,4,5-triphenylcyclopentadienone) with N,N′-o-, -m-, and -p-phenylenedimaleimide. The polydihydrophthalimides were soluble in dimethylformamide (DMF) and had intrinsic viscosities that ranged from 0.33 to 1.01, the polymers were dehydrogenated thermally and chemically to afford the corresponding phenylated polyphthalimides. The totally aromatic polyimides were also soluble in DMF but had intrinsic viscosities only as high as 0.41. The thermogravimetric analyses of the polyphthalimides showed breaks near 530°C in air and in nitrogen atmospheres.     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

Error estimates in the determination of rigid body displacements in protein crystals

We report the estimation of random errors in the refinement of the rigid body displacements of the -helices of the enzyme 6-phosphogluconate dehydrogenase. Least-squares refinement of the TLS parameters of the helices has been carried out using X-ray reflection data of 2.1 Å resolution, resulting in anR-factor of 19.5%. Standard deviations were estimated from the normal matrix. The results show that the translational mean-square displacements of nearly all the helices are significant at this resolution. However the libration parameters are only significant when the helices have at least four turns. Screw-rotation tensor values cannot be determined at this resolution.