Theory of tagged polymer method in small-angle X-ray scattering

Summary It was shown that the conformation of a single polymer chain in concentrated solutions and in undiluted state can be estimated from the small-angle X-ray scattering of randomly tagged polymer mixed in the systems. The randomly tagged polymer means the polymer containing heavy atoms at randomly selected positions along the molecule. The excess scattering of the tagged polymer is obtained by subtracting the scattering of the untagged polymer solution (or bulk) from that of the mixture solution (or bulk) containing the tagged and untagged polymers. The excess scattering obtained in this way contains the contributions of some undesirable cross terms of the scattering amplitude. The method for the experimental evaluation of these terms and the conditions under which these terms are negligible are discussed. It was found that the cross terms can be neglected when the contrast in scattering power between the tagged and untagged scattering units is sufficiently large, and the number of the tags per tagged molecule is not so small.The distribution of the tags in the tagged molecules was also taken into consideration. By averaging the theoretical scattered intensity over all possible positions of the tags, it was found that the excess scattering is practically proportional to the scattering function of the untagged polymer when the number of the tags per tagged molecule is not so small. Experimental verification of this theory was shown.It was also shown experimentally that the conformational change, which may be caused by the effect of the tags, can be eliminated by the extrapolation of the results obtained for a series of tagged polymers with various tag contents to zero tag content.With 2 figures     

Reversible photoswitching in a cell-sized vesicle

A photosensitive amphiphilic molecule can switch the shape of an assembled vesicle as determined by microscopic observation. Photoisomerization induces a change in membrane fluctuation behavior or a morphological transition between ellipsoid and bud shapes, depending on the asymmetrical degree of the initial shape. The mechanism of this reversible photoswitching in the vesicle morphology is interpreted in terms of a change in the effective cross-sectional area of the photosensitive molecule.     

Quasiconformal extension of biholomorphic mappings in several complex variables

Letf(z, t) be a subordination chain fort ∈ [0, α], α>0, on the Euclidean unit ballB inC ⁿ. Assume thatf(z) =f(z, 0) is quasiconformal. In this paper, we give a sufficient condition forf to be extendible to a quasiconformal homeomorphism on a neighbourhood of . We also show that, under this condition,f can be extended to a quasiconformal homeomorphism of onto itself and give some applications. Partially supported by Grant-in-Aid for Scientific Research (C) no. 14540195 from Japan Society for the Promotion of Science, 2004.     

Torsional bands of hydroxylamine

Infrared absorption spectrum of NH₂OH has been observed in its gaseous state, and the fine structures of the bands at 386 and 751 cm^?1 assignable, respectively, to the fundamental and overtone of the torsional vibration of this molecule have been examined. Band center frequencies for the n = 1 ← 0, 2 ← 1, 3 ← 2, 2 ← 0, and 3 ← 1 transitions (where n is the vibrational quantum number of the torsional oscillation) have been determined to be 386.2, 365.1, 346.3, 751.2, and 711.3 cm^?1, respectively. On the basis of these data, a discussion is given on the internal-rotation potential function.     

Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation

Let B be the unit ball in Cn with respect to an arbitrary norm and let f(z,t) be a g-Loewner chain such that e−tf(z,t)−z has a zero of order k+1 at z=0. In this paper, we obtain growth and covering theorems for . Moreover, we consider coefficient bounds and examples of mappings in .     

On some classes of bounded univalent mappings in several complex variables

Let B ⁿ be the Euclidean unit ball in C ⁿ . In this paper, we study several properties of strongly starlike mappings of order α (0 < α < 1) and bounded convex mappings on B ⁿ . We prove that K-quasiregular strongly starlike mappings of order α on B ⁿ have continuous and univalent extensions to ${\overline{B}^n}$ . We show that bounded convex mappings on B ⁿ are strongly starlike of some order α. We give a coefficient estimate for K-quasiregular strongly starlike mappings of order α on B ⁿ . Finally, we give examples of strongly starlike mappings of order α and bounded convex mappings on B ⁿ .