Trace Construction of a Basis for the Solution Space¶of sl N qKZ Equation

The trace of intertwining operators over the level one irreducible highest weight modules of the quantum affine algebra of type A_Nу⁽¹⁾ is studied. It is proved that the trace function gives a basis of the solution space of the qKZ equation at a generic level. The highest-highest matrix elements of the composition of intertwining operators are explicitly determined as rational functions up to an overall scalar function. The integral formula for the trace is presented.     

(NH4)3[VO2(SO4)2(H2O)2]·1.5H2O

The title compound, tri­ammonium cis‐di­aqua‐cis‐dioxo‐trans‐disulfatovanadate 1.5‐hydrate, was obtained by oxidizing V^IV to V^V in a 2 M sulfuric acid solution of vanadyl­ sulfate and adding ammonium sulfate. Here, the V atom is sandwiched by two sulfate groups by corner‐sharing to form a discrete [VO₂(SO₄)₂(OH₂)₂]^3? anion. The water mol­ecules occupy cis positions in the equatorial plane of the vanadium octahedron.     

Wavy texture in pressure-driven startup flows of liquid crystalline polymer solutions through a slit cell: effects of polymer concentration and solution temperature

Dependences of wavy texture on polymer concentration and solution temperature were examined using aqueous solutions of hydroxypropylcellulose (HPC). The phase of aqueous solution of HPC varied from an isotropic (I) system to a liquid crystalline (LC) one through a biphasic (I+LC, LC+I) system with increasing the HPC concentration and/or decreasing the solution temperature. The wavy texture emerged not only in the LC system but also in the LC+I system. Furthermore, induction time of wavy texture was evaluated in terms of apparent shear strain. It is suggested that polydomain structures included in liquid crystalline systems and droplets of isotropic phase in biphasic systems affect the initial stage of emergence of wavy texture at low shear rates.     

Automorphisms of normal quasi-circular domains

It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal quasi-circular domains in C²${\mathbb{C}}^2$ is linear.     

Seshadri constants and degrees of defining polynomials

In this paper, we study a relation between Seshadri constants and degrees of defining polynomials. In particular, we compute the Seshadri constants on Fano varieties obtained as complete intersections in rational homogeneous spaces of Picard number one.     

The effect of pressure on the phase transition behavior of tridecane, pentadecane, and heptadecane: a Fourier transform infrared spectroscopy study

The effect of pressure on the phase transition behavior of tridecane (C(13)), pentadecane (C(15)), and heptadecane (C(17)) has been investigated up to 489, 220, and 387 MPa, respectively, using Fourier transform infrared spectroscopy at 25 °C. The transition between the high pressure ordered (HPO) and high pressure rotator (HPR) phases has been observed in the pressure ranges of 270-220, 106-95, and 152-181 MPa for C(13), C(15), and C(17), respectively, and the transition between the HPR and liquid phases was observed in the pressure ranges of 171-112, 73-47, and 43-70 MPa for C(13), C(15), and C(17), respectively. The P(1)+P(3) band of the methylene rocking mode exhibits factor group splitting caused by intermolecular vibrational coupling. This was observed in both the HPO and HPR phases, while the P(1)+P(3) band did not split in the liquid phase. The separation of the peaks in the P(1)+P(3) band changed discontinuously at the HPO-HPR and HPR-liquid phase transitions, even though the separation is known to change continuously in the transition from the liquid to the high temperature rotator (HTR) phase. In the HPR phase, the ratio of the intensities of the higher and lower frequency components in the P(1)+P(3) doublet is roughly unity independent of pressure, while it is known to be much less than unity in the HTR phase. The separation of the P(1)+P(3) doublet in the HPR phase is found to be larger for longer alkanes. From the intensity ratio, a large proportion of alkane molecules is believed to participate in intermolecular vibrational coupling and possess herringbone-type short-range positional order in the HPR phase. Conversely, in the HTR phase only small proportion of alkane molecules participate in intermolecular vibrational coupling. From the pressure dependence of the separation of the doublet, intermolecular vibrational coupling and herringbone-type short-range positional order is considered to change discontinuously at the HPR-liquid phase transition, while they are reported to change continuously at the HTR-liquid phase transition. The HPR-liquid phase transition is governed by the effect of molecular packing while the HTR-liquid phase transition is predominantly governed by the difference in entropy between the herringbone-type and parallel-type packing.