Matrix Concentration for Products

Foundations of Computational Mathematics - This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize...     

Interplay of thermochemistry and Structural Chemistry,the Journal (volume 22, 2011, issues 1–3) and the discipline

In the current review of the journal Structural Chemistry, the content of the first three issues for the calendar year 2011 is related to thermochemistry. Each paper is summarized and followed by a short thermochemical comment.     

Saccharin: a combined experimental and computational thermochemical investigation of a sweetener and sulfonamide

The standard molar enthalpies of combustion, sublimation, and formation in the crystalline and gaseous phase at a temperature of 298.15?K have been experimentally determined for saccharin and for benzenesulfonamide. These compounds were also studied theoretically using density functional theory, the B3LYP functional and extended basis sets.     

Effect of biaxial orientation on dielectric and breakdown properties of poly(ethylene terephthalate)/poly(vinylidene fluoride‐co‐tetrafluoroethylene) multilayer films

Polymer films with enhanced dielectric and breakdown properties are essential for the production of high energy density polymer film capacitors. By capitalizing on the synergistic effects of forced assembly nanolayer coextrusion and biaxial orientation, polymer multilayer films using poly(ethylene terephthalate) (PET) and a poly(vinylidene fluoride‐co‐tetrafluoroethylene) [P(VDF‐TFE)] copolymer were produced. These films exhibited breakdown fields, under a divergent field using needle/plane electrodes, as high as 1000 kV mm^?1. The energy densities of these same materials, under a uniform electric field measured using plane/plane electrodes, were as high as 16 J cm^?3. The confined morphologies of both PET and P(VDF‐TFE) were correlated to the observed breakdown properties and damage zones. On‐edge P(VDF‐TFE) crystals induced from solid‐state biaxial stretching enhanced the effective P(VDF‐TFE) layer dielectric constant and therefore increased the dielectric contrast between the PET and P(VDF‐TFE) layers. This resulted in additional charge buildup at the layer interface producing larger tree diameters and branches and ultimately increasing the breakdown and energy storage properties. In addition to energy storage and breakdown properties, the hysteresis behavior of these materials was also evaluated. By varying the morphology of the P(VDF‐TFE) layer, the low‐field dielectric loss (or ion migration behavior) could be manipulated, which in turn also changed the observed hysteresis behavior. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 882–896     

Design and implementation of an array of micro-electrochemical detectors for two-dimensional liquid chromatography—Proof of principle

Simultaneous two-dimensional liquid chromatography (2D-LC) is an implementation of two-dimensional liquid chromatography which has the potential to provide very fast, yet highly efficient separations. It is based on the use of time × space and space × space separation systems. The basic principle of this instrument has been validated long ago by the success of two-dimensional thin layer chromatography. The construction of a pressurized wide and flat column (100 mm × 100 mm × 1 mm) operated under an inlet pressure of up to 50 bar was described previously. However, to become a modern analytical method, simultaneous 2D-LC requires the development of detectors suitable for the monitoring of the composition of the eluent of this pressurized planar, wide column. An array of five equidistant micro-electrochemical sensors was built for this purpose and tested. Each sensor is a three-electrode system, with the working electrode being a 25 μm polished platinum micro-electrode. The auxiliary electrode is a thin platinum wire and the reference electrode an Ag/AgCl (3 M sat. KCl) electrode. In this first implementation, proof of principle is demonstrated, but the final instrument will require a much larger array.     

A definition of the crystal commutor using Kashiwara’s involution

Henriques and Kamnitzer defined and studied a commutor for the category of crystals of a finite dimensional complex reductive Lie algebra. We show that the action of this commutor on highest weight elements can be expressed very simply using Kashiwara’s involution on the Verma crystal. The second author was supported by the RTG grant DMS-0354321.     

Development of a practical solid-phase synthesis approach to 1,3,5-triazepan-2,6-diones

1,3,5-Triazepan-2,6-diones are a class of conformationally restricted heterocycles derived from dipeptides. With the aim to develop a general and practical method useful for library production, three polymer-assisted syntheses, all based on a catch and release approach, have been evaluated and compared. The method involving a Hofmann rearrangement of N-Boc dipeptide carboxamides and subsequent trapping of the isocyanate on polymer-supported N-hydroxysuccinimide (PS-HOSu) was found to be the most reliable and versatile, allowing rapid access to the 1,3,5-triazepan-2,6-dione skeleton.     

Correlation functions for nematic liquid crystals

We show that the correlation functions of a system of hard ellipsoids whose axes are constrained to be parallel are simply related to the corresponding functions of a hard sphere fluid with the same packing fraction. The existence of simple, accurate approximations for the latter system make the oriented ellipsoid fluid a suitable ‘reference system’ for the nematically ordered phase of liquid crystals and other orientationally ordered molecular fluids such as polar fluids in an external field. The properties of such fluids, with a given angular distribution f(ω), may then be obtained via ‘standard’ perturbation theory. Methods for obtaining f(ω) near the perfectly ordered state are discussed.