Non-classical law of the iterated logarithm behaviour for trimmed sums

Summary We study the law of the iterated logarithm for the partial sum of i.i.d. random variables when the r _n largest summands are excluded, where r _n=o(log logn). This complements earlier work in which the case log log_n=O(r_n) was considered. A law of the iterated logarithm is again seen to prevail for a wide class of distributions, but for reasons quite different from previously.Research supported in part by NSF Grant DMS-8501732     

Variational principles and convergence of finite element approximations of a holonomic elastic-plastic problem

Summary It is shown that a boundary-value problem based on a holonomic elastic-plastic constitutive law may be formulated equivalently as a variational inequality of the second kind. A regularised form of the problem is analysed, and finite element approximations are considered. It is shown that solutions based on finite element approximation of the regularised problem converge.     

Distoriton of area and conditioned Brownian motion

Summary In a simply connected planar domainD the expected lifetime of conditioned Brownian motion may be viewed as a function on the set of hyperbolic geodesics for the domain. We show that each hyperbolic geodesic induces a decomposition ofD into disjoint subregions and that the subregions are obtained in a natural way using Euclidean geometric quantities relating toD. The lifetime associated with on each _j is then shown to be bounded by the product of the diameter of the smallest ball containing _j and the diameter of the largest ball in _j . Because this quantity is never larger than, and in general is much smaller than, the area of the largest ball in _j it leads to finite lifetime estimates in a variety of domains of infinite area.Research of the first author was supported in part by NSF Grant DMS-9100811Research of the second author was supported in part by NSF Grant DMS-9105407     

Structure of a self-assembled hydrogen-bonded ‘living’ main chain liquid crystalline polymer

A main chain hydrogen-bonded liquid crystalline polymer was formed by melt mixing two complementary components, A and B, which in their individual states do not exhibit liquid crystallinity. The structure of the polymer and the thermal stability of its mesophase were studied using synchrotron radiation SAXS/WAXS/DSC at Daresbury (UK) and by variable temperature Fourier transform infrared. The chain extension, or “polymerization” process, was accelerated at the point when the polymer formed a liquid crystalline phase upon cooling from the isotropic melt. The polymer has an aabb chain structure and forms a smectic layer with a length of the A-B repeating unit. The hydrogen-bonded main chain polymer studied here is a monotropic liquid crystal. Above 150°C, it exhibits kinetic stabilization of its monotropic smectic phase. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1617–1624, 1998     

High-performance selective excitation pulses for solid- and liquid-state NMR spectroscopy.

Computer-optimized selective pulses are routinely used in solution-state NMR spectroscopy. At the same time, their utility and importance for solid-state applications has yet to be fully realized. We suggest a new computational approach that makes the design of soft selective pulses with desired properties relatively straightforward. By applying this technique to the generic selective excitation problem, we have arrived at a family of high performance selective excitation pulses, dubbed E-Family, that allows more flexibility and better performance than analogous pulses previously reported in the literature. The new pulses have been successfully tested in both solid- and solution-state NMR experiments. A theoretical treatment of the effects of chemical shift anisotropy (CSA) on the selective excitation in magic-angle spinning (MAS) experiments in solids is presented. The set of heuristics that comprise our new strategy were incorporated into a general NMR simulation program SPINEVOLUTION.     

Photoinduced cycloadditions of electron deficient nitrones to alkenes

Oxaziridines are proposed as intermediates in the photoinduced cycloadditions of electron deficient nitrones to dipolarophiles.     

Low-load rotor-synchronised Hahn-echo pulse train (RS-HEPT) 1H decoupling in solid-state NMR: factors affecting MAS spin-echo dephasing times

Transverse dephasing times T(2)' in spin-echo MAS NMR using rotor-synchronised Hahn-echo pulse-train (RS-HEPT) low-load (1)H decoupling are evaluated. Experiments were performed at 300 and 600 MHz for (13)CH-labelled L-alanine and (15)NH(delta)-labelled L-histidine.HCl.H(2)O, together with SPINEVOLUTION simulations for a ten-spin system representing the crystal structure environment of the (13)CH carbon in L-alanine. For 30 kHz MAS and nu(1)((1)H) = 100 kHz at 300 MHz, a RS-HEPT T(2)' value of 17 +/- 1 ms was obtained for (13)CH-labelled L-alanine which is approximately 50% of the XiX T(2)' value of 33 +/- 2 ms. Optimum RS-HEPT decoupling performance is observed for a relative phase of alternate RS-HEPT pi-pulses, Deltaphi = phi'- phi, between 40 and 60 degrees . For experiments at 600 MHz and 30 kHz MAS with (13)CH-labelled L-alanine, the best RS-HEPT (nu(1)((1)H) = 100 kHz) T(2)' value was 3 times longer than that observed for low-power continuously applied sequences with nu(1)((1)H) < or =40 kHz, i.e. corresponding to the same average power dissipated in the probe. A marked improvement in RS-HEPT (1)H decoupling is observed for increasing MAS frequency: at 55.6 kHz MAS, a best RS-HEPT T(2)' value of 34 +/- 5 ms was recorded for (13)CH-labelled L-alanine. Much improved RS-HEPT broadband performance was also observed at 55.6 kHz MAS as compared to 30 kHz MAS.     

Targeting orphan nuclear receptors for treatment of metabolic diseases and autoimmunity

The nuclear receptor (NR) superfamily is composed of 48 members in humans and includes receptors for steroid hormones, thyroid hormone, various lipids and oxysterols. This superfamily has been a rich source of drug targets for myriad diseases including inflammation, cancer, and metabolic disorders. Approximately half of the superfamily have well characterized natural ligands whereas the remaining receptors are considered orphan receptors and remain a focus of a number of investigators assessing their ability to be regulated by ligands. Here, we review recent discoveries that yield important insight into the druggability of three orphan nuclear receptors: the retinoic acid receptor-like orphan receptors (RORs), peroxisome proliferator-activated receptor γ (PPARγ), and liver receptor homolog-1 (LRH-1).