On the limiting profile arising from orthonormalizing shifts of exponentially decaying functions

It is shown that, under certain conditions, orthonormalizingthe positive integer shifts of an exponentially decaying functionon the half line by the Gram-Schmidt process leads to a limitingprofile given by orthonormalizing all their integer shifts onthe whole line. These results derive from properties of Choleskyfactorization of bi-infinite and semi-infinite matrices. Anexample is provided by the negative exponential function andconjectures are given, supported by numerical evidence, forthe Gaussian and Lorentz function.     

Accordion-type laser-Raman scattering by drawn linear polyethylene

One can reproduce the observed accordion-type laser-Raman (ALR) scattering of highly drawn linear polyethylene if one assums that any gauche defect in the crystal lattice which interrupts the all-trans conformation sequence of the molecular chain completely decouples the accordion-type longitudinal oscillations of the two sections on both sides of the defect. Each oscillates independently of the rest. The length of the section, smaller than the full length of the straight chain between the crystal surfaces, determines the frequency of the ALR absorption. One such defect per five chain stems of the ideal crystal yields a straight-length distribution which agrees sufficiently well with that derived from the ALR spectrum. Small-angle x-ray scattering very generally registers the resulting decrease of the electron density of the crystalline component without yielding more detailed information about the location and frequency of such gauche defects.     

Leading neuroblastoma cells to die by multiple premeditated attacks from a multifunctionalized nanoconstruct

To conquer complex and devastating diseases such as cancer, more coordinated and combined attack strategies are needed. We suggest that these can be beautifully achieved by using nanoconstruct design. We present an example showing that neuroblastoma cells are selectively killed by a nanoconstruct that specifically targets neuroblastoma cells, pushes cells to the vulnerable phase of the cell cycle, and greatly enhances radiation-induced cell death. The success of this multipronged attack approach launched by cell-embedded nanoconstructs demonstrates the power and flexibility of nanotechnology in treating cancer, a difficult task for a small molecule.     

Contributions to reversed-phase column selectivity. I. Steric interaction

In reversed-phase chromatography (RPC), the restricted retention of "bulky" solutes can occur in one of two ways, giving rise to either "shape selectivity" or "steric interaction." Starting with data for 150 solutes and 167 monomeric type-B alkylsilica columns, the present study examines the steric interaction process further and compares it with shape selectivity. The dependence of column hydrophobicity and steric interaction on column properties (ligand length and concentration, pore diameter, end-capping) was determined and compared. The role of the solute in steric interaction was found to be primarily a function of solute molecular length, with longer solutes giving increased steric interaction. We find that there are several distinct differences in the way shape selectivity and steric interaction are affected by separation conditions and the nature of the sample. Of particular interest, steric interaction exhibits a maximum effect for monomeric C(18) columns, and becomes less important for either a C(1) or C(30) column; shape selectivity appears unimportant for monomeric C(1)-C(18) columns at ambient and higher temperatures, but becomes pronounced for C(30) - as well as polymeric columns with ligands ≥C(8). One hypothesis is that shape selectivity involves the presence or creation of cavities within the stationary phase that can accommodate a retained solute (a primarily enthalpic process), while steric interaction mainly makes greater use of spaces that pre-exist the retention of the solute (a primarily entropic process). The related dependence of hydrophobic interaction on column properties was also examined.     

A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation

This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead-Segel equation on R^n.We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation,including deriving a classical Harnack inequality and characterizing standing solutions and traveling wave solutions.     

CGC using a programmable electronic pressure controller

Capillary gas chromatographic separations were performed with an electronic pressure control system developed to provide precise closed-loop control of inlet pressure through the use of a solid state micro-machined pressure sensor and electronically controlled proportional valve. The closed-loop control of the electronic system provided better precision than the open-loop control achieved by manual pressure regulation. Closed-loop control can perform pressure programming, which can be combined with temperature programming to optimize separations. The pressure sensor monitors the integrity of the flow system and singals the controller to reduce flow in the presence of a sudden loss of system pressure.     

Direct optical detection of singlet oxygen from a single cell

Singlet oxygen has been detected in single nerve cells by its weak 1270 nm phosphorescence (a1deltag --> X3sigmag-) upon irradiation of a photosensitizer incorporated in the cell. Thus, one can now consider the application of direct optical imaging techniques to mechanistic studies of singlet oxygen at the single-cell level.     

Prospects for Higgs search at DØ

The status of the Higgs search at the upgraded DØ detector is discussed.