1-Meixner Random Vectors

Journal of Theoretical Probability - A definition of d-dimensional n-Meixner random vectors is given first. This definition involves the commutators of their semi-quantum operators. After that we...     

Nonexistence of bounded energy solutions for a critical exponent problem

In this paper, we discuss positive solutions for certain weighted elliptic equations with critical Sobolev exponent in R^N. The weights depend on a positive parameter γ, which is allowed to increase to infinity. While for small values of γ solutions are completely classified, an attempt to such a classification is much more difficult for large values of the parameter. In the present work we prove the nonexistence of solutions with bounded energy as γ increases to infinity. We also prove a multiplicity result for high energy solutions.     

160 GHz harmonic mode-locked AlGaInAs 1.55 μm strained quantum-well compound-cavity laser

We characterized the reflectivity and the modal discrimination of intracavity reflectors (ICRs) with different numbers of slots and presented harmonic mode-locking operation of a monolithic semiconductor laser comprising a compound cavity formed by a single deeply etched slot ICR fabricated from 1.55 μm AlGaInAs strained quantum well material. Gaussian pulses were generated at a 161.8 GHz repetition rate with a pulse duration of 1.67 ps and a time-bandwidth product of 0.81.     

A Genetically Encoded,Phage‐Displayed Cyclic‐Peptide Library

Superior to linear peptides in biological activities, cyclic peptides are considered to have great potential as therapeutic agents. To identify cyclic‐peptide ligands for therapeutic targets, phage‐displayed peptide libraries in which cyclization is achieved by the covalent conjugation of cysteines have been widely used. To resolve drawbacks related to cysteine conjugation, we have invented a phage‐display technique in which its displayed peptides are cyclized through a proximity‐driven Michael addition reaction between a cysteine and an amber‐codon‐encoded N^?‐acryloyl‐lysine (AcrK). Using a randomized 6‐mer library in which peptides were cyclized at two ends through a cysteine–AcrK linker, we demonstrated the successful selection of potent ligands for TEV protease and HDAC8. All selected cyclic peptide ligands showed 4‐ to 6‐fold stronger affinity to their protein targets than their linear counterparts. We believe this approach will find broad applications in drug discovery.     

On the Caffarelli‐Kohn‐Nirenberg inequalities: Sharp constants,existence (and nonexistence), and symmetry of extremal functions

Consider the following inequalities due to Caffarelli, Kohn, and Nirenberg [6] where, for N ≥ 3, −∞ < a < (N − 2)/2, a ≤ b ≤ a + 1, and p = 2N/(N − 2 + 2(b − a)). We shall answer some fundamental questions concerning these inequalities such as the best embedding constants, the existence and nonexistence of extremal functions, and their qualitative properties. While the case a ≥ 0 has been studied extensively and a complete solution is known, little has been known for the case a < 0. Our results for the case a < 0 reveal some new phenomena which are in striking contrast with those for the case a ≥ 0. Results for N = 1 and N = 2 are also given. © 2001 John Wiley & Sons, Inc.     

CWDM source based on AlGaInAs/InP monolithically integrated DFB laser array

The monolithic integration of four 1.5?μm range AlGaInAs/InP distributed feedback lasers with a 4×1 multimode-interference optical combiner, a curved semiconductor optical amplifier, and an electro-absorption modulator using relatively simple technologies--sidewall grating and quantum well intermixing--has been demonstrated. The four channels span the wavelength range of 1530 to 1566?nm with a channel spacing of 12?nm. The epitaxial structure was designed to produce a far-field pattern as small as 21.2°×25.1°, producing a coupling efficiency with an angled-end single-mode fiber at twice that of a conventional device design.     

Probing the origin of the compromised catalysis of E. coli alkaline phosphatase in its promiscuous sulfatase reaction

The catalytic promiscuity of E. coli alkaline phosphatase (AP) and many other enzymes provides a unique opportunity to dissect the origin of enzymatic rate enhancements via a comparative approach. Here, we use kinetic isotope effects (KIEs) to explore the origin of the 109-fold greater catalytic proficiency by AP for phosphate monoester hydrolysis relative to sulfate monoester hydrolysis. The primary 18O KIEs for the leaving group oxygen atoms in the AP-catalyzed hydrolysis of p-nitrophenyl phosphate (pNPP) and p-nitrophenylsulfate (pNPS) decrease relative to the values observed for nonenzymatic hydrolysis reactions. Prior linear free energy relationship results suggest that the transition states for AP-catalyzed reactions of phosphate and sulfate esters are "loose" and indistinguishable from that in solution, suggesting that the decreased primary KIEs do not reflect a change in the nature of the transition state but rather a strong interaction of the leaving group oxygen atom with an active site Zn2+ ion. Furthermore, the primary KIEs for the two reactions are identical within error, suggesting that the differential catalysis of these reactions cannot be attributed to differential stabilization of the leaving group. In contrast, AP perturbs the KIE for the nonbridging oxygen atoms in the reaction of pNPP but not pNPS, suggesting a differential interaction with the transferred group in the transition state. These and prior results are consistent with a strong electrostatic interaction between the active site bimetallo Zn2+ cluster and one of the nonbridging oxygen atoms on the transferred group. We suggest that the lower charge density of this oxygen atom on a transferred sulfuryl group accounts for a large fraction of the decreased stabilization of the transition state for its reaction relative to phosphoryl transfer.     

DNA electrochemistry with tethered methylene blue

Methylene blue (MB'), covalently attached to DNA through a flexible C(12) alkyl linker, provides a sensitive redox reporter in DNA electrochemistry measurements. Tethered, intercalated MB' is reduced through DNA-mediated charge transport; the incorporation of a single base mismatch at position 3, 10, or 14 of a 17-mer causes an attenuation of the signal to 62 ± 3% of the well-matched DNA, irrespective of position in the duplex. The redox signal intensity for MB'-DNA is found to be least 3-fold larger than that of Nile blue (NB)-DNA, indicating that MB' is even more strongly coupled to the π-stack. The signal attenuation due to an intervening mismatch does, however, depend on DNA film density and the backfilling agent used to passivate the surface. These results highlight two mechanisms for reduction of MB' on the DNA-modified electrode: reduction mediated by the DNA base pair stack and direct surface reduction of MB' at the electrode. These two mechanisms are distinguished by their rates of electron transfer that differ by 20-fold. The extent of direct reduction at the surface can be controlled by assembly and buffer conditions.     

Determination of epoxides by high-performance liquid chromatography following derivatization with <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-diethyldithiocarbamate

A reversed-phase, high-performance liquid chromatography (RP-HPLC) method that allows quantitation of low levels of epoxides has been described. The method involved derivatization of epoxides using 100- to 1,000-fold excess N,N-diethyldithiocarbamate (DTC) at 60 °C for 20 min at neutral pH. The unreacted DTC was then decomposed to CS₂ and diethyl amine by acidification of the reaction mixture to pH 2 using orthophosphoric acid. The first two steps could be performed in the same reaction vessel by sequential addition of reagents. In the final step, an aliquot (20 μL) of the derivatized sample was analyzed for the presence of stable esters of DTC by RP-HPLC using a Supelcosil LC-18-S (150 × 4.6-mm) column and a mobile phase consisting of 40% (v/v) acetonitrile in water at a flow of 1 mL min⁻¹. Using UV detection at 278 nm, the epoxides gave linear responses in the concentration range of 0.25 to 50 μM. The method is robust, and as low as 5 pmol of the analyte could be successfully detected and quantified with recoveries of ≥94%. Following a minimal pretreatment such as ultrafiltration (molecular weight cutoff 5,000 Da), the method is suitable for analysis of epoxides in complex physiological fluids (e.g., fetal bovine serum). The method has been rigorously evaluated and adapted in our laboratory for routine analysis and determination of stability of epoxides of 1,3-butadiene and other alkenes added to cell cultures.     

490 fs pulse generation from a passive C-band AlGaInAs/InP quantum well mode-locked laser

We report femtosecond pulses from a passive C-band two-section AlGaInAs/InP mode-locked laser with a monolithically integrated passive waveguide made by quantum well intermixing. Without any external pulse compression, Lorentzian pulses are generated at a repetition frequency of ~38 GHz with 490 fs pulse duration, which is, to the best of our knowledge, the shortest pulse from any directly electrically pumped quantum well semiconductor mode-locked laser. The mode-locking range is relatively large and the ultranarrow pulse width is very stable over a broad range of driving conditions.