The Combinatorics of Laguerre,Charlier, and Hermite Polynomials

This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so-called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three-term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal polynomials.     

Improved synthesis of functionalized 5,6-dihydro-pyrimido[4,5-b][1,4]oxazepines

Novel synthetic approaches toward 5,6-dihydro-pyrimido[4,5-b][1,4]oxazepines were reported that led to successful introduction of poorly reactive anilines and various 2-hydroxybenzaldehydes to this therapeutically relevant scaffold. More extensive SAR studies on this scaffold hence became possible.     

The promise of electrochemical impedance spectroscopy as novel technology for the management of patients with diabetes mellitus

Self-monitoring of blood glucose is the standard of care in management of hyperglycemia among patients with diabetes mellitus. To increase the sensitivity and specificity of current devices, a novel method of detecting glucose using electrochemical impedance spectroscopy (EIS) technology is explored. The enzyme glucose oxidase (GOx) was fixed to gold electrodes and a sine wave of sweeping frequencies was induced using a wide range of concentrations of glucose. Each frequency in the impedance sweep was analyzed for the highest response and R-squared value. The frequency with both factors optimized is specific for the glucose-GOx binding interaction and was determined to be 1.17 kHz in purified solutions in both higher and lower ranges of glucose. The correlation between the impedance response and concentration at the low range of detection (0-100 mg dL(-1) of glucose) was determined to be 3.53 ohm/ln (mg dL(-1)) with an R-squared value of 0.90 with a 39 mg dL(-1) lower limit of detection. The same frequency of 1.17 kHz was verified in whole blood under the same glucose range. The above data confirm that EIS offers a new method of glucose detection as an alternative to current technology in use by patients. Additionally, the unique frequency response of individual markers allows for modulation of signals so that several other markers important in the management of diabetes could be measured with a single sensor.     

Influence of interparticle interactions on the kinetics of self-assembly and mechanical strength of nanoparticulate aggregates

Computer simulations based on Discrete Element Method have been performed in order to investigate the influence of interparticle interactions on the kinetics of self-assembly and the mechanical strength of nanoparticle aggregates.Three different systems have been considered.In the first system the interaction between particles has been simulated using the JKR (Johnson,Kendall and Roberts) contact theory,while in the second and third systems the interaction between particles has been simulated using van der Waals and electrostatic forces respectively.In order to compare the mechanical behaviour of the three systems,the magnitude of the maximum attractive force between particles has been kept the same in all cases.However,the relationship between force and separation distance differs from case to case and thus,the range of the interparticle force.The results clearly indicate that as the range of the interparticle force increases,the self-assembly process is faster and the work required to produce the mechanical failure of the assemblies increases by more than one order of magnitude.     

JT-60U装置温度分布剖面不变性的实验研究

在一系列H模放电条件下，建立了一个旨在研究等离子体温度分布剖面不变性的数据库。介绍了数据库建立过程中要解决的关键问题和所用软件，对等离子体温度分布剖面不变性及芯部约束与边缘参数的关系进行了研究。