Euler's partition theorem and the combinatorics of ℓ-sequences

Euler's partition theorem states that the number of partitions of an integer N into odd parts is equal to the number of partitions of N in which the ratio of successive parts is greater than 1. It was shown by Bousquet-Mélou and Eriksson in [M. Bousquet-Mélou, K. Eriksson, Lecture hall partitions II, Ramanujan J. 1 (2) (1997) 165–185] that a similar result holds when “odd parts” is replaced by “parts that are sums of successive terms of an ℓ-sequence” and the ratio “1” is replaced by a root of the characteristic polynomial of the ℓ-sequence. This generalization of Euler's theorem is intrinsically different from the many others that have appeared, as it involves a family of partitions constrained by the ratio of successive parts.In this paper, we provide a surprisingly simple bijection for this result, a question suggested by Richard Stanley. In fact, we give a parametrized family of bijections, that include, as special cases, Sylvester's bijection and a bijection for the lecture hall theorem. We introduce Sylvester diagrams as a way to visualize these bijections and deduce their properties.In proving the bijections, we uncover the intrinsic role played by the combinatorics of ℓ-sequences and use this structure to give a combinatorial characterization of the partitions defined by the ratio constraint. Several open questions suggested by this work are described.     

Interference by the Catecholic Cephalosporin BRL-41897-A with Diagnostic Clinical Chemistry Assays

The catecholic cephalosporin BRL-41897-A, was investigated for in vitro interference with commonly used clinical chemistry assays. An important finding was a negative interference with the enzymatic cholesterol assay that incorporates the Trinder reaction, in which hydrogen peroxide produced by an oxidase drives the oxidative coupling of a phenol with 4-aminophenazone to produce a colored quinoneimine. The suspected interference by BRL-41897-A with the Trinder reaction was investigated using a uricase driven system in which the phenol reagent was substituted or combined with BRL-41897-A. The results indicate that BRL-41897-A competes with the phenol component to react preferentially with 4-aminophenazone to produce a quinoneimine of low absorptivity. Further investigations conducted with similar enzymatic assays for creatinine, cholesterol, triglycerides, and uric acid showed the interference varied substantially with analyte and was dependent on analyte concentration.     

Effect of cellulose–lignin interactions on char structural changes during fast pyrolysis at 100–350 °C

This study investigates the cellulose–lignin interactions during fast pyrolysis at 100–350 °C for better understanding fundamental pyrolysis mechanism of lignocellulosic biomass. The results show that co-pyrolysis of cellulose and lignin (with a mass ratio of 1:1) at temperatures < 300 °C leads to a char yield lower than the calculated char yield based on the addition of individual cellulose and lignin pyrolysis. The difference between the experimental and calculated char yields increases with temperature, from ～2% 150 °C to ～6% at 250 °C. Such differences in char yields provide direct evidences on the existence of cellulose–lignin interactions during co-pyrolysis of cellulose and lignin. At temperatures below 300 °C, the reductions in both lignin functional groups and sugar structures within the char indicate that co-pyrolysis of cellulose and lignin enhances the release of volatiles from both cellulose and lignin. Such an observation could be attributed to two possible reasons: (1) the stabilization of lignin-derived reactive species by cellulose-derived reaction intermediates as hydrogen donors, and (2) the thermal ejection of cellulose-derived species due to micro-explosion of liquid intermediates from lignin. In contrast, at temperatures ≥ 300 °C, co-pyrolysis of cellulose and lignin increases char yields, i.e., with the difference between the experimental and calculated char yields increasing from ～1% at 300 °C to ～8% at 350 °C. The results indicate that the cellulose-derived volatiles are difficult to diffuse through the lignin-derived liquid intermediates into the vapor phase, leading to increased char formation from co-pyrolysis of cellulose and lignin as temperature increases. Such an observation is further supported by the increased retention of cellulose functional groups in the char from co-pyrolysis of cellulose and lignin.     

Obtaining the shear stress shear rate relationship and yield stress of liquid foods from Couette viscometry data

A method based on Tikhonov regularisation is used to convert the Couette viscometry data of a number of liquid foods into shear stress vs shear rate relationships. For liquid foods that have a yield stress and if the viscometry data cover the appropriate range of shear stress, Tikhonov regularisation is used to compute simultaneously the yield stress. The versatility of Tikhonov regularisation is demonstrated by applying it to process data from wide as well as narrow gap Couette viscometers. The results generated by Tikhonov regularisation are compared against that obtained by methods currently employed by rheologists.     

Consensus model for identification of novel PI3K inhibitors in large chemical library

Phosphoinositide 3-kinases (PI3Ks) inhibitors have treatment potential for cancer, diabetes, cardiovascular disease, chronic inflammation and asthma. A consensus model consisting of three base classifiers (AODE, kNN, and SVM) trained with 1,283 positive compounds (PI3K inhibitors), 16 negative compounds (PI3K non-inhibitors) and 64,078 generated putative negatives was developed for predicting compounds with PI3K inhibitory activity of IC₅₀ ≤ 10 μM. The consensus model has an estimated false positive rate of 0.75%. Nine novel potential inhibitors were identified using the consensus model and several of these contain structural features that are consistent with those found to be important for PI3K inhibitory activities. An advantage of the current model is that it does not require knowledge of 3D structural information of the various PI3K isoforms, which is not readily available for all isoforms.     

Functionalized Alkynylplatinum(II) Polypyridyl Complexes for Use as Sensitizers in Dye‐Sensitized Solar Cells

A series of platinum(II) alkynyl‐based sensitizers has been synthesized and found to show light‐to‐electricity conversion properties. These dyes were developed as sensitizers for the application in nanocrystalline TiO₂ dye‐sensitized solar cells (DSSCs). Their photophysical and electrochemical properties were studied. The excited‐state property was probed using nanosecond transient absorption spectroscopy, which showed the formation of a charge‐separated state that arises from the intramolecular photoinduced charge transfer from the platinum(II) alkynylbithienylbenzothiadiazole moiety (donor) to the polypyridyl ligand (acceptor). A lifetime of 3.4 μs was observed for the charge‐separated state. A dye‐sensitized solar cell based on one of the complexes showed a short‐circuit photocurrent of 7.12 mA cm^?2, an open circuit voltage of 780 mV, and a fill factor of 0.65, thus giving an overall power conversion efficiency of 3.6 %.     

Acute oral toxicity and brine shrimp lethality of Elaeis guineensis Jacq., (oil palm leaf) methanol extract

Elaeis guineensis (Arecaceae) is widely used in West African traditional medicine for treating various ailments. An evaluation on the toxicity of extracts of this plant is crucial to support the therapeutic claims. The acute oral toxicity and brine shrimp lethality of a methanolic extract of this plant was tested. Oral administration of crude extract at the highest dose of 5,000 mg/kg resulted in no mortalities or evidence of adverse effects, implying that E. guineensis is nontoxic. Normal behavioral pattern, clinical signs and histology of vital organs confirm this evidence. The E. guineensis extracts screened for toxicity against brine shrimp had 50% lethal concentration (LC??) values of more than 1.0 mg/mL (9.00 and 3.87 mg/mL, at 6 and 24 h, respectively), confirming that the extract was not toxic. Maximum mortalities occurred at 100 mg/mL concentration while the least mortalities happened to be at 0.195 mg/mL concentration. The results of both tests confirm that E. guineensis is nontoxic and hence safe for commercial utilization.     

Structural,optical and electrical properties of undoped and Si-doped AlxGa1−xN thin films on Si (1 1 1) substrate grown by PA-MBE

We have studied the structural properties of undoped and Si-doped Al_xGa_1?xN/GaN/AlN on Si (1 1 1) substrate prepared by plasma-assisted molecular beam epitaxy (PA-MBE) using high-resolution X-ray diffraction (HR-XRD) and atomic force microscopy (AFM). In comparison with undoped AlGaN, the roughness and dislocation density on the surface of the AlGaN layer decrease with Si doping. Full width half maximum (FWHM) of the undoped and Si-doped samples were equal to 0.69° and 0.52°, respectively. This indicates that the Si doping improves the crystalline quality of the Al_xGa_1?xN layer compared with the undoped one. Raman scattering measurement reveals that the optical phonon modes of A₁(LO) and E₂(H) of the AlGaN show a one-mode and two-modes behavior, respectively. The Fourier-transform infrared reflectance (FTIR) investigation confirms the one-mode (two-mode) behavior of the LO (TO) phonon in our samples. This is in good agreement with Raman measurement. Finally, the barrier height (Φ_B) of undoped and Si-doped Al_xGa_1?xN samples was found to be 0.86 and 0.74 eV, respectively.