Analogue of the degree conjecture over function fields

Under a certain assumption, similar to Manin's conjecture, we prove an upper bound on the degree of modular parametrizations of elliptic curves by Drinfeld modular curves, which is the function field analogue of the conjectured bound over the rational numbers.

     

关于Erdos-Jacobson-Lehel 问题的门槛

设σ(k,n）表示最小的正整数m，使得对于每个n项正可图序列，当其项和至少为m时，有一个实现含k 1个顶点的团作为其子图。Erdos等人猜想：σ(k,n）＝（k-1)(2n-k) 2.Li等人证明了这个猜想对于k≥5，n≥（^k2））＋3是对的，并且提出如下问题：确定最小的整数N（k），使得这个猜想对于n≥N(k）成立。他们同时指出：当k≥5时，[5k-1/2]≤N(k）≤（^k2) 3.Mubayi猜想：当k≥5时，N(k）＝[5k-1/2]。在本文中，我们证明了N（8）＝20，即Mubayi猜想对于k=8是成立的。     

Directed triangles in directed graphs

We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3.     

p-Laplace方程正解的存在性和多重性

这篇文章讨论边值问题-(| u′|p-2u′)′=λf(t ,u) ,t∈(0,1) ,p >1,u(0) =u(1) =0,其中f(t ,u)≥-M( M是正常数) ,对(t ,u)∈0,1×0,∞) .我们利用度理论和锥上的不动点定理得到方程存在两个正解.     

Neutral oxygen atom density in the MESOX air plasma solar furnace facility

The density of neutral oxygen atoms in the MESOX set-up, one device of the PROMES-CNRS solar facilities, was determined by a fiber-optics catalytic probe (FOCP). Plasma was created in a flowing air within a quartz tube with the outer diameter of 5 cm by a 2.45 GHz microwave generator with the output power up to 1000 W. The flow of air was varied between 4 and 20 l/h. The O-atom density was found to increase monotonously with the increasing discharge power, and it decreased with the increasing flow rate. The degree of dissociation of oxygen molecules in the plasma column depended largely on the flow rate. At the air flow of 4 l/h it was about 80% but it decreased to about 20% at the flow of 20 l/h.     

Identification of a chemical indicator of the rupture of 1,4-β-glycosidic bonds of cellulose in an oil-impregnated insulating paper system

In this study, headspace gas chromatography/mass spectrometry has been used to assess the volatile by-products generated by the ageing of oil-impregnated paper insulation of power transformers. Sealed-glass ampoules were used to age under oxidative conditions 0.5-g specimens of insulating paper in 9 mL of inhibited mineral oil in a temperature range of 60–120 °C and moisture of 0.5, 1 and 2% (w/w). A linear relationship between one of the oil-soluble degradation by-products, i.e. methanol, and the number of ruptured 1,4-β-glycosidic bonds of cellulose, regardless of the type of paper (ordinary Kraft or thermally-upgraded (TU) Kraft paper), was established for the first time in this field. Ageing at 130 °C of model compounds of the Kraft paper constituents (α-cellulose, hemicellulose and lignin) and two cellulosic breakdown by-products (D-(+)-glucose and 1,6-anhydro-β-d-glucopyranose) confirmed that the α-cellulose degradation was mostly responsible for the presence of this molecule in the system. Furthermore, additional 130 °C-tests with six different papers and pressboard samples under a tight control of initial moisture indicated that at least one molecule of methanol is formed for each rupture of 1,4-β-glucosidic bond of the molecular chains. Stability tests showed that the ageing indicator is stable under the oxygen and temperature conditions of open-breathing transformers. The presence of methanol was detected in 94% of oil samples collected from over than 900 in-service pieces of equipment, confirming the potential for this application. Lastly, the tests have shown that oil-oxidation by-products and TU-nitrogenous agents modify the methanol partitioning coefficients in the paper/oil/air system, which makes their study essential over a range of field conditions encountered by power transformers. Results are presented and discussed in comparison with 2-furfuraldehyde, which is the current reference in the domain.     

Determination of degree of conversion as a function of depth of a photo-initiated dental restoration composite—III application to commercial Prodigy Condensable™

In this third work, we evaluated the degree of conversion (DC) versus depth of dental filling composite named Prodigy Condensable™ using infrared spectroscopy. Confirming previous results, there was a gradual reduction of DC with increasing depth but the composite exhibited extreme values of DC, an upper value (45.9%) on the surface and a lower one (6.1%) at a depth of 5 mm. The composite presented the worst performance among materials studied. The composite formulation was 80% of inorganic fillers and BisfenolA/dimethacrylate (BisGMA) (18%)/triethyleneglycoldimethacrylate (TEGDMA) (2.0%) as monomers. As stated before, type/ratio/viscosity of monomers and type, amount, size and size distribution of fillers all together had an important role in the cure reaction contributing to the final performance of the composite.     

SYNTHESIS, STRUCTURE AND PROPERTIES OF INTERPENETRATING SULFONIC ACID RESINS WITH HIGH CAPACITY

Two series of interpenetrating sulfonic acid resins (ISAR), 10×n and n×10, were prepared by means of the wet method, and the physicochemical, thermodynamic and kinetic properties of the ISAR were measured. The results show: 10×n resins exhibit better properties than n×10 ones, mainly in higher apparent degree of crosslinking and larger conformational entropy effect, among which, 10×1 resin exhibits the best thermodynamic and kinetic properties. In the DTA graphs of n×10 resins, there are two T_g and two T_(ox), but in those of 10×n, only one T_g and one T_(ox). This result well supports the conclusion that 10×n resins have much better interpenetrating structural aspects.