关于Golomb尺子的长度

令x_1,x_2,…,x_n为首项为0的递增整数序列,满足下列条件:如果|x_i-x_j|=|x_p-x_q|,则{i,j}={p,q}。我们的目标是对任意正整数n,求得最小x_n的幂次。显然,O(x_n)≥n~2。我们将证明O(x_2)≤n~3。且该序列不可能被任何二次多项式x_i=ai~2 bi c,i=1,2,…,n,产生出来,其中a,b,c为任何有理数。     

High-performance liquid chromatography and thin-layer chromatography assays for Devil's Club (Oplopanax horridus)

Devil's root, Oplopanax horridus, is a widely used folk medicine in Alaska and British Columbia. The inner bark of the root and stem has been used to treat colds, cough, fever, and diabetes. The present study involves the development of high-pressure liquid chromatography (HPLC) and thin-layer chromatography (TLC) methods to detect the presence of trans-nerolidol and sterols in the root bark. The HPLC and TLC analytical methods presented are suitable for the characterization and identification of Oplopanax horridus.     

Preparative chromatography of xylanase using expanded bed adsorption

Expanded bed adsorption was used to purify a marketable xylanase often used in the kraft pulp bleaching process. Experiments in packed and expanded beds were carried out mainly to study the adsorption of xylanase on to a cationic adsorbent (Streamline SP) in the presence of cells. In order to study the presence of cells, a Bacillus pumilus mass (5% wet mass) was mixed with the enzyme extract and submitted to an expanded bed adsorption system. One xylanase was purified to homogeneity in the packed bed. However, the 5% cell content hampered purification.