Ramanujan conjectured that if n is of a specific form then/>(«), the number of unrestricted partitions of n, is divisible by a high power of 7. A modified version of Ramanujan's conjecture was proved by G. N. Watson. In this paper we establish appropriate generating formulae, from which Watson's results follow easily. Our proofs are more straightforward than those of Watson. They are elementary...

Here we investigate a novel signal-on electrochemical DNA sensor based on the use of a clamp-like DNA probe that binds a complementary target sequence through two distinct and sequential events, which lead to the formation of a triplex DNA structure. We demonstrate that this target-binding mechanism can improve both the affinity and specificity of recognition as opposed to classic probes solely...

Hydroxyl radicals are potent mutagens that attack DNA to form various base and ribose derivatives. One of the major damaged thymine derivatives is 5-formyluracil (fU), which induces pyrimidine transition during replication. In order to establish the structural basis for such mutagenesis, the crystal structures of two kinds of DNA d(CGCGRATfUCGCG) with R = A/G have been determined by X-ray cryst...

Anderson, C. M. (1960). Histological changes in the duodenal mucosa in coeliac disease: reversibility during treatment with a wheat gluten free diet. Archives of Disease in Childhood, 35, 419. Dyer, N. H. and Verbov, J. (1968). Malabsorption and the skin (correspondence). British Medical Journal, 4, 455. Fraser, N. G., Ferguson, A., and Murray, D. (1968). Dermatitis herpetiformis in two patient...

Machine learning applications often involve data that can be analyzed as unit vectors on a d-dimensional hypersphere, or equivalently are directional in nature. Spectral clustering techniques generate embeddings that constitute an example of directional data and can result in different shapes on a hypersphere (depending on the original structure). Other examples of directional data include text...

the solid state; 1711 cm-' in chloroform) is caused mainly by a C = 0 vibration. 30 Miles, H. T., unpublished experiments. 31 Davies, D. R., Nature, 186, 1030 (1960). Dr. Davies has informed the author that in his opinion the Watson-Crick arrangement (XIII) is more likely for steric reasons but that the X-ray data could not exclude XIV (R' = H) without a great deal of additional work. 32 Watson...

These commands provide regression diagnostic tools specific to time series. You must tsset your data before using these commands; see [TS] tsset. estat archlm tests for time-dependent volatility. estat bgodfrey, estat durbinalt, and estat dwatson test for serial correlation in the residuals of a linear regression. For non-time-series regression diagnostic tools, see [R] regress postestimation. ...