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When subset-sums do not cover all the residues modulo p

โœ Scribed by Jean-Marc Deshouillers; Gregory A. Freiman

Book ID
104024362
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
216 KB
Volume
104
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let c4

ffiffi ffi 2 p : We prove that a subset A of Z=pZ; where p is a prime number, with cardinality larger than c ffiffi ffi p p such that its subset sums do not cover Z=pZ has an automorphic image which is rather concentrated; more precisely, there exists s prime to p such that X aAA as p o1 รพ Oรฐp ร€1=4 ln pรž:

๐Ÿ“œ SIMILAR VOLUMES

Saliva and serum samples were collected
Saliva and serum samples were collected from eight healthy volunteers every two hours during a 26-hour period. Melatonin concentrations were measured by radioimmunoassay after chloroform extraction using radioiodinated melatonin as a tracer. Five of the subjects had high serum melatonin levels at night (peak levels higher than 75 pg/ml); in three subjects the highest serum melatonin concentration was 20-40 pg/ml. All subjects had low levels (P <0.001, was obtained for all detectable value pairs (n= 73). The regression and correlation coefficients were almost equal for the peak values of melatonin and during the rising and descending phases of the secretion patterns. However, no significant correlation was found between low daytime salivary and serum concentrations when calculated separately. In the five high-secretors the melatonin levels in saliva reflected reliably the changes in serum, but in the three low-secretors the correlation between salivary and serum melatonin was not significant. The proportion of melatonin found in saliva decreased with increasing serum melatonin levels. Circadian rhythm parameters were estimated by single cosinor analysis. The acrophases did not differ significantly within a subject in the concomitant measurements of serum and salivary melatonin. The measurements of salivary melatonin levels seem valid for studies on melatonin rhythms, but the melatonin concentrations measured in saliva do not always consistently reflect the absolute concentrations in blood.
โœ Maija-Liisa Laakso; Tarja Porkka-Heiskanen; Aino Alila; Dag Stenberg; Gunnar Joh ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 622 KB