On sign changes of cusp forms and the halting of an algorithm to construct a supersingular elliptic curve with a given endomorphism ring

Chevyrev and Galbraith recently devised an algorithm which inputs a maximal order of the quaternion algebra ramified at one prime and infinity and constructs a supersingular elliptic curve whose endomorphism ring is precisely this maximal order. They proved that their algorithm is correct whenever it halts, but did not show that it always terminates. They did however prove that the algorithm halts under a reasonable assumption which they conjectured to be true. It is the purpose of this paper to verify their conjecture and in turn prove that their algorithm always halts. More precisely, Chevyrev and Galbraith investigated the theta series associated with the norm maps from primitive elements of two maximal orders. They conjectured that if one of these theta series "dominated" the other in the sense that the $n$th (Fourier) coefficient of one was always larger than or equal to the $n$th coefficient of the other, then the maximal orders are actually the same. We prove that this is the case.Comment: 12 page

DEMAND AND PRICE-MARKUP FUNCTIONS FOR CANNED CLING PEACHES AND FRUIT COCKTAIL

This study formulates and estimates a six-equation model for canned cling peaches and fruit cocktail in which processors are viewed as price setters, with qualities not sold at the set price carried over to the next year. The system consists of two price-markup equations, two quantity-dependent demand equations and two inventory change identities. The three-stage least squares estimation results tend to support the behavioral hypotheses.Demand and Price Analysis,

The Sugar Content of Blood

Summary and Conclusions: 1 We have shown that the picric acid methods are not accurate. 2. We have shown that the titrimetric methods are not adapted to clinical use. 3. We have demonstrated that the Folin-Wu method, which gives the same results as the titrimetric methods, and is the most accurate method used in clinics, gives results approximately 15 per cent too high, because of interfering substances. 4. We have developed a mercuric nitrate method, specific for blood sugar by virtue of the fact that it precipitates interfering substances before making the determination. 5. We have developed an acetone method, specific for blood sugar, which gives the same results as the mercuric nitrate method. 6. We have adapted our mercuric nitrate method and acetone method for determining glucose in tissue extracts

Notes on three raptor species new to Flores

Details are given of sightings of Bonelli's Eagle Hieraaetus fasciatus. Rufous-bellied Eagle H. kienerii and a Honey-Buzzard Pernis sp. on Flores, extending the known range of these specie