Exponential Sums and Stationary Phase (I)

2000 ◽  
pp. 195-208 ◽  
Author(s):  
Carlos Julio Moreno
Keyword(s):  
Stationary Phase ◽  
Phase I ◽  
Exponential Sums

scholarly journals Gas Chromatographic Analysis of Remedies and Food Additives Using High Vaccum Silicone Grease as Stationary Phase (I) : On Gas Chromatographic Activity of Some Drugs

Eisei kagaku ◽  
1966 ◽  
Vol 12 (1) ◽  
pp. 38-46
Author(s):  
Tadahiro Narafu ◽  
Junko Hayakawa ◽  
Hiroaki Takahashi ◽  
Yasuo Ishida
Keyword(s):  
Stationary Phase ◽  
Phase I ◽  
Chromatographic Analysis ◽  
Food Additives ◽  
Silicone Grease ◽  
Gas Chromatographic Analysis

scholarly journals Sub-Weyl subconvexity for Dirichlet -functions to prime power moduli

2015 ◽  
Vol 152 (4) ◽  
pp. 825-875 ◽  
Author(s):  
Djordje Milićević
Keyword(s):  
Stationary Phase ◽  
Phase Analysis ◽  
Wide Class ◽  
Prime Power ◽  
Exponential Sums ◽  
New Method ◽  
Central Value ◽  
Stationary Phase Analysis

We prove a subconvexity bound for the central value $L(\frac{1}{2},{\it\chi})$ of a Dirichlet $L$-function of a character ${\it\chi}$ to a prime power modulus $q=p^{n}$ of the form $L(\frac{1}{2},{\it\chi})\ll p^{r}q^{{\it\theta}+{\it\epsilon}}$ with a fixed $r$ and ${\it\theta}\approx 0.1645<\frac{1}{6}$, breaking the long-standing Weyl exponent barrier. In fact, we develop a general new theory of estimation of short exponential sums involving $p$-adically analytic phases, which can be naturally seen as a $p$-adic analogue of the method of exponent pairs. This new method is presented in a ready-to-use form and applies to a wide class of well-behaved phases including many that arise from a stationary phase analysis of hyper-Kloosterman and other complete exponential sums.

Behavior of Chromatography Columns with a Varying Stationary Phase: I. Segmented Liquid Phase Loadings

1982 ◽  
Vol 20 (8) ◽  
pp. 357-362 ◽  
Author(s):  
E. F. Barry ◽  
K. P. Li ◽  
M. Charles
Keyword(s):  
Liquid Phase ◽  
Stationary Phase ◽  
Phase I ◽  
Chromatography Columns

scholarly journals Phase Variation in Xenorhabdus nematophilus

1998 ◽  
Vol 64 (4) ◽  
pp. 1188-1193 ◽  
Author(s):  
Antonia Volgyi ◽  
Andras Fodor ◽  
Attila Szentirmai ◽  
Steven Forst
Keyword(s):  
Stationary Phase ◽  
Phase I ◽  
Phase Ii ◽  
Phase Variation ◽  
Symbiotic Bacterium ◽  
Phenotypic Traits ◽  
Variant Form ◽  
Cell Type ◽  
Variant Cell ◽  
Xenorhabdus Nematophilus

ABSTRACT Xenorhabdus nematophilus is a symbiotic bacterium that inhabits the intestine of entomopathogenic nematodes. The bacterium-nematode symbiotic pair is pathogenic for larval-stage insects. The phase I cell type is the form of the bacterium normally associated with the nematode. A variant cell type, referred to as phase II, can form spontaneously under stationary-phase conditions. Phase II cells do not elaborate products normally associated with the phase I cell type. To better define phase variation in X. nematophilus, several strains (19061, AN6, F1, N2-4) of this bacterium were analyzed for new phenotypic traits. An analysis of pathogenicity in Manduca sexta larvae revealed that the phase II form of AN6 (AN6/II) was significantly less virulent than the phase I form (AN6/I). The variant form of N2-4 was also avirulent. On the other hand, F1/II and 19061/II were as virulent as the respective phase I cells. Strain 19061/II was found to be motile, and AN6/II regained motility when the bacteria were grown in low-osmolarity medium. In contrast, F1/II remained nonmotile. The phase II cells did not produce the outer membrane protein, OpnB, that is normally induced during the stationary phase. Both phase I and phase II cells were able to support nematode growth and development. These findings indicate that while certain phenotypic traits are common to all phase II cells, other characteristics, such as virulence and motility, are variable and can be influenced by environmental conditions.

scholarly journals A stationary phase formula for exponential sums over $ℤ/p^{m}ℤ$ and applications to GL(3)-Kloosterman sums

1997 ◽  
Vol 80 (1) ◽  
pp. 1-48 ◽  
Author(s):  
Romuald Dąbrowski ◽  
Benji Fisher
Keyword(s):  
Stationary Phase ◽  
Exponential Sums ◽  
Kloosterman Sums
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