A Bound for the Order of Characteristic Set Elements of an Ordinary Prime Differential Ideal and some Applications

2000 ◽  
Vol 10 (3) ◽  
pp. 251-268 ◽  
Author(s):  
Brahim Sadik
Keyword(s):  
Characteristic Set ◽  
Differential Ideal

Computing Characteristic Sets of Ordinary Radical Differential Ideals

2006 ◽  
Vol 13 (3) ◽  
pp. 515-527
Author(s):  
Brahim Sadik
Keyword(s):  
Upper Bounds ◽  
Algebraic Methods ◽  
Characteristic Set ◽  
Finitely Generated ◽  
Differential Ideal ◽  
Characteristic Sets

Abstract We give upper bounds for the order of the elements in a characteristic set of a regular differential ideal or a radical of a finitely generated differential ideal with respect to some specific orderings. We then show how to compute characteristic sets of these ideals using algebraic methods.

LOCAL AND MICROLOCAL CAUCHY PROBLEM FOR NON-EFFECTIVELY HYPERBOLIC OPERATORS

2014 ◽  
Vol 11 (01) ◽  
pp. 185-213 ◽  
Author(s):  
TATSUO NISHITANI
Keyword(s):  
Cauchy Problem ◽  
Differential Operators ◽  
Energy Estimates ◽  
Characteristic Set ◽  
Finite Speed ◽  
Hyperbolic Operators ◽  
New Energy ◽  
The Cauchy Problem ◽  
Well Posed

We study differential operators of order 2 and establish new energy estimates which ensure that the micro supports of solutions to the Cauchy problem propagate with finite speed. We then study the Cauchy problem for non-effectively hyperbolic operators with no null bicharacteristic tangent to the doubly characteristic set and with zero positive trace. By checking the energy estimates, we ensure the propagation with finite speed of the micro supports of solutions, and we prove that the Cauchy problem for such non-effectively hyperbolic operators is C∞ well-posed if and only if the Levi condition holds.

Urea inhibits hypertonicity-inducible TonEBP expression and action

2001 ◽  
Vol 280 (5) ◽  
pp. F904-F912 ◽  
Author(s):  
Wei Tian ◽  
David M. Cohen
Keyword(s):  
Transcription Factor ◽  
Molecular Mechanism ◽  
Reporter Gene ◽  
Gene Transcription ◽  
Phorbol Ester ◽  
Renal Medulla ◽  
Inhibitory Effect ◽  
Characteristic Set ◽  
Enhancer Element ◽  
Enhancer Binding Protein

Tonicity-responsive genes are regulated by the TonE enhancer element and the tonicity-responsive enhancer binding protein (TonEBP) transcription factor with which it interacts. Urea, a permeant solute coexistent with hypertonic NaCl in the mammalian renal medulla, activates a characteristic set of signaling events that may serve to counteract the effects of NaCl in some contexts. Urea inhibited the ability of hypertonic stressors to increase expression of TonEBP mRNA and also inhibited tonicity-inducible TonE-dependent reporter gene activity. The permeant solute glycerol failed to reproduce these effects, as did cell activators including peptide mitogens and phorbol ester. The inhibitory effect of urea was evident as late as 2 h after the application of hypertonicity. Pharmacological inhibitors of known urea-inducible signaling pathways failed to abolish the inhibitory effect of urea. TonEBP action is incompletely understood, but evidence supports a role for proteasome function and p38 action in regulation; urea failed to inhibit proteasome function or p38 signaling in response to hypertonicity. Consistent with its effect on TonEBP expression and action, urea pretreatment inhibited the effect of hypertonicity on expression of the physiological effector gene, aldose reductase. Taken together, these data 1) define a molecular mechanism of urea-mediated inhibition of tonicity-dependent signaling, and 2) underscore a role for TonEBP abundance in regulating TonE-mediated gene transcription.

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