scholarly journals THE SUBSTITUTION THEOREM FOR RIEMANN INTEGRALS

2001 ◽  
Vol 27 (1) ◽  
pp. 309
Author(s):  
Bagby
1990 ◽  
Vol 16 (1) ◽  
pp. 215
Author(s):  
Cater
Keyword(s):  

2012 ◽  
Vol 23 (04) ◽  
pp. 1250031 ◽  
Author(s):  
JOSÉ F. FERNANDO ◽  
J. M. GAMBOA

In this work we define a semialgebraic set S ⊂ ℝn to be irreducible if the noetherian ring [Formula: see text] of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we use it fruitfully to approach four classical problems in Real Geometry for the ring [Formula: see text]: Substitution Theorem, Positivstellensätze, 17th Hilbert Problem and real Nullstellensatz, whose solution was known just in case S = M is an affine Nash manifold. In fact, we give full characterizations of the families of semialgebraic sets for which these classical results are true.


2005 ◽  
Vol 56 (1) ◽  
pp. 25-36 ◽  
Author(s):  
Takao Fujimoto ◽  
Jose A. Silva ◽  
Antonio Villar

1993 ◽  
Vol 33 (3) ◽  
pp. 331-343 ◽  
Author(s):  
Geoffrey K. Turnbull

1964 ◽  
Vol 37 (5) ◽  
pp. 311
Author(s):  
Lyle E. Pursell
Keyword(s):  

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