scholarly journals Global Euler obstruction, global Brasselet numbers and critical points

2019 ◽  
Vol 150 (5) ◽  
pp. 2503-2534
Author(s):  
Nicolas Dutertre ◽  
Nivaldo G. Grulha
Keyword(s):  
Critical Points ◽  
Polynomial Function ◽  
Algebraic Set ◽  
Euler Obstruction

AbstractLet X ⊂ ℂn be an equidimensional complex algebraic set and let f: X → ℂ be a polynomial function. For each c ∈ ℂ, we define the global Brasselet number of f at c, a global counterpart of the Brasselet number defined by the authors in a previous work, and the Brasselet number at infinity of f at c. Then we establish several formulas relating these numbers to the topology of X and the critical points of f.

Criteria for Algebraicity of Analytic Functions

2019 ◽  
Author(s):  
Jacek Bochnak ◽  
Janusz Gwoździewicz ◽  
Wojciech Kucharz
Keyword(s):  
Analytic Function ◽  
Power Series ◽  
Formal Power Series ◽  
Open Subset ◽  
Analytic Functions ◽  
Algebraic Curves ◽  
Polynomial Function ◽  
Algebraic Set ◽  
Formal Power

Abstract We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend only on the behavior of such a function along irreducible nonsingular algebraic curves passing through a given point. In the proofs we use results on algebraicity of formal power series, which are also established in this paper.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

Critical points of metallic plasmas and electrolytes

2000 ◽  
Vol 10 (PR5) ◽  
pp. Pr5-373-Pr5-376 ◽  
Author(s):  
A. A. Likalter ◽  
H. Schneidenbach
Keyword(s):  
Critical Points

Application of graphical analysis of taxonomical structure of diatom complexes in identification of critical conditions of the Neopleistocene lakes (on the example of Bibirevo section)

2019 ◽  
pp. 78-87
Author(s):  
Elena V. Bespalova
Keyword(s):  
Lake Sediments ◽  
Critical Points ◽  
Graphical Analysis ◽  
Volga Region ◽  
Critical Conditions ◽  
Ancient Lake ◽  
Diatom Complexes

Ancient lake sediments of Bibirevo section in the Yaroslavl and Kostroma Volga region are studied by means of graphical analysis of taxonomical structure of diatom complexes. This method allowed to record critical points (change of areas of stability) in the development of a Neopleistocene lake during the transition from stage to stage, as well as from phase to phase.

Some features of phase transitions in solutions with two critical points

1996 ◽  
Vol 166 (6) ◽  
pp. 683-685 ◽  
Author(s):  
K.V. Kovalenko ◽  
S.V. Krivokhizha ◽  
Immanuil L. Fabelinskii ◽  
L.L. Chaikov
Keyword(s):  
Phase Transitions ◽  
Critical Points
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