bases of cones
Recently Published Documents


TOTAL DOCUMENTS

5
(FIVE YEARS 0)

H-INDEX

3
(FIVE YEARS 0)

2011 ◽  
Vol 20 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Winfried Bruns ◽  
Raymond Hemmecke ◽  
Bogdan Ichim ◽  
Matthias Köppe ◽  
Christof Söger

2010 ◽  
Vol 75 (1) ◽  
pp. 191-207 ◽  
Author(s):  
Johanna N.Y. Franklin

AbstractWe study the connection between Schnorr triviality and genericity. We show that while no 2-generic is Turing equivalent to a Schnorr trivial and no 1-generic is tt-equivalent to a Schnorr trivial, there is a 1-generic that is Turing equivalent to a Schnorr trivial. However, every such 1-generic must be high. As a corollary, we prove that not all K-trivials are Schnorr trivial. We also use these techniques to extend a previous result and show that the bases of cones of Schnorr trivial Turing degrees are precisely those whose jumps are at least 0″.


1994 ◽  
Vol 26 (03) ◽  
pp. 597-615
Author(s):  
Vladimir P. Nosko

The horizon ξ T (x) of a random field ζ (x, y) of right circular cones on a plane is investigated. It is supposed that bases of cones are centered at points sn = (xn , yn ), n = 1, 2, ···, on the (X, Y)-plane, constituting a Poisson point process S with intensity λ 0 > 0 in a strip Π T = {(x, y): – ∞< x <∞, 0 ≦ y ≦ T}, while altitudes of the cones h 1, h 2, · ·· are of the form hn = hn * + f(yn ), n = 1, 2, ···, where f(y) is an increasing continuous function on [0,∞), f(0) = 0, and h 1*, h 2*, · ·· is a sequence of i.i.d. positive random variables which are independent of the Poisson process S and have a distribution function F(h) with density p(h). Let denote the expected mean number of local maxima of the process ξ T (x) per unit length of the X-axis. We obtain an exact formula for under an arbitrary trend function f(y). Conditions sufficient for the limit being infinite are obtained in two cases: (a) h 1* has the uniform distribution in [0, H], f(y) = ky γ; (b) h 1* has the Rayleigh distribution, f(y) = k[log(y + 1)] γ . (In both cases γ 0 and 0 < k∞.) The corresponding sufficient conditions are: 0 < γ< 1 in case (a), 0 < γ< 1/2 in case (b).


1994 ◽  
Vol 26 (3) ◽  
pp. 597-615 ◽  
Author(s):  
Vladimir P. Nosko

The horizon ξ T(x) of a random field ζ (x, y) of right circular cones on a plane is investigated. It is supposed that bases of cones are centered at points sn = (xn, yn), n = 1, 2, ···, on the (X, Y)-plane, constituting a Poisson point process S with intensity λ0 > 0 in a strip ΠT = {(x, y): – ∞< x <∞, 0 ≦ y ≦ T}, while altitudes of the cones h1, h2, · ·· are of the form hn = hn* + f(yn), n = 1, 2, ···, where f(y) is an increasing continuous function on [0,∞), f(0) = 0, and h1*, h2*, · ·· is a sequence of i.i.d. positive random variables which are independent of the Poisson process S and have a distribution function F(h) with density p(h).Let denote the expected mean number of local maxima of the process ξ T(x) per unit length of the X-axis. We obtain an exact formula for under an arbitrary trend function f(y). Conditions sufficient for the limit being infinite are obtained in two cases: (a) h1* has the uniform distribution in [0, H], f(y) = kyγ; (b) h1* has the Rayleigh distribution, f(y) = k[log(y + 1)]γ. (In both cases γ 0 and 0 < k∞.) The corresponding sufficient conditions are: 0 < γ< 1 in case (a), 0 < γ< 1/2 in case (b).


Sign in / Sign up

Export Citation Format

Share Document