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The SzemerédiTrotter theorem in the complex plane
, 305
"... This paper generalizes of the SzemerédiTrotter theorem to the complex plane. Szemerédi and Trotter proved that the number of pointline incidences of n points and e lines in the real Euclidean plane is O(n 2/3 e 2/3 + n + e). This bound is tight. Although several short proofs were found to this the ..."
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Cited by 22 (0 self)
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This paper generalizes of the SzemerédiTrotter theorem to the complex plane. Szemerédi and Trotter proved that the number of pointline incidences of n points and e lines in the real Euclidean plane is O(n 2/3 e 2/3 + n + e). This bound is tight. Although several short proofs were found
On Spin and Matrix Models in the Complex Plane
"... We describe various aspects of statistical mechanics defined in the complex temperature or couplingconstant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupli ..."
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Cited by 1 (0 self)
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We describe various aspects of statistical mechanics defined in the complex temperature or couplingconstant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new
ON BIRATIONAL TRANSFORMATIONS OF PAIRS IN THE COMPLEX PLANE
, 2008
"... This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject. ..."
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Cited by 2 (1 self)
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This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.
Strange objects in the complex plane
 J. Statist. Phys
"... Julia sets are examined as examples of strange objects which arise in the study of long time properties of simple dynamical systems. Technically they are the closure of the set of unstable cycles of analytic maps. Physically, they are sets of points which lead to chaotic behavior. The map f(z) = z2+ ..."
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Cited by 5 (0 self)
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Julia sets are examined as examples of strange objects which arise in the study of long time properties of simple dynamical systems. Technically they are the closure of the set of unstable cycles of analytic maps. Physically, they are sets of points which lead to chaotic behavior. The map f(z) = z2+ p is analyzed for smallp where the Julia set is a closed curve, and for largep where the Julia set is completely disconnected. In both cases the Hausdorff dimension is calculated in perturbation theory and numerically. An expression for the rate at which points escape from the neighborhood of the Julia set is derived and tested in a numerical simulation of the escape. KEY WORDS: Julia set. Chaos; dynamical systems; fractal dimension; escape rate;
Operator of fractional derivative in the complex plane
"... The paper deals with fractional derivative introduced by means of Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the correspondence with some well known approaches is shown. In particular i ..."
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Cited by 2 (0 self)
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The paper deals with fractional derivative introduced by means of Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the correspondence with some well known approaches is shown. In particular
Hybrid Inflation in the Complex Plane
, 2014
"... Supersymmetric hybrid inflation is an exquisite framework to connect inflationary cosmology to particle physics at the scale of grand unification. Ending in a phase transition associated with spontaneous symmetry breaking, it can naturally explain the generation of entropy, matter and dark matter. C ..."
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. Coupling Fterm hybrid inflation to soft supersymmetry breaking distorts the rotational invariance in the complex inflaton plane—an important fact, which has been neglected in all previous studies. Based on the δN formalism, we analyze the cosmological perturbations for the first time in the full two
ALGEBRAIC CURVES IN THE COMPLEX PLANE
"... Introduction and previous results An algebraic curve C in C2 is given by an algebraic equation ( , ) 0f x y From the geometrical point of view it is a Riemann surface. This surface has following invariants: geometrical genus, singular points and punctures (which correspond ..."
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Introduction and previous results An algebraic curve C in C2 is given by an algebraic equation ( , ) 0f x y From the geometrical point of view it is a Riemann surface. This surface has following invariants: geometrical genus, singular points and punctures (which correspond
On the Divergence of Polynomial Interpolation in the Complex Plane
, 2001
"... We extend the results in [1] and [2] from the divergence of Hermite–Fejér interpolation in the complex plane to the divergence of arbitrary polynomial interpolation in the complex plane. In particular, we prove the following theorem: Let 1n D ¡1 • t.n/1 < ¢ ¢ ¢ < t.n/n < 1. Let ’.n/k b ..."
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We extend the results in [1] and [2] from the divergence of Hermite–Fejér interpolation in the complex plane to the divergence of arbitrary polynomial interpolation in the complex plane. In particular, we prove the following theorem: Let 1n D ¡1 • t.n/1 < ¢ ¢ ¢ < t.n/n < 1. Let ’.n
Results 1  10
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8,348