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Analytical Proof that
"... We show analytically that g A ! 0 in the ultrarelativistic limit for the harmonic oscillator relativistic constituent quark model. I. PROOF Our notation essentially follows Berestetskii and Terent'ev [24]. Upon application of the Melosh transformation [5] one finds that g A is reduced from i ..."
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We show analytically that g A ! 0 in the ultrarelativistic limit for the harmonic oscillator relativistic constituent quark model. I. PROOF Our notation essentially follows Berestetskii and Terent'ev [24]. Upon application of the Melosh transformation [5] one finds that g A is reduced from
394 Analytic and Nonanalytic Proofs
"... O. Abstract]n automated theorem In'oving different kinds of proof systems have been used. Traditional proof systems, such as Iiill)ertstyle proofs or natural deduction we call nonanalytic, while resolution or mating proof sysi.ems we call analytic. There are many good reasons to study the con ..."
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O. Abstract]n automated theorem In'oving different kinds of proof systems have been used. Traditional proof systems, such as Iiill)ertstyle proofs or natural deduction we call nonanalytic, while resolution or mating proof sysi.ems we call analytic. There are many good reasons to study
AN ANALYTIC PROOF OF THE RIEMANN HYPOTHESIS
, 903
"... Abstract. Using the ζ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the ζ zeros is established. We then demonstrate that on the critical line, ζ  is convex, and that in the region 0 < ℜ(s) ≤ 0.5, ζ  has a negative slope. In each case, ..."
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Abstract. Using the ζ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the ζ zeros is established. We then demonstrate that on the critical line, ζ  is convex, and that in the region 0 < ℜ(s) ≤ 0.5, ζ  has a negative slope. In each case
An Analytic Proof of Four Color Problem
"... Abstract – An analytical proof of the Four Color Conjecture has been described in this article. Kempe’s chain argument and Heawood’s technique to prove `Five color theorem ' has been exploited. Success has come through the searching of special triangles, around a vertex of degree, for three rec ..."
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Abstract – An analytical proof of the Four Color Conjecture has been described in this article. Kempe’s chain argument and Heawood’s technique to prove `Five color theorem ' has been exploited. Success has come through the searching of special triangles, around a vertex of degree, for three
An analytic proof of the geometric quantization conjecture
 of GuilleminSternberg, Invent. Math 132
, 1998
"... Abstract. We present a direct analytic approach to the GuilleminSternberg conjecture [GS] that ‘geometric quantization commutes with symplectic reduction’, which was proved recently by Meinrenken [M1], [M2] and Vergne [V1], [V2] et al. Besides providing a new proof of this conjecture, our methods a ..."
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Cited by 55 (8 self)
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Abstract. We present a direct analytic approach to the GuilleminSternberg conjecture [GS] that ‘geometric quantization commutes with symplectic reduction’, which was proved recently by Meinrenken [M1], [M2] and Vergne [V1], [V2] et al. Besides providing a new proof of this conjecture, our methods
An analytic proof of the matrix spectral factorization theorem
, 2007
"... An analytic proof is proposed of Wiener’s theorem on factorization of positive definite matrixfunctions. ..."
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Cited by 1 (0 self)
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An analytic proof is proposed of Wiener’s theorem on factorization of positive definite matrixfunctions.
A COMPLEXANALYTIC PROOF OF CATALAN’S THEOREM
"... Abstract. According to the ColdingMinicozzi theory, embedded minimal discs in R 3 resemble, loosely speaking, either graphs or multigraphs. The latter gives the familiar helicoidlike pattern. Hence, away from the set where the Gaussian curvature vanishes, the product of the curvatures of the asymp ..."
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Cited by 1 (1 self)
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the structure of embedded minimal discs using classical tools, we give in this paper a complexanalytic proof of this theorem, using the idea behind the Catalan curvature. In terms of the WeierstrassEnneper representation the problem is reduced, after careful normalizations, to the uniqueness of solutions
PeriodDoublings to Chaos in A Simple Neural Network: An Analytical Proof
 COMPLEX SYSTEMS
, 1991
"... The dynamics of discretetime neural networks with the sigmoid function as neuron activation function can be extraordinarily complex as some authors have displayed in numerical simulations. Here we consider a simple neural network of only two neurons, one excitatory and the other inhibitory, with no ..."
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Cited by 32 (3 self)
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, with no external inputs and no time delay as a parameterized family of two dimensional maps, and give an analytical proof for existence of perioddoublings to chaos and strange attractors in the network.
An Analytic Proof for the Sensitivity of Chaos to Initial Condition and Perturbations
"... Abstract An analytic method to prove the sensitivity of chaotic motion to initial states and perturbations is proposed in this paper. With the fundamental perturbation method, a second order nonlinear differential equation is expanded into a series of perturbation equations, and by means of variati ..."
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Abstract An analytic method to prove the sensitivity of chaotic motion to initial states and perturbations is proposed in this paper. With the fundamental perturbation method, a second order nonlinear differential equation is expanded into a series of perturbation equations, and by means
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