On a Constructive Proof of Kolmogorov’s Superposition Theorem

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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Two variable implicational calculi of prescribed many-one degrees of unsolvability

Journal of Symbolic Logic ◽

10.1017/s0022481200051732 ◽

1976 ◽

Vol 41 (1) ◽

pp. 39-44 ◽

Cited By ~ 1

Author(s):

Charles E. Hughes

Keyword(s):

Decision Problems ◽

Constructive Proof ◽

Distinct Variable ◽

The Family ◽

Propositional Calculi ◽

Degrees Of Unsolvability

AbstractA constructive proof is given which shows that every nonrecursive r.e. many-one degree is represented by the family of decision problems for partial implicational propositional calculi whose well-formed formulas contain at most two distinct variable symbols.

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A New and Simpler Formulation for Radiative Angle Factors

Journal of Heat Transfer ◽

10.1115/1.3686058 ◽

1963 ◽

Vol 85 (2) ◽

pp. 81-87 ◽

Cited By ~ 87

Author(s):

E. M. Sparrow

Keyword(s):

Numerical Evaluation ◽

Energy Exchange ◽

Analytical Calculation ◽

Additional Benefit ◽

Finite Area ◽

Reduced Order ◽

Practical Utility ◽

New Formulation ◽

Superposition Theorem

A new representation for diffuse angle factors has been derived which replaces the usual area integrals by more tractable contour (i.e., line) integrals. The new formulation generally simplifies analytical calculation of angle factors. The advantages of the new representation are associated with the reduced order of the integrals (i.e., double reduced to single, quadruple reduced to double) which must be evaluated to calculate the angle factor. An additional benefit of the new representation is that integrals of simpler form are encountered than in the present representation. For the numerical evaluation of angle factors, the reduction in the order of the integrals should have great practical utility. In the case of energy exchange between an infinitesimal element and a finite area, a superposition theorem has been derived which permits results for certain basic surfaces to be linearly combined to yield angle factors for surfaces at other orientations. Several illustrations of the application of the new formulation are presented.

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A Constructive Proof that Learning in Repeated Games Leads to Nash Equilibria

The B E Journal of Theoretical Economics ◽

10.2202/1935-1704.1462 ◽

2009 ◽

Vol 8 (1) ◽

Author(s):

Patrick L Leoni

Keyword(s):

Repeated Games ◽

Nash Equilibria ◽

Constructive Proof

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A constructive proof for FLP

Information Processing Letters ◽

10.1016/j.ipl.2004.06.008 ◽

2004 ◽

Vol 92 (2) ◽

pp. 83-87 ◽

Cited By ~ 3

Author(s):

Hagen Völzer

Keyword(s):

Constructive Proof

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Constructive Proof of Preisach Right Inverse With Applications to Inverse Compensation of Smart Actuators With Hysteresis

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4027922 ◽

2014 ◽

Vol 136 (6) ◽

Cited By ~ 2

Author(s):

Yangyang Dong ◽

Hong Hu ◽

Zijian Zhang

Keyword(s):

Iterative Algorithm ◽

Control Design ◽

Geometric Interpretation ◽

Constructive Proof ◽

Preisach Model ◽

Compensation Scheme ◽

Fundamental Idea ◽

Model Inversion ◽

Significant Challenge ◽

Piezoelectric Stack Actuator

Hysteresis poses a significant challenge for control of smart material actuators. If unaccommodated, the hysteresis can result in oscillation, poor tracking performance, and potential instability when the actuators are incorporated in control design. To overcome these problems, a fundamental idea in coping with hysteresis is inverse compensation based on the Preisach model. In this paper, we address systematically the problem of Preisach model inversion and its properties, employing the technique of three-step composition mapping and geometric interpretation of the Preisach model. A Preisach right inverse is achieved via the iterative algorithm proposed, which possesses same properties with the Preisach model. Finally, comparative experiments are performed on a piezoelectric stack actuator (PEA) to test the efficacy of the compensation scheme based on the Preisach right inverse.

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Constructing Gröbner bases for Noetherian rings

Mathematical Structures in Computer Science ◽

10.1017/s0960129513000509 ◽

2013 ◽

Vol 24 (2) ◽

Cited By ~ 4

Author(s):

HERVÉ PERDRY ◽

PETER SCHUSTER

Keyword(s):

Gröbner Basis ◽

Finite Depth ◽

Commutative Rings ◽

Polynomial Ideal ◽

Constructive Proof ◽

Noetherian Rings ◽

Grobner Basis ◽

Finitely Generated ◽

Prime Decomposition ◽

Separate Paper

We give a constructive proof showing that every finitely generated polynomial ideal has a Gröbner basis, provided the ring of coefficients is Noetherian in the sense of Richman and Seidenberg. That is, we give a constructive termination proof for a variant of the well-known algorithm for computing the Gröbner basis. In combination with a purely order-theoretic result we have proved in a separate paper, this yields a unified constructive proof of the Hilbert basis theorem for all Noether classes: if a ring belongs to a Noether class, then so does the polynomial ring. Our proof can be seen as a constructive reworking of one of the classical proofs, in the spirit of the partial realisation of Hilbert's programme in algebra put forward by Coquand and Lombardi. The rings under consideration need not be commutative, but are assumed to be coherent and strongly discrete: that is, they admit a membership test for every finitely generated ideal. As a complement to the proof, we provide a prime decomposition for commutative rings possessing the finite-depth property.

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