A Generalized Approach for the Modeling of Goodwin-Type Cycles

2016 ◽  
Vol 16 (4) ◽  
Author(s):  
Matteo Madotto ◽  
Marcellino Gaudenzi ◽  
Fabio Zanolin
Keyword(s):  
Recent Literature ◽  
Growth Cycle ◽  
Qualitative Behavior ◽  
Necessary And Sufficient Condition ◽  
Cycle Model ◽  
Small Perturbations ◽  
Essential Requirement ◽  
New Approach ◽  
All Solutions ◽  
Necessary And Sufficient

AbstractGoodwin’s celebrated growth cycle model has been widely studied since its introduction in 1967. In recent years several contributions have appeared with the aim of amending the original model so as to improve its economic coherence and enrich its structure. In this article we propose a new and generalized approach, within the theory of planar Hamiltonian systems, for the modeling of Goodwin-type cycles. This new approach, which includes and improves various attempts by the recent literature, is very general and fulfills the essential requirement that the orbits lie entirely in the economically feasible interval. We provide a necessary and sufficient condition for all solutions to be cycles lying entirely in the unit box. In addition, we study the period length of the cycles near the equilibrium and close to the boundary of the domain. Finally, we discuss an example of how small perturbations of the model may affect the qualitative behavior of the solutions.

On the Indispensability of Intentionality

1972 ◽  
Vol 2 (1) ◽  
pp. 127-133
Author(s):  
Harold Morick
Keyword(s):  
Recent Literature ◽  
Essential Property ◽  
Sufficient Condition ◽  
Conceptual Scheme ◽  
Necessary And Sufficient Condition ◽  
Definition Of ◽  
Necessary And Sufficient

In the last two decades, there has been a great deal of interest in providing an intentional criterion of the psychological. Of the various ones proferred, it seems to me that the best was the earliest, which was Chisholm’s initial criterion in his 1955 essay “Sentences about Believing.” In this present paper I first single out a basic misconception pervading the recent literature on intentionality and suggest that a consequence of this misconception has been the futile attempt to use the notion of intentionality to provide a kind of definition of “mind”; that is, to use intentionality to provide a necessary and sufficient condition for the psychological. Secondly, I point out how intentionality as captured by my own criterion is indispensable in that it is an essential property of certain particulars (persons) which are basic to our conceptual scheme and apparently basic to any conceptual scheme whatsoever.

Oscillation and Global Attractivity in a Periodic Delay Equation

1996 ◽  
Vol 39 (3) ◽  
pp. 275-283 ◽  
Author(s):  
J. R. Graef ◽  
C. Qian ◽  
P. W. Spikes
Keyword(s):  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
All Solutions ◽  
Periodic Delay ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient

AbstractConsider the delay differential equationwhere α(t) and β(t) are positive, periodic, and continuous functions with period w > 0, and m is a nonnegative integer. We show that this equation has a positive periodic solution x*(t) with period w. We also establish a necessary and sufficient condition for every solution of the equation to oscillate about x*(t) and a sufficient condition for x*(t) to be a global attractor of all solutions of the equation.

YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS

1999 ◽  
Vol 01 (01) ◽  
pp. 1-50 ◽  
Author(s):  
YANYAN LI ◽  
MEIJUN ZHU
Keyword(s):  
Riemannian Manifolds ◽  
Compact Riemannian Manifold ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Dimensional Sphere ◽  
Compact Set ◽  
Curvature Function ◽  
Necessary And Sufficient Condition ◽  
All Solutions ◽  
Necessary And Sufficient

A theorem of Escobar and Schoen asserts that on a positive three dimensional smooth compact Riemannian manifold which is not conformally equivalent to the standard three dimensional sphere, a necessary and sufficient condition for a C2 function K to be the scalar curvature function of some conformal metric is that K is positive somewhere. We show that for any positive C2 function K, all such metrics stay in a compact set with respect to C3 norms and the total Leray-Schauder degree of all solutions is equal to -1. Such existence and compactness results no longer hold in such generality in higher dimensions or on manifolds conformally equivalent to standard three dimensional spheres. The results are also established for more general Yamabe type equations on three dimensional manifolds.

scholarly journals Continuous embedding between P-de Branges spaces

2021 ◽  
Vol 8 (1) ◽  
pp. 125-134
Author(s):  
Carlo Bellavita
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
De Branges Spaces ◽  
New Approach ◽  
Additional Hypothesis ◽  
Continuous Embedding ◽  
Embedding Operator ◽  
Necessary And Sufficient

Abstract In this paper we study the continuity of the embedding operator ℓ : ℋ p (E) ↪ ℋ q (E) when 0 < p < q ⩽ ∞. The necessary and sufficient condition has already been described in [10] if p > 1. In this work, we address the problem when p = 1, using a new approach, but asking some additional hypothesis about the Hermite-Biehler function E. We give also a different proof for the case p > 1.

Comaximal factorization of lifting ideals

2020 ◽  
pp. 2250044
Author(s):  
Esmaeil Rostami ◽  
Sina Hedayat ◽  
Reza Nekooei ◽  
Somayeh Karimzadeh
Keyword(s):  
Commutative Ring ◽  
Proper Ideal ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Approach ◽  
Ideal Formula ◽  
Basic Properties ◽  
Necessary And Sufficient

A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is called lifting whenever idempotents of [Formula: see text] lift to idempotents of [Formula: see text]. In this paper, many of the basic properties of lifting ideals are studied and we prove and extend some well-known results concerning lifting ideals and lifting idempotents by a new approach. Furthermore, we give a necessary and sufficient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal lifting ideals.

Oscillations of Second Order Neutral Equations

1988 ◽  
Vol 40 (6) ◽  
pp. 1301-1314 ◽  
Author(s):  
G. Ladas ◽  
E. C. Partheniadis ◽  
Y. G. Sficas
Keyword(s):  
Second Order ◽  
List Type ◽  
Necessary And Sufficient Condition ◽  
Real Numbers ◽  
Neutral Equations ◽  
Deviating Arguments ◽  
Real Roots ◽  
All Solutions ◽  
Image Position ◽  
Necessary And Sufficient

Consider the second order neutral differential equation1where the coefficients p and q and the deviating arguments τ and σ are real numbers. The characteristic equation of Eq. (1) is2The main result in this paper is the following necessary and sufficient condition for all solutions of Eq. (1) to oscillate.THEOREM. The following statements are equivalent:(a) Every solution of Eq. (1) oscillates.(b) Equation (2) has no real roots.

Necessary and sufficient conditions for the two-point phase probability function of two-phase random media

2008 ◽  
Vol 464 (2095) ◽  
pp. 1761-1779 ◽  
Author(s):  
John A Quintanilla
Keyword(s):  
Random Media ◽  
Probability Function ◽  
Recent Literature ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Condition ◽  
Two Phase ◽  
Decomposition Formula ◽  
Positive Matrices ◽  
Necessary And Sufficient

Constructing realizations of random media with a specified two-point phase probability function S 2 has attracted considerable attention in the recent literature. However, little is known about conditions under which a prescribed S 2 is realizable. The only known necessary and sufficient condition, due to McMillan, involves a class of square matrices, called corner-positive matrices, about which almost nothing is known except their definition. As a result, McMillan's theorem has gone mostly unused in the literature for over 50 years. In this paper, we present a general decomposition formula for corner-positive matrices, which allows McMillan's theorem to be written in a significantly more tractable and testable form. We also connect McMillan's theorem with many known but heretofore unrelated necessary conditions on S 2 , extending many of these conditions.

The Fine Characters of a Sort of Biorthogonal Four-Dimensional Nonseparable Wavelet Packs

2010 ◽  
Vol 159 ◽  
pp. 7-12
Author(s):  
Hong Lin Guo ◽  
Yu Min Yu
Keyword(s):  
Iteration Method ◽  
Wavelet Packets ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Wavelet Frames ◽  
New Approach ◽  
Decomposition Scheme ◽  
Necessary And Sufficient

In this article, the notion of orthogonal nonseparable four-dimensional wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is introduced. A new approach for constructing them is presented by iteration method and wavelets as well wavelet frames. The biorthogonality properties of four-dimensi- -onal wavelet packets are discussed. Three biorthogonality formulas concerning these wavelet packs are estabished. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented.

scholarly journals A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Wang ◽  
Bin Zhen ◽  
Jian Xu
Keyword(s):  
System Approach ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Necessary And Sufficient Condition ◽  
Simple Analysis ◽  
Projective System ◽  
New Approach ◽  
Modified Projective Synchronization ◽  
Different Chaotic Systems ◽  
Necessary And Sufficient

A new approach, the projective system approach, is proposed to realize modified projective synchronization between two different chaotic systems. By simple analysis of trajectories in the phase space, a projective system of the original chaotic systems is obtained to replace the errors system to judge the occurrence of modified projective synchronization. Theoretical analysis and numerical simulations show that, although the projective system may not be unique, modified projective synchronization can be achieved provided that the origin of any of projective systems is asymptotically stable. Furthermore, an example is presented to illustrate that even a necessary and sufficient condition for modified projective synchronization can be derived by using the projective system approach.

The Nice Feature of a Sort of Orthogonal Finitely Supported Five-Variant Wavelet Packages

2012 ◽  
Vol 459 ◽  
pp. 289-292
Author(s):  
Hong Wei Gao ◽  
Lan Ran Fang
Keyword(s):  
Iteration Method ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Wavelet Frames ◽  
New Approach ◽  
Decomposition Scheme ◽  
Necessary And Sufficient

In this article, the notion of orthogonal nonseparable five-variant wavelet packages, whi- ch is the generalization of orthogonal univariate wavelet packages, is introduced. A new approach for constructing the wavelet packages is presented by iteration method as well wavelet frames. The orthogonality properties for five-dimensional wavelet packages are discussed. Three orthogonality formulas concerning these wavelet packages are estabished. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented.

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