Some Reconsiderations of Simon's City-Size Distribution Model

1977 ◽  
Vol 9 (9) ◽  
pp. 1043-1053 ◽  
Author(s):  
A Okabe
Keyword(s):  
Steady State ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
City Size ◽  
Distribution Model ◽  
Type Model ◽  
Size Distributions ◽  
City Size Distribution ◽  
Necessary And Sufficient ◽  
Over Time

In conjunction with the empirical findings that the form of city-size distributions is stable over time, this paper reexamines Simon's (1955) model and provides a better understanding of that model. First, a Simon-type model is proposed which is a generalization of Simon's model. Second, Simon's model is reexamined with respect to the ‘steady state’. Third, in the context of the Simon-type model, the necessary and sufficient conditions for the ‘steady state’ with the Yule (1924) city-size distributions are investigated. Last, the necessary and sufficient conditions for the ‘asymptotically steady state’ are obtained.

scholarly journals Multiple cycles and the Bautin bifurcation in the Goodwin model of a class struggle

2013 ◽  
Vol 18 (3) ◽  
pp. 265-274 ◽  
Author(s):  
Giovanni Bella
Keyword(s):  
Steady State ◽  
Limit Cycles ◽  
Sufficient Conditions ◽  
Class Struggle ◽  
Necessary And Sufficient Conditions ◽  
Goodwin Model ◽  
Multiple Cycles ◽  
Bautin Bifurcation ◽  
Necessary And Sufficient

The aim of this paper is to present the necessary and sufficient conditions for the emergence of a generalized Hopf (i.e., Bautin) bifurcation in the Goodwin’s model of a class struggle, and determine the parameter regions where multiple attracting and repelling limit cycles around the steady state may coexist.

scholarly journals Learning about the Future and Dynamic Efficiency

2009 ◽  
Vol 99 (4) ◽  
pp. 1576-1587 ◽  
Author(s):  
Alex Gershkov ◽  
Benny Moldovanu
Keyword(s):  
Sufficient Conditions ◽  
Allocation Problem ◽  
Necessary And Sufficient Conditions ◽  
Static Case ◽  
Efficient Allocation ◽  
Dynamic Efficiency ◽  
Basic Model ◽  
Necessary And Sufficient ◽  
Informational Externalities ◽  
Over Time

We study an allocation problem where a set of objects needs to be allocated to agents arriving over time. The basic model is of the private, independent values type. The dynamically efficient allocation is implementable if the distribution of agents' values is known. Whereas lack of knowledge about the distribution is inconsequential in the static case, endogenous informational externalities arise if the designer gradually learns about the distribution by observing present values. These externalities may prevent the implementation of the dynamically efficient allocation. We provide necessary and sufficient conditions for the efficient allocation to be implementable. (JEL D11, D82)

Why Small, Centrist Third Parties Motivate Policy Divergence by Major Parties

2006 ◽  
Vol 100 (3) ◽  
pp. 403-417 ◽  
Author(s):  
JAMES ADAMS ◽  
SAMUEL MERRILL
Keyword(s):  
Spatial Model ◽  
Sufficient Conditions ◽  
Third Parties ◽  
Necessary And Sufficient Conditions ◽  
Third Party ◽  
Explicit Formulas ◽  
The Third ◽  
The Third Party ◽  
Necessary And Sufficient ◽  
Over Time

Plurality-based elections between two major parties or candidates sometimes feature small, centrist, third parties. We modify the standard two-party spatial model of policy-seeking parties to incorporate a centrist third party, and we show that the presence of such a party—even if it has no chance of winning—motivates the major parties to propose policies that are much more divergent than without the third party. We derive explicit formulas for party locations at a three-party equilibrium and provide necessary and sufficient conditions for existence of that equilibrium. We show that, over time, the major parties can be expected to shift their policies in thesamedirection relative to each other but in theoppositedirection relative to the minor party. The predictions of this model are compared with estimates of party policy locations during appropriate periods in postwar Britain.

Locke on Being Self to My Self

2021 ◽  
pp. 118-144
Author(s):  
Ruth Boeker
Keyword(s):  
Personal Identity ◽  
Final Section ◽  
John Locke ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Present Moment ◽  
Intuitive Knowledge ◽  
The Past ◽  
Necessary And Sufficient ◽  
Over Time

John Locke accepts that every perception gives me immediate and intuitive knowledge of my own existence. However, this knowledge is limited to the present moment when I have the perception. If I want to understand the necessary and sufficient conditions of my continued existence over time, Locke argues that it is important to clarify what “I” refers to. According to Locke, persons are thinking intelligent beings who can consider themselves as extended into the past and future and who are concerned for their happiness and accountable for their actions. I show that the concept of self that he develops in the context of his discussion of persons and personal identity is richer and more complex than the I-concept that he invokes in his version of the cogito. In the final section I turn to the reception of Locke’s view by some of his early critics and defenders, including Elizabeth Berkeley Burnet, an anonymous author, and Catharine Trotter Cockburn.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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