In this paper we present Hopfield model of a neuron dynamics given by the neuronic equation. In the first model second order neuronic equation describe the behavior of a neuron in the presence of some local positive feedback. The second model portray two neurons in which first order neuronic equation represents dynamics of the second neuron in the presence of a discharged pulse coded signal fun...

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite v...

Uncertain differential game investigates interactive decision making of players over time and the system dynamics can be described by an uncertain differential equation. This paper goes further to study the two players zero-sum uncertain differential game. In order to guarantee the saddle-point Nash equilibrium, a Max-Min theorem is provided. Furthermore, when the system dynamics is described b...

This paper develops a method for solving for the dynamic general equilibrium of a deterministic continuous time overlapping generations model with a finite-horizon life-cycle. The model has isoelastic preferences and allows for general assumptions about individual endowments and demographics. Solving for an equilibrium reduces to solving a nonlinear integral equation. In the special case of log...

A general equation for the centroid motion of free, continuous, intense beams propagating off axis in solenoidal periodic focusing fields is derived. The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for off-axis beam propagation is also obtained. The properties of the equilibrium and the relevance of ...

Azimuthal rotation in Tokamaks and other fusion machines is observed, for example, when the con ned plasma is subjected to neutral beam heating. The impacts of the beam particles with plasma electrons and ions amounts to a net momentum transfer with causes rotation in the toroidal direction [1, 2]. Plasma rotation with high Mach numbers have been observed in almost all operating regimes of Toka...

In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships among the securities in the asset market. In special case where the interest ...

3 Thermodynamic State Variables and State Equations 8 3.1 State Variables and Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.1 Exhaustive set of state variables? . . . . . . . . . . . . . . . . . . . . 8 3.1.2 Are state variables de ned only in equilibrium? . . . . . . . . . . . . 11 3.1.3 Concept of local equilibrium . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.4 C...

  In this paper asymmetric price transmission mechanism and nonlinear adjustment between producer and retail prices of milk were examined in Zanjan Province of Iran. For this purpose, a Two-Regime Threshold Vector Error Correction Model (TVECM) and a Sup-LM Test developed by Hansen and Seo (2002) were employed for checking presence of a threshold effect. Application of unit root tests indicated...

For nonnegative real numbers α, β, γ , A, B, and C such that B C > 0 and α β γ > 0, the difference equation xn 1 α βxn γxn−1 / A Bxn Cxn−1 , n 0, 1, 2, . . . has a unique positive equilibrium. A proof is given here for the following statements: 1 For every choice of positive parameters α, β, γ , A, B, and C, all solutions to the difference equation xn 1 α βxn γxn−1 / A Bxn Cxn−1 , n 0, 1, 2, . ...