These notes present various priority arguments in classical computability theory, effective model theory, and complexity theory in a uniform style. Our notation usually follows Soare (1986) with some exceptions. We view Turing functionals as c.e. sets Φ of triples ⟨x, y, σ⟩, denoting that Φ(σ;x) ↓= y. (Of course, we have to impose the obvious compatibility condition, namely, that if ⟨x, y, σ⟩, ...

in this paper, we present an application of the stochastic calculusto the problem of modeling electrical networks. the filtering problem have animportant role in the theory of stochastic differential equations(sdes). in thisarticle, we present an application of the continuous kalman-bucy filter for a rlcircuit. the deterministic model of the circuit is replaced by a stochastic model byadding a ...

In this paper‎, ‎a bidirectional ring network with three cells and different time delays is presented‎. ‎To propose this model which is a good extension of three-unit neural networks‎, ‎coupled cell network theory and neural network theory are applied‎. ‎In this model‎, ‎every cell has self-connections without delay but different time delays are assumed in other connections‎. ‎A suitable Lyapun...

A novel computational fluid dynamics and molecular kinetic theory (CFD-MK) method was developed to simulate the impingement of a nanodroplet onto a solid surface. A numerical solution of the Navier–Stokes equation using a volume-of-fluid (VOF) technique was used to model nanodroplet deformation. Dynamic contact angle during droplet impact was obtained by molecular kinetic theory. This dynamic c...

In this paper, vibration of the protein microtubule, one of the most important intracellular elements serving as one of the common components among nanotechnology, biotechnology and mechanics, is investigated using stress and strain gradient elasticity theory and orthotropic elastic shells model. Microtubules in the cell are influenced by internal and external stimulation and play a part in con...

Motivated by computer science challenges, we suggest to extend the approach and methods of nite model theory beyond nite structures. We study de nability issues and their relation to complexity on meta nite structures which typically consist of (i) a primary part, which is a nite structure, (ii) a secondary part, which is a (usually in nite) structure that can be viewed as a structured domain o...

This term paper is a summary of topological properties of automorphisms and modeltheoretic consequences on countable structures. It is based on Section 4.1 of [1].