This paper makes a short study of Fredholm integral equations related to potential theory and elasticity, with a view to preparing the ground for their exploitation in the numerical solution of difficult boundary-value problems. Attention is drawn to the advantages of Fredholm's first equation and of Green's boundary formula. The latter plays a fundamental and hitherto unrecognized role in the ...

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels ...

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T ),Ω = {(x,y) : √ x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T ]. Also in...

The importance of constructing the appropriate Green function to solve a wide range of problems inelectromagnetics and partial differential equations is well-recognized by those dealing with classical electrodynamics and related fields. Although the subject of obtaining the Green function for certain geometries has been extensively studied and addressed in numerous sources, in this paper a syst...

in this paper, numerical investigation of a flat passive micromixer with heterogeneous surface properties that the flow through it, is driven by the electroosmotic flow have been presented. the governing equations, which consist of a laplace equation for the distribution of external electric potential, a poisson equation for the distribution of electric double layer potential, modified navier-s...

The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is deriv...

an analytical equation of state was applied to calculate the thermodynamic properties for argon.the equation of state is that of song and mason. it is based on a statistical-mechanical perturbationtheory of the hard convex bodies and can be written as fifth-order polynomial in the density. thereexist three temperature-dependent parameters: the second virial coefficient, an effective molecularvo...