We proved uniqueness and instability of the symmetric subsonic– sonic flow solution of the compressible potential flow equation in a surface with convergent areas of cross–sections. Such a surface may be regarded as an approximation of a two–dimensional convergent nozzle in aerodynamics. Mathematically these are uniqueness and nonexistence results of a nonlinear degenerate elliptic equation wit...

On the basis of the continuity equation and the Bernoulli equation in the steady form, a differential equation is developed to evaluate the successive water levels within compartments of an upright perforated wave absorber. Then the initial and boundary conditions are introduced and the differential equation is solved as an initial value problem. Finally the reflection coefficient from the wave...

The stationary equilibrium of an axisymmetric plasma characterized by toroidal and poloidal flows is considered within the framework of ideal double adiabatic magnetohydrodynamic equations. The problem is reduced to a nonlinear partial differential equation for the poloidal magnetic flux function, containing six surface functions, plus a nonlinear algebraic Bernoulli equation defining the plasm...

We show that recently published assertions that advection dominated accretion flows (ADAFs) require the presence of strong winds are unfounded because they assume that low radiative efficiency in flows accreting at low rates onto black holes implies vanishing radial energy and angular momentum fluxes through the flow (which is also formulated in terms of the ‘Bernoulli function’ being positive)...

Recently, several Bell based polynomials such as Bernoulli, Euler, Genocchi and Apostol versions were defined investigated. The main aim of this paper is to introduce the general family Appell polynomials, which includes many new members in addition existing ones, investigate their properties including determinantal representation, recurrence relation, derivative formula, shift operators differ...

a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...