Singular Concept Research Articles

Self-graviting anisotropic fluids with plane symmetry

The general solution to Einstein’s equations coupled to an anisotropic fluid described by two perfect-fluid components is obtained in the case that (1) the space–time is plane-symmetric, (2) each fluid component is irrotational, and (3) each one obeys the equation of state pressure = energy density. The method used consists of solving the equivalent problem of the Einstein’s equations coupled to a complex massless-scalar field. The space-time singularities are studied using the concept of velocity-dominated singularity. Comoving systems of coordinates are also studied.

Dynamics of vorticity at a sphere

The article discusses the two-dimensional flow of an incompressible liquid between two infinitely close concentric spheres, due to an initial distribution of the vorticity differing from zero. The concept of point singularities (vortices, sources, and sinks) at a sphere is introduced. Equations of motion are obtained for point vortices, as well as invariants of the motion, known for the plane case [1]. The simplest case of the mutual motion of a pair of vortices is considered. Equations are obtained for the motion of point vortices at a rotating sphere. Integral invariants for the continuous distribution of the vorticity are obtained, having the dynamic sense of the total kinetic energy and the momentum of the liquid at the sphere. The effect of the topology of the sphere on the dynamics of the vorticity is noted, and a comparison is made with the plane case.

Self-gravitating fluids with cylindrical symmetry

The general solution of the Einstein field equation is obtained under the assumptions that (1) the source of the gravitational field is a perfect fluid with pressure p, equal to energy density ρ, (2) the space–time is cylindrically symmetric, and (3) the metric is given by three functions of two variables. The coordinate transformation to comoving coordinates is discussed. The energy and the Hawking–Penrose inequalities are studied. The singularities of a class of solutions is studied using the concept of velocity-dominated singularity. A relation between Einstein–Rosen waves and a class of solutions is shown.

Integral Equation Method for Subsonic Flow Past Airfoils in Ventilated Wind Tunnels

The method of contour distribution of sources and vortices, used to calculate potential flows about twodimensional airfoils in free air, is extended to flows around airfoils under the constraint of ventilated wind tunnel walls. Based on the concept of fundamental solutions, the source and vortex singularities are modified to satisfy the boundary conditions at the walls. The application of the airfoil boundary condition reduces the problem to a Fredholm integral equation of the second kind for the source density function. The numerical solutions obtained by a finite element technique are in good agreement with experimental results. I. Introduction A LARGE part of established wall interference theory is based on the simplifying assumption that the wall effects can be evaluated from an estimated far flowfield of the model, considering only the wind tunnel wall boundary condition. The result is interpreted in terms of modifications to the freestream. If the model is small enough, these can be expressed as corrections to the direction and speed of the stream, constant over the model (the angle of attack and Mach number corrections). If the model has appreciable length, a more refined interpretation, involving the streamline curvature and buoyancy (pressure gradient) effects, is required. The model boundary condition enters the problem only in the final stage, if there is a need to evaluate the wall effects in terms of model quantities, such as the surface pressure distribution, aerodynamic forces, moments, etc. A comprehensive account of this approach, its applicability and limitations is given in Ref. 1. It is perhaps worth emphasizing that the above concept

Critique of the directional singularity concept

By considering a family of trajectories in a particular Weyl gravitational field, a class is found for which the scalar R ijklR ijkl becomes infinite in a direction of approach previously believed to be singularity-free. Further objection arises from the finiteness of the scalar in the singular region of another Weyl field.

On singularity and Lebesgue type decomposition for operator-valued measures

The concepts of absolute continuity and singularity for operator-valued measures are introduced and Radon-Nikodym and Lebesgue decomposition theorems for such measures are established. These theorems reduce directly to the classical results in the scalar case. The results have interesting applications to the theory of infinite-dimensional stationary stochastic processes.

The Institution of the Benai Qeiama and Benat Qeiama in the Ancient Syrian Church

The Syriac term qeiama, “covenant,”1 with its derivations benai qeiama, “the sons of the covenant,” and benat qeiama, “the daughters of the covenant,”2 not only marks the idiosyncracy of primitive Syrian Christianity but it also mirrors a development which parallels the whole process of transformation in ancient Syrian Christianity. Originally the term qeiama designated the whole church comprised of ascetically oriented Christians.3.Standing face to face with this singular concept of church and the peculiar profile of primitive Syrian Christianity, we must be reminded that the first Christian impulses in the lands of the Euphrates and Tigris did not come from Hellenistic Christianity via Antioch but from Palestinian Jewish Christianity.4 Therefore the earliest traditions implanted here reveal the Palestinian Aramaean influence not only in the contacts which these Christian Jews had with the Palestinian Jewish Christians5 but also in the use of the ancient Palestinian Targum as the first biblical texts translated into Syriac6 and in the fundamentally ascetic orientation of the Christian Kerygma7 which echoes the Palestinian ascetic trends.8 These archaic conditions, which understood the qeiama as the whole