For the existence of a branched covering Σ̃→ Σ between closed surfaces there are easy necessary conditions in terms of χ(Σ̃), χ(Σ), orientability, the total degree, and the local degrees at the branching points. A classical problem dating back to Hurwitz asks whether these conditions are also sufficient. Thanks to the work of many authors, the problem remains open only when Σ is the sphere, in wh...

Limit equilibrium (LE) methods have been commonly used to analyze stability of geosynthetic-reinforced slopes. LE methods assume a potential slip surface, the soils along this slip surface providing shear resistance, and geosynthetic reinforcement providing tensile forces and resisting moments. Continuum mechanics-based numerical method has become increasingly used in recent years for slope sta...

Ever since Mendel promulgated his famous laws, probability theory and statistics have played an important role in the study of heredity (9). Etherington introduced some concepts of modern algebra when he showed how a nonassociative algebra can be made to correspond to a given genetic system (1, 4). The fact that many of these algebras have common properties has led to their study from a purely ...

A two-stage dye amplifier design has been developed to amplify tunable, blue-green, subpicosecond dye laser pulses which are generated from a hybrid synchronously modelocked dye oscillator directly (800 fs) or shorter to 200 fs by a fiber compressor stage. This system has achieved single pulse energies of 2 mJ, with an amplified spontaneous emission content of less than 0.1%. Using 40 mJ of the...

We treat the two-dimensional projection of the (2 + 1) BTZ black hole (known as Achucarro-Ortiz black hole or as (1+1) dilatonic black hole) as a Casimir-type system. The stress tensor of a massless scalar field satisfying Dirichlet boundary conditions on two one-dimensional “walls” (“Dirichlet walls”) is explicitly calculated in three different vacua. Without employing known regularization tec...

in this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. the stages for prey have been considered. the proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. the model is analyzed by using linear stability analysis to ob...

In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n, H n (A, X) = 0 if and only if the n-th cohomology group approximately vanishes.

A polytope in R is said to be stable on a facet if and only if the perpendicular to that facet through the center of gravity meets the facet itself. One may consider the stability of a body with respect to an arbitrary "center of gravity on the interior of the body [1,3,6], or one may take the center of gravity to be determined by the shape of the body itself. Most typically, the center of grav...