World after exponential growth and leading parts.

Stringy World Branes and Exponential Hierarchies

We describe heterotic string and M-theory realizations of the Randall-Sundrum (RS) scenario with N = 2 and N = 1 supersymmetry in the bulk. Supersymmetry can be broken only on the world brane, a scenario that has been proposed to account for the smallness of the cosmological constant. An interesting prediction from string duality is the generation of a warp factor for conventional type II Calab...

Military Expenditures and World Economic Growth under Hybrid Warfare Conditions

The article examines the impact of the dynamics of military expenditures, public debt, arms exports on the economic growth of the six countries (US, China, Russia, Israel, Ukraine, Moldova). The paper empirically tested the hypothesis of the possibility of further maintaining the positive macroeconomic effects in the process of confronting and persistent ‘hybrid’ military conflicts in either ‘h...

Compositions with Parts Constrained by the Leading Summand

Uniform Growth in Groups of Exponential Growth

This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free...

Eigenvector approximation leading to exponential speedup of quantum eigenvalue calculation.

We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schrödinger equation, on a discrete grid. We start with a classically obtained eigenvector for a problem discretized on a coarse grid, and we efficiently construct, quan...