It is well known that the system ∂xf = a, ∂yf = b on R 2 has a solution if and only if the closure condition ∂xb = ∂ya holds. In this case the solution f is the work done by the force U = (a, b) from the origin to the point (x, y). This paper deals with a similar problem, where the vector fields ∂x, ∂y are replaced by the Heisenberg vector fields X1, X2. In this case the subRiemannian system X1...

We consider the problem of recovering a block (or group) sparse signal from an underdetermined set of random linear measurements, which appear in compressed sensing applications such as radar and imaging. Recent results of Donoho, Johnstone, and Montanari have shown that approximate message passing (AMP) in combination with Stein’s shrinkage outperforms group LASSO for large block sizes. In thi...

We study the Lyaponov exponent y A (E) of (h u) (n) = u(n + 1) + u(n-l) + A V (n) u (n) in the limit as A +a where V is a suitable random potential. We prove that yA(E)-ln A as A +CO uniformly as E/A runs through compact sets. We also describe a formal expansion (to order A-*) for random and almost periodic potentials. In this note, we study one-dimensional tight binding Hamiltonians h = ho + A...

where is the problem? health scientists are constantly trying to support people by diagnosing, managing the diseases, and improving health in all possible dimensions. attention has been drawn to all aspects of health including biological, psychological, social and spiritual. the problem may lay in behavior, clinical issues, organ cites, genome and epigenome. thus it falls on us, the medical soc...

introduction kurdish sheep breed is one of the most important native breeds of iran. they are fat-tailed, large-sized, well adapted to the mountainous regions in northern khorasan province and mainly raising for meat production under pastoral production system (28). feed efficiency is a major component in the profitability of the small ruminant enterprise, because quality of range and pasture i...