mowing. It is run along the ground on one large wheel which is f ree of the motor operat ing the cutter bar. I t can be tilted to cut up or down slopes and can be pivoted sharply in any direction. It has been found part icularly valuable for cutting around trees, boulders, t raps, creek-bottoms, and other golf course obstructions which formerly required hand cutt ing. The motor scythe, powered ...

We give upper and lower bounds on the largest singular value of a matrix using analogues to walks in graphs. For nonnegative matrices these bounds are asymptotically tight. In particular, the following result improves a bound due to Schur. If A = (aij) is an m× n complex matrix, its largest singular value satisfies σ (A) ≤ max i∈[m] ∑ j∈[n] |aij| cj ≤ max aij 6=0 ricj, where ri = ∑ k∈[n] |aik| ...

The goal of many early visual filtering processes is to remove noise while at the same time sharpening contrast. An historical succession of approaches to this problem, starting with the use of simple derivative and smoothing operators, and the subsequent realization of the relationship between scale-space and the iso-tropic diffusion equation, has recently resulted in the development of " geom...

The space-time Greens functions for 3-D poststack and 3-D prestack migration in a homogeneous medium are derived under the far-field approximation. These Greens functions can be used to practically compute synthetic migrated images. Examples are given for the recording footprint noise associated with a point scatterer and a meandering river channel. The Greens functions also provide fundamental...

Throughout this work, we shall consider a real-valued Lévy process ξ = (ξt, t ≥ 0), refering to [5, 60] for background. This means that the process ξ starts from ξ0 = 0, has right-continuous paths with left-limits, and if (Ft)t≥0 denotes the natural filtration generated by ξ, then the increment ξt+s − ξt is independent of Ft and has the same law as ξs for every s, t ≥ 0. It is well-known (see e...

Across four studies we demonstrate that consumers adapt more slowly to products that are sentimentally valuable as compared to products that are not. Specifically, we show that consumers adapt more slowly to gifts that they received during a holiday shopping period as compared to comparable items that they purchased during the same period because gifts have more sentimental value than purchases...

Let n ≥ 2, A = (aij) n i,j=1 be a real symmetric matrix, a = (ai) n i=1 ∈ R . Consider the differential operator DA = ∑n i,j=1 aij ∂ ∂xi∂xj + ∑n i=1 ai ∂ ∂xi . Let E be a bounded domain in R, p > 0. Denote by L DA (E) the space of solutions of the equation DAf = 0 in the domain E provided with the Lp-norm. We prove that, for matrices A, B, vectors a, b, bounded domains E, F, and every p > 0 whi...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...