Images consist of structures of varying scales: large scale structures such as flat regions, and small scale structures such as noise, textures, and rapidly oscillatory patterns. In the hierarchical (BV, L(2)) image decomposition, Tadmor, et al. (2004) start with extracting coarse scale structures from a given image, and successively extract finer structures from the residuals in each step of t...

We are concerned with the approximation of undercompressive, regularizationsensitive, nonclassical solutions of hyperbolic systems of conservation laws by high-order accurate, conservative, and semidiscrete finite difference schemes. Nonclassical shock waves can be generated by diffusive and dispersive terms kept in balance. Particular attention is given here to a class of systems of conservati...

We consider a family of constrained `p minimizations: min x∈Rn {||x||`p ∣∣ Ax = Ax∗}, where only A, Ax∗ and ||x∗||`0 are known. Such family of problems has been extensively studied in the Compressed Sensing Community and are used to recover sparse signals. We then go through the reasoning on why p = 1 would be the most suitable choice. Due to the possible ill-posedness of the constrained `1 min...

We construct, analyze, and implement a new nonoscillatory high-resolution scheme for two-dimensional hyperbolic conservation laws. The scheme is a predictor-corrector method which consists of two steps: starting with given cell averages, we first predict pointvalues which are based on nonoscillatory piecewise-linear reconstructions from the given cell averages; at the second corrector step, we ...

Epididymal semen was obtained from rams with a fistula present in the vas deferens (Tadmor & Schindler, 1966). It was deproteinized immediately, and the protein-free clear supernatant evaporated to dryness in vacuo at a temperature not exceeding 55\s=deg\C. The residue was taken up with about 10 ml water, and the solution thus obtained used for determination of both amines and amino acids. For ...

Response to a high salinity treatment of 300 mM NaCl was studied in a cultivated barley Hordeum vulgare Syrian cultivar Tadmor and in a halophytic wild barley H. marinum. Differential salinity tolerance of H. marinum and H. vulgare is underlied by qualitative and quantitative differences in proteins involved in a variety of biological processes. The major aim was to identify proteins underlying...

We present a preliminary study of a new phenomena associated with the Euler-Poisson equations — the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the initial configuration crosses an intrinsic, O(1) critical threshold. We investigate a class of Euler-Poisson equations, ranging from one-dimensional problem ...

In this dissertation we present two kinds of multidimensional schemes for hyperbolic systems based on triangular meshes. The first kind of schemes are evolution Galerkin schemes (EG) which are truly multidimensional schemes and the second kind is a new space-time conservative central-type method which we name a slope propagation (SP) method. Our first scheme is an extension of the EG schemes fo...

Experiments have shown that the interaction of deformation waves propagating through heterogeneous energetic solids with confining boundaries can result in combustion of these materials. Wilson, et al. [1], observed ignition at an anvil-explosive interface while loading an explosive with shock levels below the plane shock initiation threshold. These observations are of practical significance si...